arXiv subjects

S. P. Miao

Publications and source records attributed to S. P. Miao.

At least 19 recordsLinked to original sources

arXiv2026

Universal Secular External Leg Corrections for Gauge Independent Scalar Self-Mass on de Sitter

This work concerns a procedure for removing gauge dependence from graviton corrections to the effective field equations for a massless, minimally coupled scalar on de Sitter background. The procedure involves combining diagrams in the same way as the scattering amplitude for the $t$-channel exchange of the massless scalar between two massive particles, but {\it without} taking the asymptotic limits which are problematic in cosmology. Implementing this at 1-loop on flat space background requires five classes of diagrams, in addition to the naive exchange, and the combination of those diagrams does eliminate dependence on the graviton gauge fixing functional. When those same diagrams are generalized to de Sitter background, their combination cancels the most important (``nonlocal'') secular gauge dependence, but it leaves (``local'') secular gauge dependence that is associated with external legs. Local secular gauge dependence can be removed by adding two additional classes of diagrams, and making secular corrections to the external wavefunctions. The purpose of this paper is to include these additional corrections on de Sitter background in order to derive fully gauge independent effective field equations at 1-loop order.

gr-qc↗

arXiv2026

Sub-Leading Logarithms for Scalar Potential Models on de Sitter

The continual production of long wavelength scalars and gravitons during inflation injects secular growth into loop corrections which would be constant in flat space. One typically finds that each additional factor of the loop counting parameter can induce up to a certain number of logarithms of the scale factor. Loop corrections that attain this number are known as ``leading logarithms''; those with fewer are sub-leading. Starobinsky's stochastic formalism has long been known to reproduce the leading logarithms of scalar potential models. We show that the first sub-leading logarithm is captured by applying the stochastic formalism to a certain part of the 1-loop effective potential. This is checked at 2-loops for a massless, minimally coupled scalar with a quartic self-interaction on de Sitter background.

gr-qc↗

arXiv2026

Quantum Cosmology in Accelerating Spacetimes II

This paper is a sequel in which we further analyze the recently derived quantum gravity equations which apply in accelerating cosmological spacetimes and whose solutions should be equivalent to all order re-summations of the perturbative leading logarithms that appear. In particular we study their implications concerning the primordial tensor power spectrum and the gravitational force due to a test source.

gr-qc↗

arXiv2025

Quantum Cosmology in Accelerating Spacetimes

We simplify the gravitational equations which apply in accelerating spacetimes and are consistent with the cosmological principle. Solutions to these equations should be tantamount to all order re-summations of the perturbative leading logarithms. We discuss the null hypothesis and we study the local expansion rate observable.

gr-qc↗

arXiv2025

Leading Logarithm Quantum Gravity II

This paper is a sequel in which we derive and simplify the gravitational equations that apply in accelerating cosmological spacetimes. Solutions to these equations should be tantamount to all order resummations of the perturbative leading logarithms. We also discuss possible phenomenological applications to cosmological observables.

gr-qc↗

arXiv2025

The Third Structure Function

We re-consider the graviton self-energy induced by a loop of massless, minimally coupled scalars on de Sitter background. On flat space background it can be represented as a sum of two tensor differential operators acting on scalar structure functions. On a general background these tensor differential operators can be constructed from the linearized Ricci scalar and the linearized Weyl tensor. However, in cosmology one requires a third contribution which we derive here.

gr-qc↗

arXiv2024

Summing Gravitational Effects from Loops of Inflationary Scalars

We develop a procedure for re-summing the large logarithms induced in gravity by loops of inflationary scalars. We first show how the scalar can be integrated out of the field equations in the presence of constant graviton field. We then extend this result to a fully conserved form which explains the need for a finite renormalization of the cosmological constant which was previously inferred from explicit computation. A variant of the renormalization group turns out to explain the large logarithmic corrections revealed by explicit computation in the electric field strength of gravitational radiation and in the potentials which characterize the response to a point mass. The implications for graviton loops are discussed.

gr-qc↗

arXiv2024

Leading Logarithm Quantum Gravity

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation these factors eventually overwhelm the small loop-counting parameter of $G H^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. We generalize the new technique to quantum gravity, resulting in a Langevin equation in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field.

gr-qc↗

arXiv2024

Alternate Computation of Gravitational Effects from a Single Loop of Inflationary Scalars

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.

gr-qc↗

arXiv2024

Gauge Independent Logarithms from Inflationary Gravitons

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.

hep-th↗

arXiv2023

Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons

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.

gr-qc↗

arXiv2023

K-Essence Induced by Derivative Couplings of the Inflaton

We consider two models which couple derivatives of the inflaton to ordinary matter, both to fermions and to scalars. Such couplings induce changes to the inflaton kinetic energy, analogous to the cosmological Coleman-Weinberg potentials which come from nonderivative couplings. Our purpose is to investigate whether these quantum-induced K-Essence models can provide efficient reheating without affecting the observational constraints on primordial inflation. Our numerical studies show that it is difficult to preserve both properties.

gr-qc↗

arXiv2022

Reheating with Effective Potentials

We consider reheating for a charged inflaton which is minimally coupled to electromagnetism. The evolution of such an inflaton induces a time-dependent mass for the photon. We show how the massive photon propagator can be expressed as a spatial Fourier mode sum involving three different sorts of mode functions, just like the constant mass case. We develop accurate analytic approximations for these mode functions, and use them to approximate the effective force exerted on the inflaton $0$-mode. This effective force allows one to simply compute the evolution of the inflaton $0$-mode and to follow the progress of reheating.

hep-ph↗

arXiv2022

Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter

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.

gr-qc↗

arXiv2022

Summing Inflationary Logarithms in Nonlinear Sigma Models

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.

gr-qc↗

arXiv2021

Inflaton Effective Potential from Photons for General $ε$

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 on de Sitter background, while the flat space limit agrees with the classic result of Coleman and Weinberg.

gr-qc↗

arXiv2021

One-loop Graviton Corrections to Conformal Scalars on a de Sitter Background

We exploit a recent computation of one graviton loop corrections to the self-mass [1] to quantum-correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the $R^2 ϕ^2$ counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.

gr-qc↗

arXiv2020

Bose-Fermi Cancellation of Cosmological Coleman-Weinberg Potentials

Cosmological Coleman-Weinberg potentials are induced when normal matter is coupled to the inflaton. It has long been known that the corrections from bosonic fields are positive whereas those from fermionic fields are negative. In flat space both take the form $\pm φ^4 \ln(φ)$, and they can be made to cancel by appropriately choosing the coupling constants. In an expanding universe the bosonic and fermionic results no longer take the same form, although their large field limits do. We choose the coupling constants so that the large field limits cancel, and then follow the deviations which result as inflation progresses. Although the result is not satisfactory we discuss how adding scalars with various conformal couplings likely solves the problem.

gr-qc↗