REVIEW
Mimicking Dark Energy with Lemaitre-Tolman-Bondi Models: Weak Central Singularities and Critical Points
Astrophysics · Submitted 21 Feb 2006 · 33 references
Pith's verdict: A careful analytic resolution of the LTB dark-energy mimic debate: the earlier q0<0 models are weakly singular, and nonsingular models force q0>=0; the inverse-problem critical point analysis is the real new work.
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Referee report
The paper
The paper claims
LTB models without a central singularity must have a positive deceleration parameter q0.
The reading
What carries the argument
The argument is carried by the radial expansion of the LTB metric function, R(r,t) = r [a0(t) + a1(t) r + ...], together with the smoothness conditions t0'(0) = 0 and k'(0) = 0 that set a1(t) = 0 and make the central density smooth. This forces the central second time derivative of R' to be negative, which in turn forces q0 >= 0. For the inverse problem, the central object is the critical variable V(z) = 1 - 2 r_FRW $\sqrt$(1+z) / (3 $X^{{3/2}}$) with X = $T^{2}$(1+z); the reconstruction equations become singular at V = 0, and a transcritical solution requires the additional condition (1+z) d ln r_FRW / dz = 1 at the critical redshift.
Extended reading notes
Core claim
The central claim is that LTB models without weak central singularities are forced to have q0 >= 0, in agreement with general theorems, while the q0 < 0 models explored earlier all violate this smoothness requirement. Concretely, a weak singularity corresponds to a nonzero coefficient rho1(t) in the density expansion, equivalently R''(0,t) != 0, which implies that the Ricci-scalar wave operator diverges at the center. Excluding this singularity imposes t0'(0) = 0 and k'(0) = 0, and under those conditions the central deceleration parameter is positive in all three LTB solution branches. The paper also shows that negative effective deceleration can still occur at nonzero redshifts in non-singular models, but the inverse problem of reconstructing a model from luminosity-distance data generically develops a critical-point singularity at a redshift zcrit where d ln r_FRW / d ln(1+z) = 1. Only specially constructed transcritical solutions pass through this critical point and extend to arbitrarily high redshift; explicit examples display phantom-like regions with weff < -1 yet disagree with supernova data.
Load-bearing premise
The load-bearing premise is that a weak central singularity—nonzero rho1(t) giving divergent second derivatives of the density and divergent wave operator of the Ricci scalar at r=0—is physically unacceptable, so models must satisfy t0'(0)=0 and k'(0)=0; if such singularities were allowed, q0<0 LTB models would remain valid.
Editorial extensions
If this is right
- If the central claim holds, all previously proposed LTB models with q0 < 0 are invalid as descriptions of our universe because they place a weak singularity at the observer.
- Non-singular LTB models can still mimic apparent acceleration at nonzero redshift, so inhomogeneity can distort the distance-redshift relation even when local deceleration is positive.
- For a generic luminosity-distance curve, a zero-energy LTB model cannot be reconstructed beyond a critical redshift zcrit, limiting how much supernova data such models can match.
- Transcritical solutions exist and can extend to arbitrarily large redshift, but they are mathematically special and the explicit examples fail to reproduce observed distance moduli.
- Even a successful distance match would face the independent problem of reproducing large-scale structure formation in a dust-dominated model, which the paper argues is unlikely.
Reading between the lines
- A natural extension the authors leave implicit is to repeat the inverse-problem analysis with a nonzero energy function E(r); they expect similar critical behavior, but the possibility of transcritical solutions with E != 0 that fit the data is not completely excluded.
- The critical-point condition d ln r_FRW / d ln(1+z) = 1 could serve as a practical diagnostic: any pure-bang-time LTB fit to distance data that crosses this slope is suspect unless it is deliberately transcritical.
- The structure-formation failure is logically independent of the singularity and critical-point analysis, so even a future transcritical model matching DL(z) would still need to explain why cosmic growth is not over-suppressed without dark energy.
Original abstract
There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lemaitre-Tolman-Bondi (LTB) models. It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter $q_{0}$, in agreement with the general theorems. We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lemaitre-Tolman-Bondi (LTB) models. It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter $q_{0}$, in agreement with the general theorems. We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | There has been much debate over whether or not one could explain the observed acceleration of the Universe with inhomogeneous cosmological models, such as the spherically-symmetric Lemaitre-Tolman-Bondi (LTB) models. | background 1.00 | 0.03 | 0.02 | hedged possibility 0.67 |
| s1 | It has been claimed that the central observer in these models can observe a local acceleration, which would contradict general theorems. | background 0.93 | 0.03 | 0.03 | asserted 0.74 |
| s2 | We resolve the contradiction by noting that many of the models that have been explored contain a weak singularity at the location of the observer which makes them unphysical. | result 0.47 | 0.76 | 0.22 | asserted 0.99 |
| s3 | In the absence of this singularity, we show that LTB models must have a positive central deceleration parameter $q_{0}$, in agreement with the general theorems. | result 0.98 | 0.93 | 0.57 | asserted 1.00 |
| s4 | We also show that it is possible to achieve a negative apparent deceleration parameter at nonzero redshifts in LTB models that do not contain this singularity. | result 0.99 | 0.93 | 0.13 | asserted 0.70 |
| s5 | However, we find other singularities that tend to arise in LTB models when attempting to match luminosity distance data, and these generally limit the range of redshifts for which these models can mimic observations of an accelerating Universe. | result 0.60 | 0.91 | 0.11 | asserted 0.97 |
| s6 | Exceptional models do exist that can extend to arbitrarily large redshift without encountering these pathologies, and we show how these may be constructed. | result 0.60 | 0.91 | 0.09 | asserted 0.96 |
| s7 | These special models exhibit regions with negative effective equation of state parameter, which may fall below negative one, but we have failed to find any singularity-free models that agree with observations. | result 0.84 | 0.92 | 0.26 | asserted 0.64 |
| s8 | Moreover, models based on dust-filled LTB metrics probably fail to reproduce observed properties of large scale structure. | limitation 0.55 | 0.32 | 0.06 | hedged possibility 0.97 |
What was examined, and what was not
- arXiv listing abstract v2
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- P abstract
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Figures
Figures reproduced from arXiv:astro-ph/0602476 by the authors.
References
How the literature uses it
16 arXiv papers cite this in 25 sentences
Papers citing it · 18 sentences without a confident label
Uses its method or tool 1 paper
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In the FLRW gauge in order to to avoid a weak central singularity [ref] we need the following expansion for $k(r)$ and $t_b(r)$: k(r) = k_0+k_2 r^2 t_b(r) = t^b_0+t^b_2 r^2
Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable? · Calculating $D_L(z)$ and $mn(z)$ · 0.89
Cites it as background 6 papers
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In a previous paper [ref] (henceforth VFW) we studied spherically symmetric, dust cosmological models, which are described by the Lemaître-Tolman-Bondi (LTB) metric.
Lemaitre-Tolman-Bondi cosmological models, smoothness, and positivity of the central deceleration parameter · Introduction · 0.81
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Apart from these two approaches, there are also several related works on the inverse construction [ref] .
Inverse Construction of the $\Lambda$LTB Model from a Distance-redshift Relation · Introduction · 0.97
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Light propagation through these models has been vastly studied, especially with the purpose of studying the effects of inhomogeneities on CMB and supernova observations (see e.g. [ref] for some examples) [Other models breaking either the assumption of homogeneity or isotropy have also been used to study light propagation.
Studying the precision of ray tracing techniques with Szekeres models · introduction · 0.91
Discussion
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