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arXiv · 2502.08748

Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect

Ali Kaya
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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.

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Ali Kaya. 2025-02-12. Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect. https://arxiv.org/abs/2502.08748

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