Evidence record

Is the universe infinite?

Every sentence on the exploration belongs to at least one claim below. Each says what kind of statement it is, what it rests on, what the evidence does not establish, and how far it was checked. Nothing here is a score, and none of it is a verdict on a belief or a theory.

Last checked 24 September 2026.

Source checked: 39
A judgement, not a fact: 10

If something here is wrong, misquoted, out of date or unfair, write to support@unknownoceans.com and give the claim number, which does not change.

What the question takes for granted

A question about the whole of space asked with evidence that reaches only the observable part. Curvature is measured; size is not, and may not be measurable.

The shape of space can be measured
Established
Its curvature can, from the microwave background combined with galaxy surveys, and it is flat to about 0.2 per cent.
Measuring the shape would settle the size
Open
The page rejects this. A flat space can be infinite or finite, and a finite one larger than the horizon leaves no trace.
What lies beyond the horizon resembles what we see
Open
The usual working assumption, and the one any statement about the whole rests on. The standard review says observations cannot test it.
There is one universe to measure
Open
Eternal inflation, if it happens, makes many regions that would each look like a universe. It has no accepted test.

How the question is labelled

Claim: How much of it there is

Kind: Framing. Signposting. It asserts nothing a source could check.

Claim: Infinity

Kind: Framing. Signposting. It asserts nothing a source could check.

The question

Claim: Measuring the shape of space is possible.

Kind: What the field holds. The settled view of a field, as a review, a consensus statement or a reference work gives it. Not one study.
Review: Source checked. The cited passage was read, and it says this.

The shape here is curvature, which the microwave background and galaxy surveys measure together.

Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.3
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: The data provide an exquisite measurement of the location of the set of acoustic peaks, determining the angular-diameter distance of the last-scattering surface. In combination with other data this strongly constrains the spatial geometry, in a manner consistent with spatial flatness
Supports
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 47b and the sentence after it
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: 0.0007± 0.0019 (68 %, TT,TE,EE+lowE +lensing+BAO) ... The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %

Later work looked for

Crossref, 2020 on, "spatial curvature closed universe Planck"; DESI DR2 (2025) and the Particle Data Group review revised October 2025 both read: no significant preference for curvature in the combined data. Nothing changes the claim.

Claim 3 · checked 24 September 2026 · AI-assisted audit

Claim: Measuring how much of it there is may not be.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

Follows from the review's statement that observations cannot tell whether a flat universe extends forever. "May not be" is the page's own hedge.

Context
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true

Claim 4 · checked 24 September 2026 · AI-assisted audit

Claim: Space appears flat to the precision anyone can measure

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 47b and the sentence after it
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: 0.0007± 0.0019 (68 %, TT,TE,EE+lowE +lensing+BAO) ... The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %
Supports
DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraintssection VI, after equation 21 (DESI+CMB)
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Measurement
The source reads: We also allow for spatial curvature to vary in our cosmological fits and we do not find a significance preference for a non-flat ΛCDM model

What this does not establish

Flat to about 0.2 per cent at one standard deviation, and only in combination with galaxy surveys: the microwave background alone does not pin curvature down (claim 14 and claim 38).

Later work looked for

Claim 5 · checked 24 September 2026 · AI-assisted audit

Claim: which is consistent with infinite extent and also with a very large finite volume.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: a vanishing or negative local curvature ... does not necessarily mean that our Universe is infinite. Indeed we can still be living in a universe of finite volume due to the global topological multi-connectivity of space, even if described by the flat or hyperbolic FRW solutions
Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true

What this does not establish

Consistency with both is not evidence for either. The finite options include a large closed universe and a flat one that repeats.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 6 · checked 24 September 2026 · AI-assisted audit

Claim: The distinction is not one that light can carry

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The page's own reading of what the horizon means for the question.

Context
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true

Claim 7 · checked 24 September 2026 · AI-assisted audit

Claim: no signal from beyond the horizon has arrived yet, and because the expansion is accelerating, from far enough away none ever will.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universesection 2
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Model
The source reads: The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time.
Supports
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universesection 2; note to reference 14 (Harrison 1991)
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Model
The source reads: galaxies with redshift z ∼ 1.8 are currently crossing our event horizon. These are the most distant objects from which we will ever be able to receive information about the present day ... there will be an event horizon in such universes (accelerating universes)
Supports
Planck 2018 results. VI. Cosmological parameterssection 7.4, opening sentence
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: The late-time accelerated expansion of the Universe (Riess et al. 1998; Perlmutter et al. 1999) is still considered one of the most mysterious aspects of the standard cosmology

What this does not establish

The horizon moves outward, so some regions now beyond it will come into view. What is ruled out for ever is only what lies beyond the event horizon, in the standard model with a cosmological constant.

