Influence of finite-temperature effects on CMB power spectrum

We explore the implications of finite-temperature quantum field theory effects on cosmological parameters within the framework of the Ł CDM model and its modification. By incorporating temperature-dependent corrections to the cosmological constant, we extend the standard cosmological model to include additional density parameters, Ω Ł 2 and Ω Ł 3, which arise from finite-T quantum gravitational effects. Using the Cosmic Linear Anisotropy Solving System (CLASS), we analyze the impact of these corrections on the cosmic microwave background power spectrum and compare the results with the Planck 2018 data. Through brute-force parameter scans and advanced machine learning techniques, including quartic regression, we demonstrate that the inclusion of Ω Ł 2 and Ω Ł 3 improves the model's fit to the fine structure of the reference power spectrum. Because Ω Ł 2 and Ω Ł 3 originate from finite-temperature quantum (loop) corrections rather than being introduced as free dark-energy components, they are expected to be small a priori; their smallness is thus a prediction of the framework, not a sign that they are negligible. The improvement of the fit is measured by the coefficient of determination R squared (the fraction of variance in the parameter--distance relation captured by the regression), together with lower mean squared error and lower AIC/BIC scores than those of the Ł CDM model. Despite identified methodological limitations, these findings establish an exploratory framework for incorporating finite-temperature quantum corrections into precision cosmology and open new avenues for data-driven exploration of cosmological parameters.