Effect of a cosmological constant on propagation of vacuum polarized photons in stationary spacetimes

Sourav Bhattacharya

doi:10.1140/epjc/s10052-015-3477-7

Sourav Bhattacharya

Open Access

https://doi.org/10.1140/epjc/s10052-015-3477-7

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Abstract

Consideration of vacuum polarization in quantum electrodynamics may affect the momentum dispersion relation for photons for a non-trivial background, due to the appearance of curvature dependent terms in the effective action. We investigate the effect of a positive cosmological constant $$\Lambda $$ on this at one-loop order for stationary $$\Lambda $$ -vacuum spacetimes. To the best of our knowledge, so far it only has been shown that $$\Lambda $$ affects the propagation in a time dependent black hole spacetime. Here we consider the static de Sitter cosmic string and the Kerr–de Sitter spacetime to show that there might occur a non-vanishing effect due to $$\Lambda $$ for physical polarizations. The consistency of these results with the polarization sum rule is discussed.

Highlights

If we consider quantum electrodynamics in curved spacetime, the effective action for the photon contains, from the loop integrals, some finite part which depends on both the field strength and the background curvature
The velocity shifts of photons were investigated in various black hole backgrounds [3,5,7,8]
We have considered two physically interesting stationary -vacuum spacetimes – the de Sitter cylindrical cosmic string and the Kerr–de Sitter case

Summary

Introduction

If we consider quantum electrodynamics in curved spacetime, the effective action for the photon contains, from the loop integrals, some finite part which depends on both the field strength and the background curvature. Such finite parts originate from the curvature dependence of the propagator in curved spacetime. In [8] various stationary and time dependent black holes with were considered and it was shown that the velocity of the vacuum polarized photons gets modified, contributes to this only in the time dependent case. For the cosmic string spacetime in particular, the false vacuum of the scalar field inside the string core makes the effective value of the cosmological constant higher and for such spacetimes this effect may be considerable inside the string core

Calculation of the velocity shifts

The Linet–Tian-cosmic string spacetime

The Kerr–de Sitter spacetime

Summary and outlook