Constraining Bianchi type-I universe in f(Q) gravity by Bayesian and deep learning methods

Studying the possible anisotropy of the early universe is one of the most interesting parts of cosmology. By using a limited set of cosmological parameters, in this paper, we investigate the cosmic expansion across time, concentrating on an anisotropic Bianchi type-I (BI) space-time that is subjected to the [Formula: see text] gravity. We present a new method for parameter inference based on deep learning, and the code we used is called Cosmological Likelihood free Inference (CoLFI) (Estimating Cosmological Parameters with deep learning). In terms of best-fit values, parameter errors and correlations between parameters, the deep learning technique clearly performs good in comparison to MCMC approach because deep learning technique avoids the use of likelihoods. This is the result that emerges from contrasting the two methods. We constrained the model parameter [Formula: see text] as [Formula: see text] (MCMC) and [Formula: see text] (ANNs), [Formula: see text] (MDNs) and [Formula: see text] by deep learning techniques. These values of [Formula: see text] are comparable to its corresponding value obtained in Planck results [N. Aghanim et al., Planck 2018 results-VI. Cosmological parameters, Astron. Astrophys. 641 (2020) A6]. Some dynamical properties of the universe in connection with recent astrophysical observations are also discussed.