Stochastic analysis of finite-temperature effects on cosmological parameters by artificial neural networks

Abstract: We explore the impact of finite-temperature quantum gravity effects on cosmological parameters, particularly the cosmological constant $\Lambda$, by incorporating temperature-dependent quantum corrections into the Hubble parameter. For that purpose, we modify the Cosmic Linear Anisotropy Solving System. We introduce new density parameters, $\Omega_{\Lambda_2}$ and $\Omega_{\Lambda_3}$, arising from finite-temperature quantum gravity contributions, and analyze their influence on the cosmic microwave background power spectrum using advanced machine learning techniques, including artificial neural networks and stochastic optimization. Our results reveal that $\Omega_{\Lambda_3}$ assumes a negative value, consistent with dimensional regularization in renormalization and that the presence of $\Omega_{\Lambda_2}$ as well as $\Omega_{\Lambda_3}$ significantly enhances model accuracy. Numerical analyses demonstrate that the inclusion of these parameters improves the fit to 2018 Planck data, suggesting that finite-temperature quantum gravity effects play a non-negligible role in cosmological evolution. Although the Hubble tension persists, our findings highlight the potential of quantum gravitational corrections in refining cosmological models and motivate further investigation into higher-order thermal effects and polarization data constraints.