We consider a stochastic spectator scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. We consider the fermion to be massless, and take the one loop effective potential found earlier by using the exact fermion propagator in de Sitter spacetime. We take the potential for the spectator scalar to be quintessence-like, $V(ϕ)=α|ϕ|^p$ ($α\ensuremath{>} 0,\ p\ensuremath{>} 4$), so that the total effective potential is generically bounded from below for all values of the parameters and couplings, and a late time equilibrium state is allowed. Using next the stochastic spectral expansion method, we numerically investigate the two point correlation function, as well as the density fluctuations corresponding to the spectator field, with respect to the three parameters of the total effective potential, $α,\ p$ and the Yukawa coupling, $g$. In particular, we find that the power spectrum and the spectral index corresponds to blue tilt with increasing $g$. The three point correlation function and non-Gaussianity corresponding to the density fluctuation has also been investigated. The increasing Yukawa coupling is shown to flatten the peak of the shape function in the squeezed limit. Also in this limit, the increase in the same is shown to increase the local non-Gaussianity parameter.
We consider the possibility of enhancing the inflationary tensor mode by introducing a spectator scalar field with a small sound speed which induces gravitational waves as a second order effect. We analytically obtain the power spectra of gravitational waves and curvature perturbation induced by the spectator scalar field. We found that the small sound speed amplifies the curvature perturbation much more than the tensor mode and the current observational constraint forces the induced gravitational waves to be negligible compared with those from the vacuum fluctuation during inflation.
We study the contribution of spectator massive scalar fields to the inflationary density perturbations through the universal gravitational coupling. We find that such contribution has several remarkable properties: it does not decrease as the mass of the spectator field increases; it has a significant size and cannot be turned off by any adjustable parameters; and it applies to all massive scalars existed during inflation, making the overall effect unexpectedly large. As a result, the primordial density perturbations are anomalously sensitive to the high energy physics.
We investigate the development of spectator (light test) field condensates due to their quantum fluctuations in a de Sitter inflationary background, making use of the stochastic formalism to describe the system. In this context, a condensate refers to the typical field value found after coarse-graining using the Hubble scale $H$, which can be essential to seed the initial conditions required by various post-inflationary processes. We study models with multiple coupled spectators and for the first time we demonstrate that new forms of stationary solution exist (distinct from the standard expone…
Resilience of Primordial Black Hole Formation from Inflation with a Light Spectator Field
University of Manitoba（曼尼托巴大学）；University of Winnipeg（温尼伯大学）；Santa Cruz Institute for Particle Physics（圣克鲁兹粒子物理研究所）；University of California, Santa Cruz（加利福尼亚大学圣克鲁兹分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University of Toronto（多伦多大学）；Massachusetts Institute of Technology（麻省理工学院）
The inflationary 1-loop tensor power spectrum from an excited spectator scalar field is calculated. Recent studies on primordial black holes suggest that the inflationary curvature perturbation may be huge on small scales. An enhanced curvature perturbation may arise from a drastic enhancement of spectator scalar field fluctuations. In this letter, using the in-in formalism, we calculate 1-loop quantum corrections to primordial gravitational waves by such an excited spectator field with a sharp peak in momentum space. We find scale-invariant loop corrections in this full quantum setup, in cont…
The most conventional mechanism for gravitational waves (gw) production during inflation is the amplification of vacuum metric fluctuations. In this case the gw production can be uniquely related to the inflationary expansion rate $H$. For example, a gw detection close to the present experimental limit (tensor-to-scalar ratio $r \sim 0.1$) would indicate an inflationary expansion rate close to $10^{14} \, {\rm GeV}$. This conclusion, however, would be invalid if the observed gw originated from a different source. We construct and study one of the possible covariant formulations of the mechanis…
Non-perturbative $\langle ϕ\rangle$, $\langle ϕ^2 \rangle$ and the dynamically generated scalar mass with Yukawa interaction in the inflationary de Sitter spacetime
We elaborate on the functional integral describing the stochastic dynamics of a spectator field during inflation, comparing its diagrammatic expansion to that obtained directly from a perturbative solution of the corresponding Langevin equation. We state Feynman rules for computing arbitrary temporal $n$-point functions and perform some illustrative computations for a $λϕ^4$ interaction, paying attention to the role played by a functional Jacobian determinant in the path integral. We also briefly consider the case when the field contributes to the expansion rate, making the noise multiplicativ…
