New Approach to Cosmological Fluctuation using the Background Field Method and CMB Power Spectrum

TL;DR

This paper introduces a novel field theory approach using the background-field formalism to analyze the CMB power spectrum, emphasizing the role of statistical fluctuations and emergent gravity concepts within a curved spacetime model.

Contribution

It presents a new formulation that treats the metric as a background field and incorporates statistical effects via path integrals, offering a fresh perspective on cosmological fluctuations.

Findings

Separate treatment of classical, statistical, and quantum effects.

Cosmological fluctuations originate from microscopic movements, not quantum gravity.

IR parameter and Z2 symmetry improve regularization techniques.

Abstract

A new field theory formulation is presented for the analysis of the CMB power spectrum distribution in the cosmology. The background-field formalism is fully used. Stimulated by the recent idea of the {\it emergent} gravity, the gravitational (metric) field $g_\mn$ is not taken as the quantum-field, but as the background field. The statistical fluctuation effect of the metric field is taken into account by the path (hyper-surface)-integral over the space-time. Using a simple scalar model on the curved (dS$_4$) space-time, we explain the above things with the following additional points: 1) Clear separate treatment of the classical effect, the statistical effect and the quantum effect; 2) The cosmological fluctuation comes not from the 'quantum' gravity but from the unkown 'microscopic' movement; 3) IR parameter ($\ell$) is introduced for the time axis as the periodicity. Time reversal(Z$_2$)-symmetry is introduced in order to treat the problem separately with respect to the Z$_2$ parity. This procedure much helps both UV and IR regularization to work well.