A
bstract
We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without the gauge issue. The first model contains only a ...single field, which can be reduced to a free theory by a local field redefinition; the second contains two fields and cannot be so reduced. Loop corrections in both models produce large temporal and spatial logarithms which cause perturbation theory to break down at late times and large distances. Many of these logarithms derive from the “tail” part of the propagator and can be summed using a variant of Starobinsky’s stochastic formalism involving a curvature-dependent effective potential. The remaining logarithms derive from the ultraviolet and can be summed using a variant of the renormalization group based on a special class of curvature-dependent renormalizations. Explicit results are derived at 1-loop and 2-loop orders.
A
bstract
We present a new computation of the renormalized graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. Our result takes account of the need ...to include a finite renormalization of the cosmological constant, which was not included in the first analysis. We also avoid preconceptions concerning structure functions and instead express the result as a linear combination of 21 tensor differential operators. By using our result to quantum-correct the linearized effective field equation we derive logarithmic corrections to both the electric components of the Weyl tensor for gravitational radiation and to the two potentials which quantify the gravitational response to a static point mass.
We consider an additional fine-tuning problem which afflicts scalar-driven models of inflation. The problem is that successful reheating requires the inflaton be coupled to ordinary matter, and ...quantum fluctuations of this matter induce Coleman-Weinberg potentials which are not Planck suppressed. Unlike the flat space case, these potentials depend upon a still-unknown, nonlocal functional of the metric which reduces to the Hubble parameter for de Sitter. Such a potential cannot be completely subtracted off by any local action. In a simple model we numerically consider one possible subtraction scheme in which the correction is locally subtracted at the beginning of inflation. For fermions the effect is to make the Universe approach de Sitter with a smaller Hubble parameter. For gauge bosons the effect is to make inflation end almost instantly unless the gauge charge is unacceptably small.
We accurately approximate the contribution that photons make to the effective potential of a charged inflaton for inflationary geometries with an arbitrary first slow roll parameter ε . We find a ...small, nonlocal contribution and a numerically larger, local part. The local part involves first and second derivatives of ε , coming exclusively from the constrained part of the electromagnetic field which carries the long range interaction. This causes the effective potential induced by electromagnetism to respond more strongly to geometrical evolution than for either scalars, which have no derivatives, or spin one-half particles, which have only one derivative. For ε = 0 , our final result agrees with that of Allen Nucl. Phys. B226, 228 (1983) on de Sitter background, while the flat space limit agrees with the classic result of Coleman and Weinberg Phys. Rev. D 7, 1888 (1973).
We study one loop quantum gravitational corrections to the long range force induced by the exchange of a massless scalar between two massive scalars. The various diagrams contributing to the flat ...space S matrix are evaluated in a general covariant gauge, and we show that dependence on the gauge parameters cancels at a point considerably before forming the full S matrix, which is unobservable in cosmology. It is possible to interpret our computation as a solution to the effective field equations-which could be done even in cosmology-but taking account of quantum gravitational corrections from the source and from the observer.
A
bstract
Dependence on the graviton gauge enters the conventional effective field equations because they fail to account for quantum gravitational correlations with the source which excites the ...effective field and with the observer who measures it. Including these correlations has been shown to eliminate gauge dependence in flat space background. We generalize the technique to de Sitter background for the case of the 1-loop graviton corrections to the exchange potential of a massless, minimally coupled scalar.
We use a simplified formalism to recompute the single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on de Sitter background which was originally made by Boran ...et al., Phys. Rev. D 90, 124054 (2014); 96, 025001 (2017); 96, 105003 (2017). Our result resolves the problem with the flat space correspondence limit that was pointed out by Fröb Classical Quantum Gravity 35, 035005 (2018). We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.
A
bstract
Recent progress on nonlinear sigma models on de Sitter background has permitted the resummation of large inflationary logarithms by combining a variant of Starobinsky’s stochastic formalism ...with a variant of the renormalization group. We reconsider single graviton loop corrections to the photon wave function, and to the Coulomb potential, in light of these developments. Neither of the two 1-loop results have a stochastic explanation, however, the flow of a curvature-dependent field strength renormalization explains their factors of ln(
a
). We speculate that the factor of ln(
Hr
) in the Coulomb potential should not be considered as a leading logarithm effect.
One-graviton-loop corrections to the vacuum polarization on a de Sitter background show two interesting infrared effects: a secular enhancement of the photon electric field strength and a long-range ...running of the Coulomb potential. We show that the first effect derives solely from the “tail” term of the graviton propagator, but that the second effect does not. Our result agrees with the earlier observation that the secular enhancement of massless fermion mode functions derives solely from the tail term. We discuss the implications this has for the important project of generalizing to quantum gravity the Starobinsky technique for summing the series of leading infrared effects from inflationary quantum field theory.
We reconsider the fine-tuning problem of scalar-driven inflation arising from the need to couple the inflaton to ordinary matter in order to make reheating efficient. Quantum fluctuations of this ...matter induce Coleman-Weinberg corrections to the inflaton potential, depending (for de Sitter background) in a complex way on the ratio of the inflaton to the Hubble parameter. These corrections are not Planck-suppressed and cannot be completely subtracted because they are not even local for a general geometry. A previous study showed that it is not satisfactory to subtract a local function of just the inflaton and the initial Hubble parameter. This paper examines the other allowed possibility of subtracting a local function of the inflaton and the Ricci scalar. The problem in this case is that the new, scalar degree of freedom induced by the subtraction causes inflation to end almost instantly.
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