We investigate the enhancement of the curvature perturbations in a single-field slow-roll inflation with a spectator scalar field kinetically coupled to the inflaton. The coupling term with a periodic function of inflaton triggers the exponential growth of the spectator field perturbations, which indirectly amplifies the curvature perturbations to produce a sizable abundance of primordial black holes (PBHs). This scenario is found to be insensitive to the inflationary background. We study two distinct populations of the stochastic gravitational wave background (SGWB) produced in this scenario,…
We generalize Starobinskii's stochastic technique to the theory of a massless, minimally coupled scalar interacting with a massless fermion in a locally de Sitter geometry. The scalar is an ``active'' field that can engender infrared logarithms. The fermion is a ``passive'' field that cannot cause infrared logarithms but which can carry them, and which can also induce new interactions between the active fields. The procedure for dealing with passive fields is to integrate them out, then stochastically simplify the resulting effective action following Starobinski\uı. Because Yukawa theory is qu…
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 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, $…
We explore the consequences of the existence of a very large number of light scalar degrees of freedom in the early universe. We distinguish between participator and spectator fields. The former have a small mass, and can contribute to the inflationary dynamics; the latter are either strictly massless or have a negligible VEV. In N-flation and generic assisted inflation scenarios, inflation is a co-operative phenomenon driven by N participator fields, none of which could drive inflation on their own. We review upper bounds on N, as a function of the inflationary Hubble scale H. We then conside…
We study post-inflationary evolution in $α$-attractor T-models of inflation. We consider the dynamics of both scalar fields present in these models: the inflaton and the spectator, as a negative field-space curvature may lead to geometrical destabilization of the spectator. We perform state-of-the-art lattice simulations with a dedicated numerical code optimized for those models. We corroborate earlier findings that the perturbations of the spectator field are much more unstable than the perturbations of the inflaton field, so the dynamics of early stages of preheating is dominated by the evol…
One of the most important achievements of inflationary cosmology is to predict a departure from scale invariance of the power spectrum for scalar curvature cosmological fluctuations. This tilt is understood as a consequence of a quasi de Sitter classical equation of state describing the inflationary dark energy dominated era. Here, following previous work, we find a departure of scale invariance for the quantum Fisher information associated to de Sitter vacuum for scalar quantum spectator modes. This gives rise to a purely quantum cosmological tilt with a well defined dependence on energy scal…
We investigate two-field inflationary models in which scalar cosmological pertubations are generated via a spectator field nonminimally coupled to gravity, with the particular emphasis on curvaton scenarios. The principal advantage of these models is in the possibility to tune the spectator spectral index via the nonminimal coupling. Our models naturally yield red spectrum of the adiabatic perturbation demanded by observations. We study how the nonminimal coupling affects the spectrum of the curvature perturbation generated in the curvaton scenarios. In particular we find that for small, negat…
We demonstrate equivalence of the in-in formalism and Green's function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also ca…
If the inflaton couples to other degrees of freedom that populate the post-inflationary stage, such coupling modifies the dynamics of the inflaton \emph{during} inflation. We consider light fermions Yukawa coupled to the inflaton as "unobserved" degrees of freedom integrated out of the total density matrix. Tracing out these degrees of freedom yields a \emph{mixed} density matrix whose time evolution is described by an effective field theory. We show that the coupling leads to profuse fermion pair production for super-Hubble inflaton fluctuations which lead to the \emph{growth of entanglement …
Tachyonic Encore: A universal shift of inflationary observables
University of Groningen（格罗宁根大学）；Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究所）；Instituto de Física Téorica UAM-CSIC（马德里自治大学-西班牙国家研究委员会理论物理研究所）
The possibility to construct an inflationary universe scenario for the finite-scale gauged Nambu-Jona-Lasinio model is investigated. This model can be described by the Higgs-Yukawa type interaction model with the corresponding compositeness scale. Therefore, the one-loop Higgs-Yukawa effective potential is used with the compositeness condition for the study of inflationary dynamics. We evaluate the fluctuations in the cosmic microwave background for the model with a finite compositeness scale in the slow-roll approximation. We find the remarkable dependence on the gauge group and the number of…
We consider the inflationary universe with a spectator scalar field coupled to a $U(1)$ gauge field and calculate curvature perturbation and gravitational waves (GWs). We find that the sourced GWs can be larger than the one from vacuum fluctuation and they are statistically anisotropic as well as linearly polarized. The GW power spectrum acquires higher multipole moments as $\mathcal{P}_h \propto (1-\cos^2θ+\cos^4θ-\cos^6θ)$ irrespective of the model parameters.
