Constraints on a Bianchi type I spacetime extension of the standard $\hat{I}›$CDM model

Abstract

We consider the simplest anisotropic generalization, as a correction, to the standard $\hat{I}›$CDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term $\hat{I}{\text{c◯}}_{\ddot{I}ƒ0}{a}^{-6}$ (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 $\hat{I}{\text{c◯}}_{\sigma 0}\lesssim 10^{-3}$, 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., $\hat{I}{\text{c◯}}_{\sigma 0}\lesssim 10^{-15}$. 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 $\hat{I}{\text{c◯}}_{\sigma 0}\lesssim 10^{-23}$. 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 $\sim 11\mathrm{mK}$, though it is much beyond the CMB quadrupole temperature.

13 pages, 4 figures, 5 tables; Matches the published version in Physical Review D