Later work looked for

How the method or model works; not a finding later work revises.

Corrected

24 September 2026. Previously: “no signal from beyond the horizon has arrived or ever will.” Overstated. Light from beyond the present horizon can still arrive later; Davis and Lineweaver show that only events beyond the event horizon can never be seen. The body of the page already said "some never will".

Claim 8 · checked 24 September 2026 · AI-assisted audit

Claim: A flat sheet can be infinite.

Kind: A proved result. A mathematical theorem, as its proof or a reference work states it. What it says about the world depends on how well the mathematics fits.
Review: Source checked. The cited passage was read, and it says this.

The flat plane, and flat three-dimensional space, are the infinite covering spaces of their geometry.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchessection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: the space would be the infinite-volume covering space of one of the eight possible homogeneous 3-geometries

Claim 9 · checked 24 September 2026 · AI-assisted audit

Claim: It can also be rolled into a cylinder and the cylinder joined end to end into a torus, which is entirely finite and still flat everywhere.

Kind: A proved result. A mathematical theorem, as its proof or a reference work states it. What it says about the world depends on how well the mathematics fits.
Review: Source checked. The cited passage was read, and it says this.

A flat torus is a finite space with zero curvature at every point. The cubic torus is one of the shapes Planck tested (claim 24).

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: a vanishing or negative local curvature ... does not necessarily mean that our Universe is infinite. Indeed we can still be living in a universe of finite volume due to the global topological multi-connectivity of space, even if described by the flat or hyperbolic FRW solutions
Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 3.1, Topology
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026
The source reads: In the case of flat space, there are a finite number of compactifications, the simplest of which are those of the torus.
Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchessection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: fundamental domain with a finite extent in at least one spatial dimension

Corrected

24 September 2026. Previously: “It can also be rolled into a cylinder, joined into a torus, and be entirely finite while remaining flat everywhere.” Clarity. The old wording could be read as calling the cylinder finite; a cylinder is still infinite along its length, and only the torus is finite.

Claim 10 · checked 24 September 2026 · AI-assisted audit

Claim: So measuring the curvature of space, which has been done well, does not answer the question people mean when they ask how big the universe is.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

Follows from claim 9, claim 10 and claim 15: the curvature is measured, and curvature does not fix the size.

Context
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true
Context
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 47b and the sentence after it
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: 0.0007± 0.0019 (68 %, TT,TE,EE+lowE +lensing+BAO) ... The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %

Claim 11 · checked 24 September 2026 · AI-assisted audit

What the shape of space says

Claim: What the shape of space says

Kind: Framing. Signposting. It asserts nothing a source could check.

Space is flat, as far as anyone can measure

Claim: Space is flat, as far as anyone can measure

Kind: What the field holds. The settled view of a field, as a review, a consensus statement or a reference work gives it. Not one study.
Review: Source checked. The cited passage was read, and it says this.

Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.1
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: Observations are consistent with spatial flatness
Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.3
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: The data provide an exquisite measurement of the location of the set of acoustic peaks, determining the angular-diameter distance of the last-scattering surface. In combination with other data this strongly constrains the spatial geometry, in a manner consistent with spatial flatness

Later work looked for

Claim 13 · checked 24 September 2026 · AI-assisted audit

Claim: Curvature would distort the apparent size of features in the oldest light.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.3
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: The data provide an exquisite measurement of the location of the set of acoustic peaks, determining the angular-diameter distance of the last-scattering surface. In combination with other data this strongly constrains the spatial geometry, in a manner consistent with spatial flatness
Qualifies
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.3
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: the primary CMB on its own constrains the spatial curvature fairly weakly, due to a parameter degeneracy in the angular-diameter distance

What this does not establish

On its own the microwave background cannot separate curvature from other parameters that change the same distance; that is why the next sentence needs galaxy surveys.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 14 · checked 24 September 2026 · AI-assisted audit

Claim: Measured against the physical size those features should have, the microwave background gives a curvature consistent with zero to within a fraction of a per cent when combined with galaxy surveys.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

The galaxy surveys are baryon acoustic oscillation measurements; the 0.2 per cent is the Planck team's one standard deviation.

