Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect

TL;DR

This paper investigates how vacuum polarization effects in curved spacetime modify photon paths and influence the Sachs-Wolfe effect, leading to frequency-dependent corrections to the CMB spectrum in inflationary models.

Contribution

It introduces a quantum correction to the null geodesic equation due to a charged scalar field, affecting CMB observations in a novel way.

Findings

Significant modifications to the CMB power spectrum for light scalar fields.

Frequency-dependent $ ext{μ}$-distortion in the CMB spectrum.

Corrections depend on regularization choices.

Abstract

We show that the null geodesic equation for photons is modified in the presence of a charged scalar field, with quantum fluctuations acting as an effective mass term that changes the null paths to timelike curves. This effect can be interpreted as a vacuum polarization phenomenon in curved spacetime. The resulting contribution to the Sachs-Wolfe effect varies with photon frequency, leading to frequency-dependent corrections to the cosmic microwave background (CMB) blackbody spectrum in the form of a $\mu$-distortion, as well as modifications to the CMB power spectrum. We estimate these within a standard inflationary scenario and find that while the correction to the CMB power spectrum is significant when the scalar field is light, the magnitude of the $\mu$-distortion depends strongly on the regularization prescription.