Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect

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 $\hat{I}¼$-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 $\hat{I}¼$-distortion depends strongly on the regularization prescription.

v3: 13 pages, revtex4; comments added