Supports
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 47b and the sentence after it
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: 0.0007± 0.0019 (68 %, TT,TE,EE+lowE +lensing+BAO) ... The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %
Supports
DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraintssection VI, after equation 21 (DESI+CMB)
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Measurement
The source reads: We also allow for spatial curvature to vary in our cosmological fits and we do not find a significance preference for a non-flat ΛCDM model
Qualifies
Planck 2018 results. VI. Cosmological parameterssection 7.3
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: which is weakly broken with the addition of CMB lensing

Later work looked for

Claim 15 · checked 24 September 2026 · AI-assisted audit

Claim: Flat is not the same as infinite.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: a vanishing or negative local curvature ... does not necessarily mean that our Universe is infinite. Indeed we can still be living in a universe of finite volume due to the global topological multi-connectivity of space, even if described by the flat or hyperbolic FRW solutions

What this does not establish

The general relativity equations fix curvature locally and leave the global shape open; nothing here says which shape the universe has.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 16 · checked 24 September 2026 · AI-assisted audit

Claim: That a flat universe extends forever is the usual hypothesis, and the Particle Data Group's review of the field says observations cannot tell whether it is true.

Kind: What the field holds. The settled view of a field, as a review, a consensus statement or a reference work gives it. Not one study.
Review: Source checked. The cited passage was read, and it says this.

Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true

Later work looked for

The review was revised in October 2025 and is the current edition found; nothing later changes it.

Corrected

24 September 2026. Previously: “and this is the point at which most accounts of cosmology quietly change the subject.” A claim about "most accounts of cosmology" that no source carries. Replaced with what the field's standard reference review says on the same point.

Claim 17 · checked 24 September 2026 · AI-assisted audit

A small finite universe would leave a fingerprint, and it has not

Claim: A small finite universe would leave a fingerprint

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchessection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: the existence of matched temperature circle pairs (for some observers) is a completely generic signature of any manifold having a length scale smaller than twice the comoving distance to the last scattering surface

What this does not establish

Only a universe that repeats on a scale smaller than the visible one leaves this mark. A finite universe larger than that leaves none.

Later work looked for

How the method or model works; not a finding later work revises.

Corrected

24 September 2026. Previously: “A finite universe would leave a fingerprint, and it has not” Overstated. Only a universe that repeats within the observable region prints matched circles; a finite universe larger than that leaves no such mark.

Claim 18 · checked 24 September 2026 · AI-assisted audit

Claim: and it has not

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 6.1
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: Neither the circles-in-the-sky search nor the likelihood method find evidence for a multiply-connected topology.

What this does not establish

Not found for the shapes and scales searched (claim 23 and claim 26).

Later work looked for

Crossref, 2014 on, "cosmic topology matched circles"; the Planck 2015 topology paper (not cited here) repeats the null result with polarization, and COMPACT 2023 shows the bound depends on the shape; the page now reports the second.

Claim 19 · checked 24 September 2026 · AI-assisted audit

Claim: If space closes on itself on a scale smaller than the observable region, light could cross it more than once, and the same patch of early universe would appear in two directions.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchessection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: at points along this circle, photons can travel from the last scattering surface in two different directions to arrive at one spacetime location

What this does not establish

Assumes the space is close to homogeneous and isotropic, as the standard model does.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 20 · checked 24 September 2026 · AI-assisted audit

Claim: The matching patterns would show up as correlated circles in the microwave sky.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchessection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: an observer will see two separated circles in the microwave temperature sky that have the same pattern of hot and cold spots

What this does not establish

COMPACT notes an observer sees such circles only if a closed loop through them is shorter than the diameter of the last scattering surface.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 21 · checked 24 September 2026 · AI-assisted audit

Claim: That search was carried out systematically on the Planck maps.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 7, Discussion
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: direct searches for matching circles resulting from the intersection of the fundamental topological domain with the surface of last scattering also give a null result at high confidence

Later work looked for

Claim 22 · checked 24 September 2026 · AI-assisted audit

Claim: Nothing was found, which puts a lower bound on the size of a repeating cell for the shapes tested.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 6.1
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: We do not find any statistically significant correlation of circle pairs in any map.
Qualifies
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: Similar limits apply to a wide, although not exhaustive, range of topologies.

