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Topological implications of inhomogeneity
Cosmology and Nongalactic Astrophysics · Submitted 27 Jan 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We propose that the generic class of solutions of the Einstein equations projected back in time from the spatial section at the present epoch includes subclasses in which the spatial section evolves (with increasing time) smoothly (i) from being disconnected to being connected, or (ii) from being simply connected to being multiply connected, where the coordinate system is comoving and synchronous.
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The abstract, sentence by sentence
The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. Here, we consider the implications of inhomogeneity in dust models for the connectedness of spatial sections at early times. We consider a non-global Lemaitre-Tolman-Bondi (LTB) model designed to match observations, a more general, heuristic model motivated by the former, and two specific, global LTB models. We propose that the generic class of solutions of the Einstein equations projected back in time from the spatial section at the present epoch includes subclasses in which the spatial section evolves (with increasing time) smoothly (i) from being disconnected to being connected, or (ii) from being simply connected to being multiply connected, where the coordinate system is comoving and synchronous. We show that (i) and (ii) each contain at least one exact solution. These subclasses exist because the Einstein equations allow non-simultaneous big bang times. The two types of topology evolution occur over time slices that include significantly post-quantum epochs if the bang time varies by much more than a Planck time. In this sense, it is possible for cosmic topology evolution to be "mostly" classical.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. | background 1.00 | 0.06 | 0.03 | asserted 0.99 |
| s1 | Here, we consider the implications of inhomogeneity in dust models for the connectedness of spatial sections at early times. | contribution 0.96 | 0.76 | 0.04 | asserted 0.51 |
| s2 | We consider a non-global Lemaitre-Tolman-Bondi (LTB) model designed to match observations, a more general, heuristic model motivated by the former, and two specific, global LTB models. | method 0.88 | 0.79 | 0.03 | asserted 0.82 |
| s3 | We propose that the generic class of solutions of the Einstein equations projected back in time from the spatial section at the present epoch includes subclasses in which the spatial section evolves (with increasing time) smoothly (i) from being disconnected to being connected, or (ii) from being simply connected to being multiply connected, where the coordinate system is comoving and synchronous. | contribution 0.63 | 0.66 | 0.76 | hedged possibility 0.50 |
| s4 | We show that (i) and (ii) each contain at least one exact solution. | result 1.00 | 0.94 | 0.28 | asserted 1.00 |
| s5 | These subclasses exist because the Einstein equations allow non-simultaneous big bang times. | interpretation 0.87 | 0.38 | 0.11 | asserted 1.00 |
| s6 | The two types of topology evolution occur over time slices that include significantly post-quantum epochs if the bang time varies by much more than a Planck time. | interpretation 0.65 | 0.72 | 0.13 | asserted 0.73 |
| s7 | In this sense, it is possible for cosmic topology evolution to be "mostly" classical. | interpretation 1.00 | 0.61 | 0.20 | hedged possibility 0.98 |
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The paper
Original abstract
The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. Here, we consider the implications of inhomogeneity in dust models for the connectedness of spatial sections at early times. We consider a non-global Lemaitre-Tolman-Bondi (LTB) model designed to match observations, a more general, heuristic model motivated by the former, and two specific, global LTB models. We propose that the generic class of solutions of the Einstein equations projected back in time from the spatial section at the present epoch includes subclasses in which the spatial section evolves (with increasing time) smoothly (i) from being disconnected to being connected, or (ii) from being simply connected to being multiply connected, where the coordinate system is comoving and synchronous. We show that (i) and (ii) each contain at least one exact solution. These subclasses exist because the Einstein equations allow non-simultaneous big bang times. The two types of topology evolution occur over time slices that include significantly post-quantum epochs if the bang time varies by much more than a Planck time. In this sense, it is possible for cosmic topology evolution to be "mostly" classical.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
What it cites · 56 sentences without a confident label
Builds on 1 paper
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In order to consider a more general solution than that of [ref] , let us suppose that a comoving dust solution to the Einstein equations expressed in synchronous, comoving, spherically symmetric coordinates has $(r,θ,ϕ)$ drawn from a Gaussian distribution $G(0,σ)$, i.e. of mean zero and standard deviation $σ$ when smoothed on a length scale $Δx$.
A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model · Gaussian $(r,θ,ϕ)$ distribution · 0.85
Uses data or values from 1 paper
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In a comoving section at the present epoch $t_0$, the age of the universe increases from $t_0$ at the observer to $∼t_0 + 2$ Gyr on shells at an areal distance[The area of a zero thickness shell of radius $r$ is $4πR^2(t,r)$ in (1) of [ref] ; thus, areal.] of about 3.7 Gpc.
A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model · Observational estimate · 0.95
Compares with 3 papers
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By construction, the two fits found in [ref] provide good fits to the observed supernovae type Ia angular-diameter-distance–redshift relation and to an observational estimate of Hubble parameter evolution with redshift, based on differential stellar ages of the oldest passively evolving galaxies at different redshifts [ref] .
A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model · Observational estimate · 0.81
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By construction, the two fits found in [ref] provide good fits to the observed supernovae type Ia angular-diameter-distance–redshift relation and to an observational estimate of Hubble parameter evolution with redshift, based on differential stellar ages of the oldest passively evolving galaxies at different redshifts [ref] .
Constraints on the redshift dependence of the dark energy potential · Observational estimate · 0.81
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A similar method and result are given in [ref] .
Light-cone observations and cosmological models: implications for inhomogeneous models mimicking dark energy · Observational estimate · 0.85
Cites as support 3 papers
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The forcing of an FLRW model onto late-epoch observations requires a non-zero “dark energy” parameter $Ω_Λ$, suggesting that the latter is most simply interpreted as an artefact of forcing an oversimplified model onto the data [ref] .
A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model · Introduction · 0.98
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The forcing of an FLRW model onto late-epoch observations requires a non-zero “dark energy” parameter $Ω_Λ$, suggesting that the latter is most simply interpreted as an artefact of forcing an oversimplified model onto the data [ref] .
Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis · Introduction · 0.98
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The forcing of an FLRW model onto late-epoch observations requires a non-zero “dark energy” parameter $Ω_Λ$, suggesting that the latter is most simply interpreted as an artefact of forcing an oversimplified model onto the data [ref] .
Cosmological parameters are dressed · Introduction · 0.98
Cites as background 6 papers
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It has generally been thought that if the spatial sections of the Universe are compact, then the topology of spatial sections of the Universe cannot have evolved at post-quantum epochs, because this would imply the existence of closed timelike curves or a discontinuity in the choice of the forward light cone, as a consequence of Geroch's Theorem 2 [ref] , [ref] , [ref] , and both are generally considered unphysical.
Topology Change and Causal Continuity · Conclusion · 0.84
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It has generally been thought that if the spatial sections of the Universe are compact, then the topology of spatial sections of the Universe cannot have evolved at post-quantum epochs, because this would imply the existence of closed timelike curves or a discontinuity in the choice of the forward light cone, as a consequence of Geroch's Theorem 2 [ref] , [ref] , [ref] , and both are generally considered unphysical.
Cosmic Topology · Conclusion · 0.84
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The LTB models are comoving, synchronous, dust models with a metric that is normally written[The limit in the $g_rr$ term is not normally written, but is often required in the positively curved case.] [equation] where $c=1$, the gravitational constant $G$ is written explicitly and $E(r)$ is a curvature-related function, e.g. (1), (21), (23) [ref] ; (2.1) [ref] ; (1) [ref] ; (1) [ref] .
A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model · Observational estimate · 0.95
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