We accurately approximate the contribution of a Yukawa-coupled fermion to the inflaton effective potential for inflationary geometries with a general first slow roll parameter $ε(t)$. For $ε= 0$ our final result agrees with the famous computation of Candelas and Raine done long ago on de Sitter background, and both computations degenerate to the result of Coleman and Weinberg in the flat space limit. Our result contains a small part that depends nonlocally on the inflationary geometry. Even in the numerically larger local part, very little of the $ε$ dependence takes the form of Ricci scalars.…
We calculate the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ in a class of recently proposed two-field no-scale inflationary models in supergravity. We show that, in order to obtain correct predictions, it is crucial to take into account the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbation and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter $ε\sim 0.01$. Beyond these particular models, we e…
To what extent can the Planck satellite observations be interpreted as confirmation of the quantum part of the inflationary paradigm? Has it "seen" the Bunch-Davies state? We compare and contrast the Bunch-Davies interpretation with one using a so-called entangled state in which the fluctuations of a spectator scalar field are entangled with those of the metric perturbations $ζ$. We first show how a spectator scalar field $Σ$, with an expectation value $σ(t)$ that evolves in time, will generically generate such a state. We then use this state to compute the power spectrum $P_ζ(k)$ and thence t…
Virtual Institute of Astroparticle Physics（虚拟天体粒子物理研究所）；MG Science Institute, Gujarat University（古吉拉特大学 MG 科学研究所）；Department of Physics and Astronomy, Vanderbilt University（范德堡大学物理与天文系）；National Research Nuclear University MEPhI（俄罗斯国立核研究大学莫斯科工程物理学院）；Research Institute of Physics, Southern Federal University（南联邦大学物理研究所）
We discuss how a scenario recently proposed for the morphing of macroscopic gravitation into weak interactions at the attometer scale affects our current understanding of high-energy density phenomena. We find that the Yukawa couplings of the fundamental fermions are directly related to their event horizons, setting an upper bound $y_f\leq \sqrt{2}$ for their observability through gauge interactions. Particles with larger Yukawa couplings are not precluded, but should interact only gravitationally, providing a natural candidate for dark matter. Furthermore, the quantum vacuum contribution to t…
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）
Using 3+1 classical lattice simulations, we follow the symmetry breaking pattern and subsequent non-linear evolution of a spectator field non-minimally coupled to gravity when the post-inflationary dynamics is given in terms of a stiff equation-of-state parameter. We find that the gradient energy density immediately after the transition represents a non-negligible fraction of the total energy budget, steadily growing to equal the kinetic counterpart. This behaviour is reflected on the evolution of the associated equation-of-state parameter, which approaches a universal value $1/3$, independent…
Quark, lepton and right-handed neutrino production via inflation
Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；China Center of Advanced Science and Technology（中国高等科学技术中心）；University of Warsaw（华沙大学）
We discuss inflaton decays and reheating in no-scale Starobinsky-like models of inflation, calculating the effective equation-of-state parameter, $w$, during the epoch of inflaton decay, the reheating temperature, $T_{\rm reh}$, and the number of inflationary e-folds, $N_*$, comparing analytical approximations with numerical calculations. We then illustrate these results with applications to models based on no-scale supergravity and motivated by generic string compactifications, including scenarios where the inflaton is identified as an untwisted-sector matter field with direct Yukawa coupling…
We investigate the backreaction of the quantum fluctuations of a very light ($m \!\lesssim\! H_{\text{today}}$) nonminimally coupled spectator scalar field on the expansion dynamics of the Universe. The one-loop expectation value of the energy momentum tensor of these fluctuations, as a measure of the backreaction, is computed throughout the expansion history from the early inflationary universe until the onset of recent acceleration today. We show that, when the nonminimal coupling $ξ$ to Ricci curvature is negative ($ξ_c \!=\! 1/6$ corresponding to conformal coupling), the quantum backreacti…
