Abstract
We consider single graviton loop corrections to the effective field equation of a massless, minimally coupled scalar on de Sitter background in the simplest gauge. We find a large temporal logarithm in the approach to freeze-in at late times, but no correction to the feeze-in amplitude. We also find a large spatial logarithm (at large distances) in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization. We discuss how these results set the stage for a project to purge gauge dependence by including quantum gravitational corrections to the source which disturbs the effective field and to the observer who measures it.
Highlights
We find a large spatial logarithm in the scalar potential generated by a point source, which can be explained using the renormalization group with one of the higher derivative counterterms regarded as a curvature-dependent field strength renormalization
These doubts persist in spite of the fact that similar effects derive from loops of massless, minimally coupled scalars [9, 32], which experience the same growth (1.1) as inflationary gravitons and require no gauge fixing
Our long term goal is to establish the reality of large loop corrections from inflationary gravitons (1.1) by purging the effective field equations of gauge dependence
Summary
Where G is Newton’s constant and Λ is the cosmological constant. We define the graviton field hμν(x) as a perturbation of the conformally rescaled metric, gμν (x) ≡ a2(η)gμν (x) ≡ a2(η) ημν + κhμν , a(η) ≡ − 1 , Hη (2.2). Our gauge fixing term is a de Sitter breaking analog of (1.2) for α = β = 1 [39, 40], LGF = − 12 aD−2ημν FμFν , Fμ = ηρσ hμρ,σ − 12 hρσ,μ +(D−2)aHhμρδ0σ In this gauge the graviton propagator is the sum of three constant tensor factors times scalar propagators, i μν ∆ρσ (x; x ) =. This form is desirable because the noncovariant tensor factors multiply differences, (i∆A − i∆B) and (i∆A − i∆C), which are only logarithmically singular at coincidence. Tracereversing on both indices gives, i μν ∆ρσ.
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