Thurston geometries and parameter constraints from SNIa data

TL;DR

This work probes cosmological anisotropy by embedding Thurston geometries—homogeneous yet anisotropic spacetimes—into an extension of the flat $\Λ$CDM framework and constraining them with Pantheon+ SH0ES Type Ia supernova data. It derives direction-dependent redshift and luminosity-distance relations, evolves the anisotropic parameters via dimensionless dynamical equations, and performs a Bayesian comparison against standard $\Λ$CDM. The main finding is that while flat $\Λ$CDM remains preferred, certain Thurston geometries (notably $\mathbb{R} \times \mathbb{H}^2/S^2$) allow mild anisotropy signals (nonzero $e^2$ and $\sigma$) and larger matter densities, with curvature parameters $\Omega_\kappa$ constrained to small values. The results also indicate curvature radii larger than the Hubble radius today, and a common preferred axis across geometries, but the statistical distinctions are not decisive; more extensive data from future surveys are needed to firmly discriminate these anisotropic models and assess their physical relevance.

Abstract

Following the numerous evidence for large-scale cosmic isotropy violation with the advent of the `precision cosmology' era, we explore the possible advantages of extending the flat $Λ$CDM model to more general models in order to constrain anisotropies in the universe, otherwise absent in the standard model based on FLRW spacetime. Such extensions are offered by the topologically unique Thurston geometries, which are homogeneous but anisotropic spacetime models. In this work, we attempt to distinguish Thurston geometries from one another by introducing anisotropies via different scale factors in different directions, thereby introducing additional model parameters such as shear, eccentricity, curvature, and a preferred axis. We used the latest compilation of Pantheon+ \& SH0ES Type Ia supernova data for deriving model constraints, and found mild evidence of large-scale isotropy violation.

Figures (4)

• Figure 1: Constraints on geometries and sky map for $\bar{w} = w_a = w_b$
• Figure 2: Line of sight in $\mathbb{R} \times \mathbb{H}^2/S^2$ spacetimes
• Figure 3: Line of sight in Nil spacetime
• Figure 4: Line of sight in Solv spacetime