Later work looked for

Corrected

24 September 2026. Previously: “Nothing was found, which puts a lower bound on the size of any repeating cell.” Overstated. Planck says its limits apply to a wide "although not exhaustive" range of shapes, and COMPACT 2023 shows many shapes escape them.

Claim 23 · checked 24 September 2026 · AI-assisted audit

Claim: For the shapes that would print matching circles in opposite directions, the bound is close to the distance to the last scattering surface.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

The bound is on the radius of the largest sphere that fits inside one repeating cell, 0.94 of the distance to the last scattering surface.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: The limit for a wider class of topologies, i.e., those predicting matching pairs of back-to-back circles, among them tori and the three spherical cases listed above, coming from the matched-circles search is ... 0.94χrec at 99 % confidence level

Later work looked for

Corrected

24 September 2026. Previously: “For the shapes that would produce matched circles the bound is close to the distance to the last scattering surface.” The 0.94 bound is for shapes predicting back-to-back circles; the old wording applied it to any shape producing matched circles.

Claim 24 · checked 24 September 2026 · AI-assisted audit

Claim: The loosest shape tested, a slab, is held only to about half of it.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: of the largest sphere inscribed in topological domain ... Ri > 0.50χrec for the T1 slab

Later work looked for

Claim 25 · checked 24 September 2026 · AI-assisted audit

Claim: Later work showed that the bound is not the same for every shape: in all but the simplest, the shortest loop around the universe can miss us and be two to six or more times shorter than the diameter of that surface.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchesabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6.

What this does not establish

Worked out for the orientable flat shapes, from the existing circle-search limit, not from a new measurement.

Later work looked for

Crossref, 2023 on, "cosmic topology"; COMPACT 2023 is the newest analysis found and is added to the page.

Corrected

24 September 2026. Previously: “” Currency. COMPACT 2023 shows the circle limit does not bound every shape the same way; added so the page does not present the Planck limit as general.

Claim 26 · checked 24 September 2026 · AI-assisted audit

Claim: What the sky rules out

Kind: Framing. Signposting. It asserts nothing a source could check.

Claim: No matched circles of temperature pattern in opposite directions.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 6.1
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: we can exclude at the confidence level of 99 % any topology that predicts matching pairs of back-to-back circles larger than this radius

Later work looked for

Claim 28 · checked 24 September 2026 · AI-assisted audit

Claim: If space repeats, a loop around it that passes through us is at least about as long as the visible universe is wide.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchesabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface

Later work looked for

Crossref, 2023 on, "cosmic topology"; nothing later found that changes the 98.5 per cent.

Corrected

24 September 2026. Previously: “If space repeats, the cell is at least about as wide as the part we can see.” Overstated. The slab is held only to about half, and COMPACT 2023 shows the general limit is on loops through our position, not on the whole cell.

Claim 29 · checked 24 September 2026 · AI-assisted audit

Claim: A loop that misses us can be much shorter.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchesabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: In all but the simplest cases, the shortest non-contractible loop in the space can avoid us

What this does not establish

Allowed by the circle searches, not observed.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 30 · checked 24 September 2026 · AI-assisted audit

Claim: Curvature consistent with flat to high precision.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 47b and the sentence after it
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: 0.0007± 0.0019 (68 %, TT,TE,EE+lowE +lensing+BAO) ... The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %

Later work looked for

Claim 31 · checked 24 September 2026 · AI-assisted audit

Claim: Either genuinely flat, or curved on a scale far larger than the horizon.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

A radius of curvature at least 19 times the Hubble distance if space is closed, 33 if open, from the 2013 Planck data with lensing.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: This is equivalent to constraints on the radius of curvature R0H0 > 19 for positive curvature ... and R0H0 > 33 for negative curvature

Later work looked for

Crossref, 2020 on, "spatial curvature"; the 2018 and 2025 constraints (claim 15) are tighter, so the radius allowed is larger still.

Claim 32 · checked 24 September 2026 · AI-assisted audit

Claim: No evidence for the rotating, anisotropic geometry tested, once it is fitted together with the standard parameters.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: In the physically motivated setting where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology

What this does not establish

One family of anisotropic geometries, Bianchi VIIh, was tested.

Later work looked for

Crossref, 2014 on; the Planck 2015 paper repeats the null result with a vorticity limit of 7.6 × 10^-10. Nothing changes the claim.

