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

TL;DR

This work investigates finite-temperature quantum gravity corrections to cosmology by introducing two new density parameters, $Ω_{Λ_2}$ and $Ω_{Λ_3}$, which modify the cosmological constant and Hubble expansion via $Λ_{tot} = Λ_1 + Λ_2 a^{-4} + Λ_3 a^{-2} + \cdots$ and the associated $H(t)$. The authors implement these corrections in a modified CLASS code (mod_CLASS) and explore an eight-parameter space using brute-force scans, artificial neural networks, and stochastic optimization to fit the Planck 2018 CMB data. A key finding is that $Ω_{Λ_2}$ tends to be negative, consistent with dimensional regularization, and that including both $Ω_{Λ_2}$ and $Ω_{Λ_3}$ improves the fit over the standard model, with a best-fit distance to Planck of $y=28.8111$ in the eight-parameter case. While the results do not resolve the Hubble tension, they suggest that finite-temperature quantum-gravity corrections can meaningfully refine cosmological models and motivate further work on higher-order thermal effects and polarization data constraints, ideally via Bayesian inference in future studies. This approach demonstrates the potential of combining quantum-gravity-inspired corrections with modern ML-driven parameter estimation to probe early-universe physics.

Abstract

We explore the impact of finite-temperature quantum gravity effects on cosmological parameters, particularly the cosmological constant $Λ$, 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, $Ω_{Λ_2}$ and $Ω_{Λ_3}$, 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 $Ω_{Λ_2}$ assumes a negative value, consistent with dimensional regularization in renormalization and that the presence of $Ω_{Λ_2}$ as well as $Ω_{Λ_3}$ enhances model accuracy. Numerical analyses demonstrate that the inclusion of these parameters improves the fit to 2018 Planck data. Although further work is required, our results suggest that finite-temperature quantum gravity effects may 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.

Figures (11)

• Figure 1: vacuum diagrams in the pure gravity sector: (a) graviton loop (b) ghost loop
• Figure 2: Sampling distribution of the distance values based on 8 cosmological parameters.
• Figure 3: Sampling distribution of the distance values based on 7 cosmological parameters.
• Figure 4: The training and validation loss functions of the proposed ANN method in estimating the distance response function based on eight cosmological parameters with over 5000 epochs.
• Figure 5: The training and validation loss functions of the proposed ANN method in estimating the distance response function based on seven cosmological parameters with over 5000 epochs.