In this work, we study general features of a regime where gauge fields produced during inflation cause a strong backreaction on the background evolution and its impact on the spectrum and the correlation length of gauge fields. With this aim, the gradient-expansion formalism previously proposed for the description of inflationary magnetogenesis in purely kinetic or purely axial coupling models, is extended to the case when both types of coupling are present. As it is formulated in position space, this method allows us to self-consistently take into account the backreaction of generated gauge fields on the inflationary background because it captures the nonlinear evolution of all physically relevant gauge-field modes at once. Using this extended gradient-expansion formalism, suitable for a wide range of inflationary magnetogenesis models, we study the gauge-field production in a specific generalization of the Starobinsky $R^2$-model with a nonminimal coupling of gauge fields to gravity. In the Einstein frame, this model implies, in addition to an asymptotically flat inflaton potential, also a nontrivial form of kinetic and axial coupling functions which decrease in time and, thus, are potentially suitable for the generation of gauge fields with a scale-invariant or even red-tilted power spectrum. The numerical analysis shows, however, that backreaction, which unavoidably occurs in this model for the interesting range of parameters, strongly alters the behavior of the spectrum and does not allow us to obtain a sufficiently large correlation length for the magnetic field. The oscillatory behavior of the generated field, caused by the retarded response of the gauge field to changes of the inflaton velocity, was revealed.
We study the production and backreaction of massive vector-like fermions in the background of a classical SU(2) gauge field during axion-driven inflation. We demonstrate all ultraviolet divergences due to the interactions with the fermions can be absorbed by renormalization of the axion wavefunction and the gauge coupling. The effects of the fermion-axion interaction vanish in the massless limit as required by symmetry. For very massive fermions, contact interactions are induced between the axion, the gauge field and the gravitational field. In this massive limit, we find the usual axion-gauge…
We investigate the interplay between moduli dynamics and inflation, focusing on the KKLT-scenario and cosmological $α$-attractors. General couplings between these sectors can induce a significant backreaction and potentially destroy the inflationary regime; however, we demonstrate that this generically does not happen for $α$-attractors. Depending on the details of the superpotential, the volume modulus can either be stable during the entire inflationary trajectory, or become tachyonic at some point and act as a waterfall field, resulting in a sudden end of inflation. In the latter case there …
We study the geometrical instability arising in multi-field models of inflation with negatively-curved field space. We analyse how the homogeneous background evolves in presence of geometrical destabilisation, and show that, in simple models, a kinematical backreaction effect takes place that shuts off the instability. We also follow the evolution of the unstable scalar fluctuations. We show that they assist the kinematical backreaction while remaining in the perturbative regime. We conclude that, in the simplest models of geometrical destabilisation, inflation does not end prematurely, but ra…
We study magnetogenesis in axionlike inflation driven by a pseudoscalar field $ϕ$ coupled axially to the electromagnetic (EM) field $(β/M_{p})ϕF_{μν}\tilde{F}^{μν}$ with dimensionless coupling constant $β$. A set of equations for the inflaton field, scale factor, and expectation values of quadratic functions of the EM field is derived. These equations take into account the Schwinger effect and the backreaction of generated EM fields on the Universe expansion. It is found that the backreaction becomes important when the EM energy density reaches the value $ρ_{\rm EM}\sim (\sqrt{2ε}/β)ρ_{\rm inf…
We study the generation of electromagnetic fields during inflation when the conformal invariance of Maxwell's action is broken by the kinetic coupling $f^{2}(ϕ)F_{μν}F^{μν}$ of the electromagnetic field to the inflaton field $ϕ$. We consider the case where the coupling function $f(ϕ)$ decreases in time during inflation and, as a result, the electric component of the energy density dominates over the magnetic one. The system of equations which governs the joint evolution of the scale factor, inflaton field, and electric energy density is derived. The backreaction occurs when the electric energy…