Corrected

24 September 2026. Previously: “No fit for an anisotropically expanding geometry.” Narrowed to what was tested: one anisotropic family, fitted with the standard parameters. Uncoupled from them, a Bianchi template is favoured.

Claim 33 · checked 24 September 2026 · AI-assisted audit

Claim: No sign of that kind of rotation or preferred axis.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: constrain the vorticity of such models to (ω/H)₀ < 8.1 × 10⁻¹⁰ (95 % confidence level)
Notation restored: Subscript and superscript restored from the positions and sizes of the glyphs in the arXiv PDF (1303.5086v2, page 1), read 2026-09-24. The text as extracted reads: constrain the vorticity of such models to (ω/H)0 < 8.1× 10−10 (95 % confidence level)

Later work looked for

Crossref, 2014 on; the Planck 2015 limit is 7.6 × 10^-10. Nothing changes the claim.

Corrected

24 September 2026. Previously: “No edge, no centre, and no axis the expansion runs along.” Overstated. A Bianchi VIIh search says nothing about edges or centres, and it constrains only that family's rotation and axis.

Claim 34 · checked 24 September 2026 · AI-assisted audit

Claim: A template of it can absorb some large-scale anomalies in the same maps, but only with parameters that disagree strongly with the rest of the microwave data.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
Planck 2013 results. XXVI. Background geometry and topology of the Universeabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: the Bianchi pattern is quite efficient at accounting for some of the large-scale anomalies found in Planck data. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone.

Later work looked for

Crossref, 2014 on; the Planck 2015 paper finds the same with temperature and a polarization test that disfavours the template. Nothing changes the claim.

Corrected

24 September 2026. Previously: “The large-scale anomalies in the same maps are not that.” The old sentence gave a verdict the paper does not state. Replaced with what it reports.

Claim 35 · checked 24 September 2026 · AI-assisted audit

Where the measurement is argued about

Claim: Where the measurement is argued about

Kind: Framing. Signposting. It asserts nothing a source could check.

Whether flat really means flat

Claim: Whether flat really means flat

Kind: Framing. Signposting. It asserts nothing a source could check.

Claim: In 2019 Di Valentino, Melchiorri and Silk argued that the Planck power spectra on their own prefer a closed universe at better than 99 per cent confidence, and that assuming the universe is flat could mask a crisis in cosmology.

Kind: What scholars argue. A report of what specialists argue, or where they disagree.
Review: Source checked. The cited passage was read, and it says this.

Planck's own paper reports the same pull from the spectra alone, and reads the combined data as flat (claim 15).

Supports
Planck evidence for a closed Universe and a possible crisis for cosmologyabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Observational study: associations, not causes
The source reads: the Planck CMB spectra now preferring a positive curvature at more than ... 99% C.L.
Supports
Planck evidence for a closed Universe and a possible crisis for cosmologyabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Observational study: associations, not causes
The source reads: discordances higher than generally estimated arise for most of the local cosmological observables, including BAO. The assumption of a flat universe could therefore mask a cosmological crisis
Context
Planck 2018 results. VI. Cosmological parameterssection 7.3, equation 46b
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: an apparent detection of curvature at well over 2 σ

Corrected

24 September 2026. Previously: “In 2019 a group argued” Attribution: a contested result is named to the team that reports it.

24 September 2026. Previously: “In 2019 Di Valentino, Melchiorri and Silk argued that the Planck power spectra on their own prefer a closed universe at better than 99 per cent confidence, and that combining them with other datasets hides a tension rather than resolving it.” The paper says the assumption of a flat universe could mask a cosmological crisis; it does not say that combining the spectra with other datasets hides a tension.

Claim 38 · checked 24 September 2026 · AI-assisted audit

Claim: The argument turns on a subtle feature of how the microwave background is gravitationally lensed.

Kind: What scholars argue. A report of what specialists argue, or where they disagree.
Review: Source checked. The cited passage was read, and it says this.

The Planck spectra show more lensing smoothing than the standard flat model predicts, and a closed universe would produce more.

Supports
Planck evidence for a closed Universe and a possible crisis for cosmologymain text, after Table 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Observational study: associations, not causes
The source reads: is mostly due to the anomalous lensing amplitude at small angular scales

Claim 39 · checked 24 September 2026 · AI-assisted audit

Claim: Most of the field reads the combined data as flat

Kind: What the field holds. The settled view of a field, as a review, a consensus statement or a reference work gives it. Not one study.
Review: Source checked. The cited passage was read, and it says this.

Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.3
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: Results of this type are normally taken as justifying the restriction to flat cosmologies
Supports
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.1
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: Observations are consistent with spatial flatness

Later work looked for

Claim 40 · checked 24 September 2026 · AI-assisted audit

Claim: and a reanalysis of the same maps by Efstathiou and Gratton traces the preference for curvature to which likelihood was used and to the prior placed on curvature itself.

Kind: What scholars argue. A report of what specialists argue, or where they disagree.
Review: Source checked. The cited passage was read, and it says this.

With their own likelihood they find a pull toward closed of about 2.1 standard deviations, or 1.6 without the lowest multipoles, against the 3.4 Di Valentino and colleagues report.

Supports
The evidence for a spatially flat Universesection 4, Conclusions
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Observational study: associations, not causes
The source reads: the claims in Di Valentino et al. (2019) that Planck data strongly favour closed Universes at high significance are a consequence of using the Plik TTTEEE likelihood which differs from the CamSpec likelihood and ignoring the importance of priors
Supports
The evidence for a spatially flat Universesection 3, Likelihoods and constraints on ΩK
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026
The source reads: The posterior for the parameter ΩK is therefore sensitive to both choice of prior and to the likelihood implementation.

Corrected

24 September 2026. Previously: “and a reanalysis of the same maps traces” Attribution: the reanalysis is named, as the rival result is.

Claim 41 · checked 24 September 2026 · AI-assisted audit

Claim: The disagreement is about which combinations are legitimate, which is a real methodological question and not a rhetorical one.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

Both sides agree on what the Planck spectra alone show. Di Valentino and colleagues argue that combining them with other data is questionable while they disagree; Efstathiou and Gratton argue that the combinations break a degeneracy and are closer to the truth.

Context
The evidence for a spatially flat Universesection 4, Conclusions
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026
The source reads: Combining Planck power spectrum measurements with any one of Planck CMB lensing, Type Ia supernovae or BAO data, favours a spatially flat universe.

Claim 42 · checked 24 September 2026 · AI-assisted audit

Claim: The DESI galaxy survey's 2025 results, combined with the microwave background, find no significant preference for curvature either.

Kind: Observation. Something measured or seen, as the named source reports it.
Review: Source checked. The cited passage was read, and it says this.

Supports
DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraintssection VI, after equation 21 (DESI+CMB)
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Measurement
The source reads: We also allow for spatial curvature to vary in our cosmological fits and we do not find a significance preference for a non-flat ΛCDM model

What this does not establish

This is again a combination of datasets, which is what Di Valentino and colleagues question.

Later work looked for

Crossref and the DESI DR2 paper itself, 2025; this is the newer result, added to the page.

Corrected

24 September 2026. Previously: “” Currency. Added the most recent large combined analysis found.

Claim 43 · checked 24 September 2026 · AI-assisted audit

Beyond any signal

Claim: Beyond any signal

Kind: Framing. Signposting. It asserts nothing a source could check.

Claim: Flat is a statement about geometry. Infinite is a statement about quantity. They are not the same claim.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

A restatement of claim 16 in the page's own words.

Context
Planck 2013 results. XXVI. Background geometry and topology of the Universesection 1, Introduction
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: a vanishing or negative local curvature ... does not necessarily mean that our Universe is infinite. Indeed we can still be living in a universe of finite volume due to the global topological multi-connectivity of space, even if described by the flat or hyperbolic FRW solutions

Claim 45 · checked 24 September 2026 · AI-assisted audit

The part measurement cannot reach

Claim: The part measurement cannot reach

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universesection 2
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Model
The source reads: galaxies with redshift z ∼ 1.8 are currently crossing our event horizon. These are the most distant objects from which we will ever be able to receive information about the present day

What this does not establish

In the standard model with a cosmological constant.

Later work looked for

How the method or model works; not a finding later work revises.

Claim 46 · checked 24 September 2026 · AI-assisted audit

Claim: Everything above constrains the universe out to about the horizon.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The topology searches reach roughly the Hubble scale, and the curvature measurement is of the observable region.

