Stringent Restriction from the Growth of Large-Scale Structure on Apparent Acceleration in Inhomogeneous Cosmological Models

Probes of cosmic expansion constitute the main basis for arguments to support or refute a possible apparent acceleration due to different expansion rates in the Universe as described by inhomogeneous cosmological models. We present in this Letter a separate argument based on results from an analysis of the growth rate of large-scale structure in the Universe as modeled by the inhomogeneous cosmological models of Szekeres. We use the models with no assumptions of spherical or axial symmetries. We find that while the Szekeres models can fit very well the observed expansion history without a $\mathrm{\Lambda }$, they fail to produce the observed late-time suppression in the growth unless $\mathrm{\Lambda }$ is added to the dynamics. A simultaneous fit to the supernova and growth factor data shows that the cold dark matter model with a cosmological constant ($\mathrm{\Lambda }\mathrm{CDM}$) provides consistency with the data at a confidence level of 99.65%, while the Szekeres model without $\mathrm{\Lambda }$ achieves only a 60.46% level. When the data sets are considered separately, the Szekeres with no $\mathrm{\Lambda }$ fits the supernova data as well as the $\mathrm{\Lambda }\mathrm{CDM}$ does, but provides a very poor fit to the growth data with only 31.31% consistency level compared to 99.99% for the $\mathrm{\Lambda }\mathrm{CDM}$. This absence of late-time growth suppression in inhomogeneous models without a is consolidated by a physical explanation.

Figure 1

(a) Distance modulus-redshift plots for the Szekeres Class I model with no cosmological constant $\mathrm{\Lambda }$, and the FLRW-$\mathrm{\Lambda }\mathrm{CDM}$ concordance model, along with supernova Union2 compilation data [19]. The very close normalized ${\chi }^2$ values and the small difference in magnitude between the two models (i.e., $0.00\le |{\mu }_{{}_{\mathrm{\Lambda }\mathrm{CDM}}}-{\mu }_{{}_{\text{Szekeres}}}|\le 0.073$) show that practically the two models fit equally well the supernova data. (b) Plots of the growth rate of large-scale structure for Szekeres models with and without $\mathrm{\Lambda }$, and the $\mathrm{\Lambda }\mathrm{CDM}$. The Szekeres model with a $\mathrm{\Lambda }$ exhibits a late-time suppression of the growth similar to that of $\mathrm{\Lambda }\mathrm{CDM}$. Despite a very competitive fit to the supernova data, the Szekeres model with no $\mathrm{\Lambda }$ exhibits no such late-time suppression. (c) Plots of the growth factor and redshift space distortions data (e.g., [10, 11]). The Szekeres with $\mathrm{\Lambda }$ and the $\mathrm{\Lambda }\mathrm{CDM}$ are consistent with the growth data at 99.96% and 99.99% level of confidence, respectively. A simultaneous fit to the supernova and growth data gives 99.65% and 60.46% consistency for the $\mathrm{\Lambda }\mathrm{CDM}$ and the Szekeres without $\mathrm{\Lambda }$, respectively. The Szeskeres with no $\mathrm{\Lambda }$ that is best fit to the growth data provides only 31.31% consistency level with the growth data.