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Register a new userLarge-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data
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We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Lambda, the time evolution of the density contrast as well as kinematic quantities can be tracked through the matter- and Lambda-dominated cosmic eras up to the present and into the future. In various models of class I and class II, the growth rate is found to be stronger than that of the LCDM cosmology, and it is suppressed at later times due to the presence of Lambda. We find that there are Szekeres models able to provide a growth history similar to that of LCDM while requiring less matter content and nonzero curvature, which speaks to the importance of including the effects of large-scale inhomogeneities in analyzing the growth of large-scale structure. Using data for the growth factor f from redshift space distortions and the Lyman-alpha forest, we obtain best fit parameters for class II models and compare their ability to match observations with LCDM. We find that there is negligible difference between best fit Szekeres models with no priors and those for LCDM, both including and excluding Lyman-alpha data. We also find that the growth index gamma parametrization cannot be applied in a simple way to the growth in Szekeres models, so a direct comparison of the function f to the data is performed. We conclude that the Szekeres models can provide an exact framework for the analysis of large-scale growth data that includes inhomogeneities and allows for different interpretations of observations. (abridged)
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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 $Lambda$, they fail to produce the observed late-time suppression in the growth unless $Lambda$ 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 ($Lambda$CDM) provides consistency with the data at a confidence level of 99.65% while the Szekeres model without $Lambda$ achieves only a 60.46% level. When the data sets are considered separately, the Szekeres with no $Lambda$ fits the supernova data as well as the $Lambda$CDM does, but provides a very poor fit to the growth data with only 31.31% consistency level compared to 99.99% for the $Lambda$CDM. This absence of late-time growth suppression in inhomogeneous models without a $Lambda$ is consolidated by a physical explanation.
We present a general parallelized and easy-to-use code to perform numerical simulations of structure formation using the COLA (COmoving Lagrangian Acceleration) method for cosmological models that exhibit scale-dependent growth at the level of first and second order Lagrangian perturbation theory. For modified gravity theories we also include screening using a fast approximate method that covers all the main examples of screening mechanisms in the literature. We test the code by comparing it to full simulations of two popular modified gravity models, namely $f(R)$ gravity and nDGP, and find good agreement in the modified gravity boost-factors relative to $Lambda$CDM even when using a fairly small number of COLA time steps.
We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general relativity provide complementary theoretical frameworks for modelling large-scale structure in $Lambda$CDM cosmology; a relativistic approach is essential to determine initial conditions which can then be used in Newtonian simulations studying the non-linear evolution of the matter density. Most inflationary models in the very early universe predict an almost Gaussian distribution for the primordial metric perturbation, $zeta$. However, we argue that it is the Ricci curvature of comoving-orthogonal spatial hypersurfaces, $R$, that drives structure formation at large scales. We show how the non-linear relation between the spatial curvature, $R$, and the metric perturbation, $zeta$, translates into a specific non-Gaussian contribution to the initial comoving matter density that we calculate for the simple case of an initially Gaussian $zeta$. Our analysis shows the non-linear signature of Einsteins gravity in large-scale structure.
The cosmological constant $Lambda$ and cold dark matter (CDM) model ($Lambdatext{CDM}$) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on $Lambdatext{CDM}$ and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state $w$ ($w$CDM), the Hu & Sawicki and designer $f(R)$ models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5$sigma$, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations $S_8=sigma_8left(Omega_m/0.3right)^{0.5}$.
We derive for the first time the growth index of matter perturbations of the FLRW flat cosmological models in which the vacuum energy depends on redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which apart from a leading constant term $Lambda_0$ there is also a $H^{2}$-dependence in the functional form of vacuum, namely $Lambda(H)=Lambda_{0}+3 u (H^{2}-H^{2}_{0})$. Since $| u|ll1$ this form endows the vacuum energy of a mild dynamics which affects the evolution of the main cosmological observables at the background and perturbation levels. Specifically, at the perturbation level we find that the growth index of the running vacuum cosmological model is $gamma_{Lambda_{H}} approx frac{6+3 u}{11-12 u}$ and thus it nicely extends analytically the result of the $Lambda$CDM model, $gamma_{Lambda}approx 6/11$.
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