Context
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Astronomical observation · Reference work
The source reads: they can test the possibility of a non-trivial topology on scales up to roughly the present Hubble scale

Corrected

24 September 2026. Previously: “Everything above constrains the universe out to the horizon and slightly beyond.” No cited source measures beyond the horizon; the review says topology tests reach roughly the Hubble scale.

Claim 47 · checked 24 September 2026 · AI-assisted audit

Claim: Beyond that, nothing can be observed now, because no signal has had time to arrive, and the acceleration means that from far enough away none ever will.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universesection 2
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Model
The source reads: The particle horizon marks the size of our observable universe. It is the distance to the most distant object we can see at any particular time.
Supports
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universesection 2; note to reference 14 (Harrison 1991)
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Model
The source reads: galaxies with redshift z ∼ 1.8 are currently crossing our event horizon. These are the most distant objects from which we will ever be able to receive information about the present day ... there will be an event horizon in such universes (accelerating universes)
Supports
Planck 2018 results. VI. Cosmological parameterssection 7.4, opening sentence
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Astronomical observation · Measurement
The source reads: The late-time accelerated expansion of the Universe (Riess et al. 1998; Perlmutter et al. 1999) is still considered one of the most mysterious aspects of the standard cosmology

What this does not establish

The acceleration is measured; that it continues, which is what makes "never" true, is the standard model's assumption of a cosmological constant.

Later work looked for

How the method or model works; not a finding later work revises.

Corrected

24 September 2026. Previously: “Beyond that, no observation is possible in principle, because no signal has had time to arrive and the acceleration means some never will.” "In principle" was too strong: the horizon grows, and some of what lies beyond it now will become visible. Only what lies beyond the event horizon never will.

Claim 48 · checked 24 September 2026 · AI-assisted audit

Claim: Statements about the extent of the whole are therefore extrapolations of uniformity: the assumption that what cannot be seen resembles what can.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The review calls the flat, unbounded universe "the usual hypothesis" and says observations cannot test it.

Context
Review of Particle Physics, chapter 25: Cosmological Parameterssection 25.2.7, Cosmic topology
Cited · Link answered, 19 October 2026 · The cited passage was read, 24 September 2026 · Theory · Reference work
The source reads: The usual hypothesis is that the Universe has the simplest topology consistent with its geometry, for example that a flat Universe extends forever. Observations cannot tell us whether that is true

Claim 49 · checked 24 September 2026 · AI-assisted audit

Claim: That assumption is reasonable and it is not evidence.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The page's epistemic verdict, not a sourced finding.

Claim 50 · checked 24 September 2026 · AI-assisted audit

Whether it is one universe

Claim: Whether it is one universe

Kind: Framing. Signposting. It asserts nothing a source could check.

Claim: If inflation happened and does not stop everywhere, it produces regions that stop inflating at different times, separated by space still expanding too fast for anything to cross.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Eternal inflation and its implicationssection 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: so no pocket universe forms in the future light cone of another
Supports
Eternal inflation and its implicationssection 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: process will repeat itself literally forever

What this does not establish

A consequence of inflationary models, not an observation. Guth argues inflation is almost always eternal; that is his argument, and it depends on inflation having happened.

Later work looked for

Crossref, 2020 on, "eternal inflation": reviews and book chapters, nothing that changes what the model says.

Claim 52 · checked 24 September 2026 · AI-assisted audit

Claim: Each would look, from inside, like a universe.

Kind: What a model says. What a theory or model predicts or describes, which is not the same as what has been observed.
Review: Source checked. The cited passage was read, and it says this.

Supports
Eternal inflation and its implicationssection 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Model
The source reads: precipitating a local big bang that will evolve into ... that will eventually appear to its inhabitants as a universe

What this does not establish

What the model predicts; there is no observation of another pocket.

Later work looked for

Crossref, 2020 on, "eternal inflation": nothing that changes what the model says.

Claim 53 · checked 24 September 2026 · AI-assisted audit

Claim: This is a consequence of models built for other reasons rather than a proposal made for its own sake

Kind: What scholars argue. A report of what specialists argue, or where they disagree.
Review: Source checked. The cited passage was read, and it says this.

Guth's case: inflation was proposed to explain properties of the observed universe, and eternal inflation follows from it.

Supports
Eternal inflation and its implicationssection 1
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Argument
The source reads: inflation has been remarkably successful in explaining many important ... properties of the universe
Supports
Eternal inflation and its implicationssection 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Argument
The source reads: I think the inevitability of eternal inflation in the context of new ... is really unassailable

What this does not establish

This is one of inflation's originators arguing for it. The claim that eternal inflation is generic is his argument.

