# Constraints on a Bianchi type I spacetime extension of the standard $\Lambda$CDM model

## TL;DR

This paper investigates a Bianchi type-I anisotropic extension of the standard $
abla$CDM model, deriving extremely tight constraints on anisotropy from various cosmological data, and finds it has negligible effects on key cosmological observables.

## Contribution

It introduces a Bianchi type-I anisotropic correction to $
abla$CDM and provides the first comprehensive constraints on anisotropy from late-time and early-universe data.

## Key findings

- Constraint on anisotropy parameter $
abla_{ ext{sigma}0} extless 10^{-15}$ from combined data.
- Anisotropy does not significantly affect matter-radiation equality or matter perturbation peaks.
- BBN constraints limit anisotropy to $
abla_{ ext{sigma}0} extless 10^{-23}$, making it irrelevant for CMB quadrupole.

## Abstract

We consider the simplest anisotropic generalization, as a correction, to the standard $\Lambda$CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term $\Omega_{\sigma 0}a^{-6}$ (mimicking the stiff fluid) in the average expansion rate $H(a)$ of the Universe. From Hubble and Pantheon data, relevant to the late Universe ($z\lesssim 2.4$), we obtain the constraint $\Omega_{\sigma0}\lesssim10^{-3}$, in line with the model-independent constraints. When the baryonic acoustic oscillations and cosmic microwave background (CMB) data are included, the constraint improves by 12 orders of magnitude, i.e., $\Omega_{\sigma0}\lesssim10^{-15}$. We find that this constraint could alter neither the matter-radiation equality redshift nor the peak of the matter perturbations. Demanding that the expansion anisotropy has no significant effect on the standard big bang nucleosynthesis (BBN), we find the constraint $\Omega_{\sigma0}\lesssim10^{-23}$. We show explicitly that the constraint from BBN renders the expansion anisotropy irrelevant to make a significant change in the CMB quadrupole temperature, whereas the constraint from the cosmological data in our model provides the temperature change up to $\sim11\, \rm mK$, though it is much beyond the CMB quadrupole temperature.