Anisotropic cosmology using observational datasets: exploring via machine learning approaches

In the current study, we present the observational data constraints on the parameters space for an anisotropic cosmological model of Bianchi I type spacetime in general relativity (GR). For the analysis, we consider observational datasets of Cosmic Chronometers (CC), Baryon Acoustic Oscillation (BAO), and Cosmic Microwave Background Radiation (CMBR) peak parameters. The Markov chain Monte Carlo (MCMC) technique is utilized to constrain the best-fit values of the model parameters. For this purpose, we use the publicly available Python code from CosmoMC and have developed the contour plots with different constraint limits. For the joint dataset of CC, BAO, and CMBR, the parameter's best-fit values for the derived model are estimated as $H_0 = 69.9\pm 1.4$ km/s/Mpc, $\Omega_{m0}=0.277^{+0.017}_{-0.015}$, $\Omega_{\Lambda 0} = 0.722^{+0.015}_{-0.017}$, and $\Omega_{\sigma 0} = 0.0009\pm0.0001$. To estimate $H(z)$, we explore machine learning (ML) techniques like linear regression, Artificial Neural Network (ANN), and polynomial regression and thereafter analyze the results with the theoretically developed $H(z)$ for the proposed model. Among these ML techniques, the polynomial regression exceeds the performance compared to other techniques. Further, we also note that larger dataset provides a better understanding of the cosmological scenario in terms of ML view point.