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.
Categories: gr-qc astro-ph.CO