Testing the cosmological principle on gigaparsec scales

TL;DR

This paper develops a stochastic framework to test the cosmological principle on large scales using multiple cosmological datasets, finding current data consistent with homogeneity and isotropy on gigaparsec scales.

Contribution

It introduces a novel basis expansion method to quantify deviations from isotropy and homogeneity without assuming a privileged observer position.

Findings

Current datasets show no significant deviations from isotropy.

The framework effectively constrains large-scale anisotropies.

Results support the cosmological principle on gigaparsec scales.

Abstract

Recent observational analyses have suggested possible evidence of hemisphere asymmetry in cosmological datasets. Parameterizations of this kind place observers in a privileged position-specifically on the plane that divides the two hemispheres. To quantify potential deviations from the cosmological principle without presuming a special location, we develop a stochastic framework that parametrizes departures from statistical homogeneity and isotropy. The near-uniform temperature of the cosmic microwave background indicates that anisotropy is negligible (at the $\lesssim 10^{-5}$ level) on the last scattering surface. This serves as a zero boundary condition, enabling the construction of an orthogonal basis of functions below the recombination redshift. Within this basis, we expand the relative deviation from the Hubble diagram of isotropic models (such as $\Lambda$CDM or $w_0w_a$CDM) in a hierarchy of increasing resolution. Applying this approach, we test the cosmological principle using Type Ia supernovae, strong lensing time delays, and gravitational-wave standard sirens. For the class of large-scale anisotropies and low-order radial variations described by this framework, the current datasets are found to be consistent with statistical homogeneity and isotropy on gigaparsec scales.