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