arXiv subjects

T. Prokopec

Publications and source records attributed to T. Prokopec.

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↗

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↗

arXiv2022

Fluctuating Dark Energy and the Luminosity Distance

The origin of dark energy driving the accelerated expansion of the universe is still mysterious. We explore the possibility that dark energy fluctuates, resulting in spatial correlations. Due to these fluctuations, the Hubble rate itself becomes a fluctuating quantity. We discuss the effect this has on measurements of type Ia supernovae, which are used to constrain the luminosity distance. We show that the luminosity distance is affected by spatial correlations in several ways. First, the luminosity distance becomes dressed by the fluctuations, thereby differing from standard $\Lambda$CDM. Second, angular correlations become visible in the two-point correlation function of the luminosity distance. To investigate the latter we construct the angular power spectrum of luminosity distance fluctuations. We then perform a forecast for two supernova surveys, the ongoing Dark Energy Survey (DES) and the upcoming Legacy Survey of Space and Time (LSST), and compare this effect with relativistic lensing effects from perturbed $\Lambda$CDM. We find that the signal can rise above the lensing effects and that LSST could test this effect for a large part of the parameter space. As an example, a specific realisation of such a scenario is that quantum fluctuations of some field in the early universe imprint spatial correlations with a predictable form in the dark energy density today. In this case, the Hubble rate fluctuates due to the intrinsic quantum nature of the dark energy density field. We study whether the signal of this specific model would be measurable, and conclude that testing this model with LSST would be challenging. However, taking into account a speed of sound $c_s<1$ of the dark energy fluid can make this model observable.

astro-ph.CO↗

arXiv2021

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↗

arXiv2020

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 $R^2 \phi^2$ 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

Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background

We use a simplified formalism to re-compute 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, Kahya and Park [1-3]. Our result resolves the problem with the flat space correspondence limit that was pointed out by Fr\"ob [4]. We discuss how this computation will be used in a long-term project to purge the linearized effective field equation of gauge dependence.

gr-qc↗

arXiv2019

Breaking of scaling symmetry by massless scalar on de Sitter

We study the response of a classical massless minimally coupled scalar to a static point scalar charge on de Sitter. By considering explicit solutions of the problem we conclude that -- even though the dynamics formally admits dilatation (scaling) symmetry -- the physical scalar field profile necessarily breaks the symmetry. This is an instance of symmetry breaking in classical physics due to large infrared effects. The gravitational backreaction, on the other hand, does respect dilatation symmetry, making this an example of symmetry non-inheritance phenomenon.

gr-qc↗

arXiv2019

Graviton Propagator in a 2-Parameter Family of de Sitter Breaking Gauges

We formulate the graviton propagator on de Sitter background in a 2-parameter family of simple gauges which break de Sitter invariance. Explicit results are derived for the first order perturbations in each parameter. These results should be useful in computations to check for gauge dependence of graviton loop corrections.

gr-qc↗

arXiv2018

Inflation as a spontaneous symmetry breaking of Weyl symmetry

In this paper we study a novel realization of inflation, based on Weyl invariant gravity with torsion. We show that requiring the classical action for the scalar field to be Weyl invariant introduces a dilaton which induces a non trivial modification of the field space geometry of the scalar sector, which allows for inflationary phase that begins at the conformal point of the inflaton $\psi$, i.e. $\langle\psi\rangle=0$. Since the model is Weyl invariant, the inflaton condensation models a process of spontaneous Weyl symmetry breaking. For a wide range of parameters the spectral observables of the model are in good agreement with the CMB measurements, such that the scalar spectral index and the tensor-to-scalar ratio approximately agree with those of Starobinsky's inflation, i.e. $n_s\simeq 0.96-0.97$ and $r \approx 3\times 10^{-3}$. The simplest version of our model contains two scalar degrees of freedom, one of them being an exactly flat direction. If that degree is excited early on in inflation and if inflation lasts for about 60 e-foldings, we find that the Unverse undergoes a short period of kination that predates inflation. Such a period strongly suppresses the amplitude of large scale CMB temperature fluctuations providing thus an elegant explanation for the lack of power in the lowest CMB multipoles.

gr-qc↗

arXiv2018

The Graviton Tail almost Completely Wags the Dog

One graviton loop corrections to the vacuum polarization on de Sitter 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 from 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.

gr-qc↗

arXiv2017

Deducing Cosmological Observables from the S-matrix

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 {\it 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.

gr-qc↗

arXiv2014

Late-time backreaction from inflationary fluctuations of a non-minimally coupled massless scalar

We consider the late time one-loop quantum backreaction from inflationary fluctuations of a non-minimally coupled, massless scalar field. The scalar is assumed to be a spectator field in an inflationary model with a constant principal slow roll $ε$ parameter. We regulate the infrared by matching onto a pre-inflationary radiation era. We find a large late time backreaction when the nonminimal coupling $ξ$ is negative (in which case the scalar exhibits a negative mass term during inflation). The one-loop quantum backreaction becomes significant today for moderately small non-minimal couplings, $ξ\sim -1/20$, and it changes sign (from negative to positive) at a recent epoch when inflation lasts not much longer than what is minimally required, $N \gtrsim 66$. Since currently we do not have a way of treating the classical fluid and the quantum backreaction in a self-consistent manner, we cannot say decidely whether the backreaction from inflationary quantum fluctuations of a non-minimally coupled scalar can mimic dark energy.

gr-qc↗

arXiv2014

Electrodynamic Effects of Inflationary Gravitons

We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields of a point charge and a point magnetic dipole on a locally de Sitter space background. Results are obtained both for an observer at rest in co-moving coordinates, whose physical distance from the sources increases with the expanding universe, and for an observer at rest in static coordinates, whose physical distance from the sources is constant. The fields of both sources show the de Sitter analogs of the fractional $G/r^2$ corrections which occur in flat space, but there are also some fractional $G H^2$ corrections due to the scattering of virtual photons from the vast ensemble of infrared gravitons produced by inflation. The co-moving observer perceives the magnitude of the point charge to increase linearly with co-moving time and logarithmically with the co-moving position, however, the magnetic dipole shows only a negative logarithmic spatial variation. The static observer perceives no secular change of the point charge but he does report a secular enhancement of the magnetic dipole moment.

gr-qc↗

arXiv2012

Representing the Vacuum Polarization on de Sitter

Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.

gr-qc↗

arXiv2012

Covariant Vacuum Polarizations on de Sitter Background

We derive covariant expressions for the one loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter invariant formulation does not seem useful, even when it is possible. Our work has important implications for representations of the graviton self-energy on de Sitter.

gr-qc↗

arXiv2009

Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

In this paper we consider a massless scalar field, with a possible coupling $ξ$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=ε-1$, $ε=-{\dot{H}}/{H^2}$. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of $ε$. We resolve these divergences by explicitly matching the spacetime under consideration to a spacetime without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the spacetime of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar $ξR$ is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one loop order, unless $ξR$ is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe however, the two schemes give different late time behavior for the quantum stress energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.

gr-qc↗

arXiv2009

The Hubble Effective Potential

We generalize the effective potential to scalar field configurations which are proportional to the Hubble parameter of a homogeneous and isotropic background geometry. This may be useful in situations for which curvature effects are significant. We evaluate the one loop contribution to the Hubble Effective Potential for a massless scalar with arbitrary conformal and quartic couplings, on a background for which the deceleration parameter is constant. Among other things, we find that inflationary particle production leads to symmetry restoration at late times.

gr-qc↗