  This study explores the compatibility of Covariant Extrinsic Gravity (CEG)
with current cosmological observations. We employ the chi-square statistic and
Markov Chain Monte Carlo (MCMC) methods to fit the FLRW and Bianchi type-I and
V brane models to the latest datasets, including Hubble, Pantheon+ Supernova
samples, Big Bang Nucleosynthesis (BBN), Baryon Acoustic Oscillations (BAO),
and the structure growth rate, $f\sigma_8(z)$. Parameters for FLRW universe
consist $\left(\Omega^{\text{(b)}}_0, \Omega^{\text{(cd)}}_0,
\Omega^{\text{(k)}}_0, H_0, \gamma, \sigma_8\right)$, while for the Bianchi
model are $\left(\Omega^{\text{(b)}}_0, \Omega^{\text{(cd)}}_0,
\Omega^{{(\beta)}}_0, H_0, \gamma, \Omega^{(\theta)}_0, \sigma_8\right)$. We
determine the best values for cosmological parameters. For the FLRW model,
these values depend on the sign of $\gamma$: $\gamma > 0$ yields $\gamma
=0.00008^{+0.00015}_{-0.00011}$, and
$\Omega^{\text{(k)}}_0=0.014^{+0.024}_{-0.022}$ and $\gamma < 0$ leads to
$\gamma =-0.0226^{+0.0054}_{-0.0062}$, and
$\Omega^{\text{(k)}}_0=0.023^{+0.039}_{-0.041}$. In both cases
$\Omega^{\text{(k)}}_0>0$ represents a closed universe. Similarly, for the
Bianchi type-V brane model, the parameter values vary with the sign of
$\gamma$, resulting in $\gamma = 0.00084^{+0.00019}_{-0.00021}$,
$\Omega^{(\beta)}_0 =0.0258^{+0.0052}_{-0.0063} $, and
$\Omega^{\theta}_0(\times 10^{-5} ) = 4.19^{+0.67}_{-0.75}$ (as with the
density parameter of stiff matter) for $\gamma > 0$, and $\gamma =
-0.00107^{+0.00019}_{-0.00020}$, $\Omega^{(\beta)}_0 =
0.0259^{+0.0050}_{-0.0062} $, and $\Omega^{\theta}_0(\times 10^{-5} ) =
4.17^{+0.91}_{-0.98}$ for $\gamma < 0$. In both cases $\Omega^{(\beta)}_0>0$,
which represents the Bianchi type-V, because in the Bianchi type-I, $\beta=0$.
Utilizing these obtained best values, we analyze the behavior of key
cosmological parameters.
