Graviton corrections to vacuum polarization during inflation

Abstract

We use dimensional regularization to compute the one loop quantum gravitational contribution to the vacuum polarization on de Sitter background. Adding the appropriate BPHZ counterterms gives a fully renormalized result which can be used to quantum correct Maxwell's equations. We use the Hartree approximation to argue that the electric field strengths of photons experience a secular suppression during inflation.

One loop corrected conformally coupled scalar mode equations during inflation

“…The remaining task is then performing the integration of the right hand side of (26). One fact to keep in mind is that we have taken the initial state to be the Bunch-Davies vacuum, but we have not worked out loop corrections to the initial vacuum.…”

“…• For quantum gravity plus electrodynamics, inflationary gravitons induce secular effects on the dynamical photons and alter the electric field of a point charge and the magnetic field of a point magnetic dipole [24][25][26][27][28][29][30].…”

Causality implies inflationary back-reaction

“…One of the peculiar features of quantum field theory during inflation is the existence of secular corrections from loops of massless, minimally coupled scalars [1][2][3][4][5][6][7][8][9][10][11][12][13] and/or gravitons [14][15][16][17][18][19][20][21][22][23]. These corrections grow without bound as long as inflation lasts.…”

Representing the graviton self-energy on de Sitter background

“…The primary perturbations are a tree order effect, which means that how they interact among themselves and with other particles is a loop correction. One studies these loop effects by first computing the appropriate 1PI (one-particle-irreducible) 2-point function and then using it to quantum-correct the linearized effective field equation for the particle in question [2,3,4,5,6,7,8,9,10,11,12].…”

“…There can also be important de Sitter breaking effects from inflationary scalars [13,2,3,5] and gravitons [14,15,16,17,18,6,11,12]. And even when exact de Sitter invariance is present the cost of making it manifest can be prohibitive [19,9].…”