Constraints on a Bianchi type I spacetime extension of the standard Λ CDM model

We consider the simplest anisotropic generalization, as a correction, to the standard ΛCDM model, by replacing the spatially flat Robertson-Walker metric by the Bianchi type-I metric, which brings in a new term Ωσ0a−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≲2.4), we obtain the constraint Ωσ0≲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., Ωσ0≲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 Ωσ0≲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 ~11 mK, though it is much beyond the CMB quadrupole temperature.