Observational constraints on FLRW, Bianchi type I and V brane models

Abstract

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, $f\ddot{I}{ƒ}_8(z)$. Parameters for FLRW universe consist $\left(\hat{I}{\text{c◯}}_0^{\text{(b)}},\hat{I}{\text{c◯}}_0^{\text{(cd)}},\hat{I}{\text{c◯}}_0^{\text{(k)}},H_0,{\hat{I}}^3,\ddot{I}{ƒ}_8\right)$, while for the Bianchi model are $\left(\hat{I}{\text{c◯}}_0^{\text{(b)}},\hat{I}{\text{c◯}}_0^{\text{(cd)}},\hat{I}{\text{c◯}}_0^{({\hat{I}}^2)},H_0,{\hat{I}}^3,\hat{I}{\text{c◯}}_0^{(\hat{I}¸)},\ddot{I}{ƒ}_8\right)$. We determine the best values for cosmological parameters. For the FLRW model, these values depend on the sign of ${\hat{I}}^3$: ${\hat{I}}^3>0$ yields ${\hat{I}}^3=0.00008_{-0.00011}^{+0.00015}$, and $\hat{I}{\text{c◯}}_0^{\text{(k)}}=0.014_{-0.022}^{+0.024}$ and ${\hat{I}}^3<0$ leads to ${\hat{I}}^3=-0.0226_{-0.0062}^{+0.0054}$, and $\hat{I}{\text{c◯}}_0^{\text{(k)}}=0.023_{-0.041}^{+0.039}$. In both cases $\hat{I}{\text{c◯}}_0^{\text{(k)}}>0$ represents a closed universe. Similarly, for the Bianchi type-V brane model, the parameter values vary with the sign of ${\hat{I}}^3$, resulting in ${\hat{I}}^3=0.00084_{-0.00021}^{+0.00019}$, $\hat{I}{\text{c◯}}_0^{({\hat{I}}^2)}=0.0258_{-0.0063}^{+0.0052}$, and $\hat{I}{\text{c◯}}^{\hat{I}}{¸}_0(\times 10^{-5})=4.19_{-0.75}^{+0.67}$ (as with the density parameter of stiff matter) for ${\hat{I}}^3>0$, and ${\hat{I}}^3=-0.00107_{-0.00020}^{+0.00019}$, $\hat{I}{\text{c◯}}_0^{({\hat{I}}^2)}=0.0259_{-0.0062}^{+0.0050}$, and $\hat{I}{\text{c◯}}^{\hat{I}}{¸}_0(\times 10^{-5})=4.17_{-0.98}^{+0.91}$ for ${\hat{I}}^3<0$. In both cases $\hat{I}{\text{c◯}}_0^{({\hat{I}}^2)}>0$, which represents the Bianchi type-V, because in the Bianchi type-I, ${\hat{I}}^2=0$. Utilizing these obtained best values, we analyze the behavior of key cosmological parameters.

12 pages, 8 figures, to appear in Physics of the Dark Universe