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Influence of finite-temperature effects on CMB power spectrum

I. Y. Park, P. Y. Wui

Abstract

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 predictive accuracy, achieving higher $R^2$ values, 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 parameter inference.

Influence of finite-temperature effects on CMB power spectrum

Abstract

We explore the implications of finite-temperature quantum field theory effects on cosmological parameters within the framework of the 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, and , 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 and improves the model's predictive accuracy, achieving higher values, lower mean squared error, and lower AIC/BIC scores than those of the 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 parameter inference.

Paper Structure

This paper contains 18 sections, 52 equations, 8 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Finite-T effects on cosmological parameters
  3. On non-redundancy and relevance of $\Omega_{\Lambda_2}$ and $\Omega_{\Lambda_3}$
  4. Finite-T modifications implemented in Weinberg's approach
  5. Angular power spectrum without finite-T effects
  6. Angular power spectrum with finite-T effects
  7. Modified CLASS and machine learning techniques
  8. Brute-force scan of finite-T models by CLASSy
  9. Statistical and machine learning analysis of finite-T models
  10. Single run results
  11. The results with bootstrap resampling
  12. Comprehensive comparison: $\Lambda$CDM vs. finite-T models
  13. Regression performance and model complexity
  14. Parameter degeneracies and correlations
  15. Computational efficiency, stability, and implications for model selection
  16. ...and 3 more sections

Figures (8)

  • Figure 1: typical behaviors of the fractional ionization $X$ as a function of $\Omega_{\Lambda_2}$; four arbitrary values of $\Omega_{\Lambda_2}$ are chosen for demonstration
  • Figure 2: (a) $(h,\Omega_B,\Omega_{\Lambda_2})$-interpolation (b) $(h,\Omega_M,\Omega_{\Lambda_2})$-interpolation; for (a) $\Omega_M=0.13299/h^2$. The best fit parameters are $(h,\Omega_B,\Omega_{\Lambda_2},n_s)=(0.765515, 0.057172, 0.00005, 0.985064)$; for (b), $\Omega_B = 0.02238/h^2$. The best fit parameters are $(h,\Omega_M,\Omega_{\Lambda_2},n_s)=(0.649838, 0.272761, -1.59513\times 10^{-6}, 0.99)$
  • Figure 3: The dotted plot in panel (a) represents a curve with a distance $d \approx 1200$ from the Planck 2018 data, while the dotted plot in panel (b) corresponds to a distance $d \approx 3400$.
  • Figure 4: 7-parameter model estimation and residuals
  • Figure 5: 8-parameter model estimation and residuals
  • ...and 3 more figures