Claim 54 · checked 24 September 2026 · AI-assisted audit

Claim: which is the strongest thing that can be said for it.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The page's reading of claim 54.

Claim 55 · checked 24 September 2026 · AI-assisted audit

Claim: It also has no accepted observational test

Kind: What scholars argue. A report of what specialists argue, or where they disagree.
Review: Source checked. The cited passage was read, and it says this.

Supports
Eternal inflation and its implicationsabstract
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Argument
The source reads: pocket universes produced by eternal inflation are unobservable
Supports
Eternal inflation and its implicationssection 2
Cited · Link answered, 19 October 2026 · Read in full, 24 September 2026 · Theory · Argument
The source reads: Of course this fractal structure is entirely on ... scales much too large to be observed, so we cannot expect astronomers to see it

What this does not establish

The source is a 2007 talk; the audit found nothing since that reports an accepted test, which is absence of a result rather than a proof there can be none.

Later work looked for

Crossref, 2020 on, "eternal inflation observational test bubble collisions": reviews and book chapters, nothing reporting an accepted test.

Claim 56 · checked 24 September 2026 · AI-assisted audit

Claim: which is the strongest thing that can be said against it.

Kind: This page’s reading. A judgement the page makes from the evidence. Others read it differently.
Review: A judgement, not a fact. Reviewed for whether it is fairly put and follows from the checked claims. No source can confirm it.

The page's reading of claim 56.

Claim 57 · checked 24 September 2026 · AI-assisted audit

What was read

Planck 2018 results. VI. Cosmological parametersPlanck Collaboration, Astronomy & Astrophysics · arXiv:1807.06209v4 (9 August 2021); read sections 7.3 and 7.4Read in full, 24 September 2026 · Copyright; quoted brieflyThe extracted text sets spaces inside some symbols ("0.0007± 0.0019"); excerpts keep them as extracted.
Planck 2013 results. XXVI. Background geometry and topology of the UniversePlanck Collaboration, Astronomy & Astrophysics · arXiv:1303.5086v2 (21 December 2013); read abstract, section 1, section 6.1 and section 7Read in full, 24 September 2026 · Copyright; quoted briefly
Planck evidence for a closed Universe and a possible crisis for cosmologyDi Valentino, Melchiorri and Silk, Nature Astronomy · arXiv:1911.02087v1 (5 November 2019), the preprint of the Nature Astronomy paper; read in fullRead in full, 24 September 2026 · Copyright; quoted briefly
The evidence for a spatially flat UniverseEfstathiou and Gratton, Monthly Notices of the Royal Astronomical Society: Letters · arXiv:2002.06892v1 (17 February 2020), the preprint of the MNRAS Letter; read in fullRead in full, 24 September 2026 · Copyright; quoted briefly
Eternal inflation and its implicationsGuth, Journal of Physics A · arXiv:hep-th/0702178v1 (22 February 2007), the preprint of J. Phys. A 40, 6811; read abstract and sections 1 and 2Read in full, 24 September 2026 · Copyright; quoted brieflyThe PDF text splits some words with a stray space ("etern al"); excerpts skip those runs with " ... ".
Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searchesPetersen and others, COMPACT Collaboration, Journal of Cosmology and Astroparticle Physics · arXiv:2211.02603v4 (27 November 2024); read abstract and section 1Read in full, 24 September 2026 · Copyright; quoted briefly
Review of Particle Physics, chapter 25: Cosmological ParametersCortês, Lahav and Liddle, Particle Data Group · Review of Particle Physics, chapter 25, revised October 2025 (PDF dated 1 December 2025); read sections 25.1 to 25.3The cited passage was read, 24 September 2026 · Particle Data Group; quoted briefly
DESI DR2 results. II. Measurements of baryon acoustic oscillations and cosmological constraintsDESI Collaboration, Physical Review D · arXiv:2503.14738v3 (9 October 2025); read section VI on the curvature fitsThe cited passage was read, 24 September 2026 · Copyright; quoted briefly
Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the UniverseDavis and Lineweaver, Publications of the Astronomical Society of Australia · PASA 21, 97–109 (2004); read section 2The cited passage was read, 24 September 2026 · Copyright; quoted briefly