Testing spatial curvature and anisotropic expansion of the universe on top of the lambda-ACDM model

Abstract

In this thesis, we explore the possible advantages of extending the standard $\Lambda$CDM model by more realistic backgrounds compared to its spatially flat Robertson-Walker (RW) spacetime assumption, while preserving the underpinning physics; in particular, by simultaneously allowing non-zero spatial curvature and anisotropic expansion on top of $\Lambda$CDM, viz., the An-$o\Lambda$CDM model. This is to test whether the latest observational data still support spatial flatness and/or isotropic expansion in this case, and, if not, to explore the roles of spatial curvature and expansion anisotropy (due to its stiff fluid-like behavior) in addressing some of the current cosmological tensions associated with $\Lambda$CDM. We first present the theoretical background and explicit mathematical construction of An-$o\Lambda$CDM. We replace, in the simplest manner, the spatially flat RW spacetime assumption of the $\Lambda$CDM model with the simplest more realistic background that simultaneously allows non-zero spatial curvature and anisotropic expansion; namely, considered the simplest anisotropic generalizations of the RW spacetime, viz., the Bianchi type I, V, and IX spacetimes (having the simplest homogeneous and flat, open, and closed spatial sections, respectively) combined in one Friedmann equation. Then we constrain the parameters of this model and its particular cases, namely, An-$\Lambda$CDM (allowing anisotropic expansion), $o\Lambda$CDM (allowing non-zero spatial curvature), and $\Lambda$CDM, by using the latest data sets from different observational probes, viz., Planck CMB(+Lens), BAO, SnIa Pantheon, and CC data, and discuss the results in detail. Ultimately, we conclude that, within the setup under consideration, (i) the observational data confirm the spatial flatness and isotropic expansion assumptions of $\Lambda$CDM, though a very small amount of expansion anisotropy cannot be excluded, e.g., $\Omega_{\sigma0}\lesssim10^{-18}$ (95\% C.L.) for An-$\Lambda$CDM from CMB+Lens data, (ii) the introduction of spatial curvature or anisotropic expansion, or both, on top $\Lambda$CDM does not offer a possible relaxation to the $H_0$ tension, and (iii) the introduction of anisotropic expansion neither affects the closed space prediction from the CMB(+Lens) data nor does it improve the drastically reduced value of $H_0$ led by the closed space.