We study inflationary dynamics using a recently introduced classical-quantum correspondence for investigating the backreaction of a quantum mechanical degree of freedom to a classical background. Using specifically a coupled Einstein-Klein-Gordon system, an approximation that holds well during the very early inflationary era when modes are very deep inside the Hubble horizon, we show that the backreaction of a mode of the quantum field will renormalize the Hubble parameter only if the mode's wavelength is longer than some threshold Planckian length scale. Otherwise, the mode will destabilize t…
Primordial SU(2) gauge fields with an isotropic background lead to the production of spin-2 particles during inflation. We provide a unified formalism to compute this effect in all of the inflation models with isotropic SU(2) gauge fields such as Gauge-flation and Chromo-Natural inflation with and without spectator axion fields or the mass of the gauge field from the Higgs mechanism. First, we calculate the number and energy densities of the spin-2 particles. We then obtain exact analytical formulae for their backreaction on the background equations of motion of SU(2) and axion fields in (quas…
We analyze the onset of inflation for a simple single-field model when the system begins with significant inhomogeneities on length-scales shorter than the initial Hubble radius. We incorporate certain nonlinear interactions among the coupled degrees of freedom by using the nonperturbative Hartree approximation. Consistent with recent, more computationally intensive numerical-relativity studies, we find inflation to be robust for large-field models, even when the system begins with significant structure on sub-Hubble scales. We consider the space of initial conditions $(φ(t_0), \dotφ (t_0))$, …
In previous work we argued that the correct procedure to predict the gravitational wave signal from preheating after inflation rests on the in-in formalism. We extend here our previous analysis to include the backreaction of the produced matter on the motion of the inflaton and the expansion of the universe, and study how the latter affect the spectrum of the resulting gravitational waves. The addition of backreaction demands the appropriate renormalization of divergent expectation values, which we regularize by preserving diffeomorphism invariance in a manner that is amenable to numerical int…
We compute the graviton one-loop correction to the expectation value of the local expansion rate in slow-roll inflation, with both slow-roll parameters finite. The calculation is based on a recent method to explicitly construct gauge-invariant observables in perturbative quantum gravity at all orders in perturbation theory, and it is particularly suited in cases of highly-symmetrical space-time backgrounds. Our analysis adds to recent calculations of that correction in de Sitter space-time and in single-field inflation with constant deceleration. In the former case a vanishing one-loop correct…
We revisit the mechanism of primordial magnetogenesis during inflation by taking into account the dynamics of the stochastic noises of the electromagnetic perturbations. We obtain the associated Langevin and Fokker-Planck equations for the electromagnetic fields and solve them analytically. It is shown that while the backreactions of the electric field energy density may spoil inflation too early, but there are regions of parameter space where the usual decaying behavior of the magnetic fields are replaced by a mean-reverting process of stochastic dynamics. As a result, the magnetic fields set…
Large scale magnetic fields seem to be present in almost all astrophysical systems and scales from planets to superclusters of galaxies and in very low density intergalactic media. The upper limit of primordial magnetic fields (PMF) has been set by recent observations by the Planck observatory (2015) to be of the order of a few nG. The simple model ${f^2}FF$ used to generate the PMF during the inflation era. It is based on the breaking of conformal symmetry of electromagnetism during inflation. It is attractive because it is stable under perturbations and leads to a scale invariant PMF. Howeve…
We discuss a model which can generate scale-invariant helical magnetic fields on large scales ($\lesssim 1$Mpc) in the primordial universe. It is also shown that the electric conductivity becomes significant and terminates magnetogenesis even before reheating is completed. By solving the electromagnetic dynamics taking conductivity into account, we find that magnetic fields with amplitude $B\simeq 10^{-15}{\rm G}$ at present can be generated without encountering a backreaction or strong coupling problem.
We consider the possibility of inflationary magnetogenesis due to dynamical couplings of the electromagnetic fields to gravity. We find that large primordial magnetic fields can be generated during inflation without the strong coupling problem, backreaction problem, or curvature perturbation problem, which seed large-scale magnetic fields with observationally interesting strengths.
We study the quantum backreaction from inflationary fluctuations of a very light, non-minimally coupled spectator scalar and show that it is a viable candiate for dark energy. The problem is solved by suitably adapting the formalism of stochastic inflation. This allows us to self-consistently account for the backreaction on the background expansion rate of the Universe where its effects are large. This framework is equivalent to that of semiclassical gravity in which matter vacuum fluctuations are included at the one loop level, but purely quantum gravitational fluctuations are neglected. Our …
We show that a detectable tensor-to-scalar ratio $(r\ge 10^{-3})$ on the CMB scale can be generated even during extremely low energy inflation which saturates the BBN bound $ρ_{\rm inf}\approx (30 {\rm MeV})^4$. The source of the gravitational waves is not quantum fluctuations of graviton but those of $SU(2)$ gauge fields, energetically supported by coupled axion fields. The curvature perturbation, the backreaction effect and the validity of perturbative treatment are carefully checked. Our result indicates that measuring $r$ alone does not immediately fix the inflationary energy scale.
Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
Institute for Theoretical Physics, University of Münster（明斯特大学理论物理研究所）；Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学 Kavli 宇宙粒子与宇宙学研究所（WPI））；Physics Faculty, Taras Shevchenko National University of Kyiv（基辅塔拉斯·舍甫琴科国立大学物理系）
Zero temperature black hole solutions to the semiclassical backreaction equations are investigated. Evidence is provided that certain components of the stress-energy tensors for free quantum fields at the horizon only depend on the local geometry near the horizon. This allows the semiclassical backreaction equations to be solved near the horizon. It is found that macroscopic uncharged zero temperature black hole solutions to the equations may exist if the coefficient of one of the higher derivative terms in the gravitational Lagrangian is large enough and of the right sign for Starobinsky infl…
The simplest model of primordial magnetogenesis can provide scale-invariant magnetic fields that can explain the present abundances of it in the cosmic scales. Two kinds of solutions of the coupling function can lead to such phenomena and both of them suffer from the problems of either strong-coupling or large backreaction. In this work, we consider the coupling function as a linear combination of both kinds with a model parameter. We find that the parameter needs to be as small as $\sim 10^{-20}$ in order to evade the backreaction problem. On the other hand, requiring that the modes above Mpc…
We analyze the dynamics of inflationary models with a coupling of the inflaton $ϕ$ to gauge fields of the form $ϕF \tilde{F}/f$, as in the case of axions. It is known that this leads to an instability, with exponential amplification of gauge fields, controlled by the parameter $ξ= \dotϕ/(2fH)$, which can strongly affect the generation of cosmological perturbations and even the background. We show that scattering rates involving gauge fields can become larger than the expansion rate $H$, due to the very large occupation numbers, and create a thermal bath of particles of temperature $T$ during i…
We study the dynamical evolution of coupled one- and two-point functions of a scalar field in the 2PI framework at the Hartree approximation, including backreaction from out-of-equilibrium modes. We renormalize the 2PI equations of motion in an on-shell scheme in terms of physical parameters. We present the Hartree-resummed renormalized effective potential at finite temperature and critically discuss the role of the effective potential in a non-equilibrium system. We follow the decay and thermalization of a scalar field from an initial cold state with all energy stored in the potential, into a…
We determine corrections to the Hubble rate due to graviton loops in a cosmological background spacetime of constant deceleration parameter. The corrections are gauge-invariant, based on a recent proposal for all-order gauge-invariant observables in perturbative quantum gravity. We find explicit expressions for the cases of matter- and radiation-dominated eras and slow-roll inflation with vanishing second slow-roll parameter. Interestingly, in the latter case the corrections can be described by a quantum-corrected first slow-roll parameter, which brings the spacetime closer to de Sitter space.
We examine the validity of the classical approximation of the waterfall phase transition in hybrid inflation from an effective field theory (EFT) point of view. The EFT is constructed by integrating out the waterfall field fluctuations, up to one-loop order in the perturbative expansion. Assuming slow-roll conditions are obeyed, right after the onset of the waterfall phase, we find the backreaction of the waterfall field fluctuations to the evolution of the system can be dominant. In this case the classical approximation is completely spoiled. We derive the necessary constraint that ensures th…
Inflationary magnetogenesis from non-minimal coupling in large- and small-field potentials
Università di Camerino（卡梅里诺大学）；University at Albany-SUNY（奥尔巴尼州立大学（纽约州立大学））；INAF - Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Perugia（意大利国家核物理学院佩鲁吉亚分部）
