We examine the conditions under which a perturbative expansion around an inflating background is valid. When inflation is driven by a single field with a general sound speed, we find a lower limit on the sound speed related to the amplitude of the inflationary power spectrum. Generalizing the sound speed constraints to include scale dependence can limit the number of e-folds obtained in the perturbative regime and restrict otherwise apparently viable models. We also show that for models with a low sound speed, eternal inflation cannot occur in the perturbative regime.
We study implications of perturbative unitarity for quasi-single field inflation with the inflaton and one massive scalar. Analyzing high energy scattering, we show that non-Gaussianities with $|f_{\rm NL}|\gtrsim1$ cannot be realized without turning on interactions which violate unitarity at a high energy scale. Then, we provide a relation between $f_{\rm NL}$ and the scale of new physics that is required for UV completion. In particular we find that for the Hubble scale $H\gtrsim 6\times 10^{9}$ GeV, Planck suppressed operators can easily generate too large non-Gaussanities and so it is hard…
In quasi single field inflation there are massive fields that interact with the inflaton field. If these other fields are not much heavier than the Hubble constant during inflation ($H$) these interactions can lead to important consequences for the cosmological energy density perturbations. The simplest model of this type has a real scalar inflaton field that interacts with another real scalar $S$ (with mass $m$). In this model there is a mixing term of the form $μ{\dot π} S$, where $π$ is the Goldstone fluctuation that is associated with the breaking of time translation invariance by the time…
Axions play a central role in many realizations of large field models of inflation and in recent alternative mechanisms for generating primordial tensor modes in small field models. If these axions couple to gauge fields, the coupling produces a tachyonic instability that leads to an exponential enhancement of the gauge fields, which in turn can decay into observable scalar or tensor curvature perturbations. Thus, a fully self-consistent treatment of axions during inflation is important, and in this work we discuss the perturbative constraints on axions coupled to gauge fields. We show how the…
It is becoming increasingly clear that large but rare fluctuations of the primordial curvature field, controlled by the tail of its probability distribution, could have dramatic effects on the current structure of the universe -- {\it e.g.} via primordial black-holes. However, the use of standard perturbation theory to study the evolution of fluctuations during inflation fails in providing a reliable description of how non-linear interactions induce non-Gaussian tails. Here, we use the stochastic inflation formalism to study the non-perturbative effects from multi-field fluctuations on the sta…
Nonperturbative stochastic inflation in perturbative dynamical background
Institute of Theoretical Physics, Chinese Academy of Sciences (CAS)（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
While during inflation a phase of increasing gauge coupling allows for a scale-invariant hyperelectric spectrum, when the coupling decreases a flat hypermagnetic spectrum can be generated for typical wavelengths larger than the effective horizon. After the gauge coupling flattens out the late-time hypermagnetic power spectra outside the horizon in the radiation epoch are determined by the hyperelectric fields at the end of inflation whereas the opposite is true in the case of decreasing coupling. Instead of imposing an abrupt freeze after inflation, we consider a smooth evolution of the mode f…
In this letter we investigate gauge invariant scalar fluctuations of the metric in a non-perturbative formalism for a Higgs inflationary model recently introduced in the framework of a geometrical scalar-tensor theory of gravity. In this scenario the Higgs inflaton field has its origin in the Weyl scalar field of the background geometry. We found a nearly scale invariance of the power spectrum for linear scalar fluctuations of the metric. For certain parameters of the model we obtain values for the scalar spectral index $n_s$ and the scalar to tensor ratio $r$ that fit well with the Planck 201…
We propose a new mechanism that adapts to string theory a perturbative method for stabilizing moduli without leaving the domain of perturbative control, thereby evading the `Dine-Seiberg' problem. The only required nonperturbative information comes from the standard renormalization-group resummation of leading logarithms that allow us simultaneously to work to a fixed order in the perturbative parameter $α$ and to all orders in $α\lnτ$ where $τ$ is a large extra-dimensional modulus. The resulting potential is naturally minimized for moduli of order $τ\sim e^{1/α}$ and so can be exponentially l…
Naïve dimensional analysis seems to suggest possible unitarity violations in the framework of the Higgs and new Higgs inflationary scenarios. These violations seem to happen around the value in which the potential energy, per given Higgs boson's vacuum expectation value, crosses the perturbative cut-off scale calculated around the electroweak vacuum. Conversely to these expectations, in this paper we show that, by using an exact analysis of the background dependent cut-off scale, and by including the contribution of the phase-space volume in the perturbative scattering amplitudes, no violation…
We perform a detailed analytical and numerical analysis of the multi-field evolution of Fibre Inflation and show that, regardless of the microscopic realisation of the model, the mass-squared of one of the two ultra-light axions becomes always negative during inflation. This implies that the corresponding isocurvature perturbations experience a potential geometrical destabilisation which seems to bring the system away from the perturbative regime. Therefore we conclude that a full understanding of the inflationary evolution of Fibre Inflation can be achieved only via a non-perturbative analysi…
We have previously derived the effect of soft graviton modes on the quantum state of de Sitter using spontaneously broken asymptotic symmetries. In the present paper we reinterpret this effect in terms of particle production and relate the quantum states with and without soft modes by means of Bogoliubov transformations. This also enables us to address the much discussed issues regarding the observability of infrared effects in de Sitter from a new perspective. While it is commonly agreed that infrared effects are not visible to a single sub-horizon observer at late times, we argue that the qu…
Inflation can be supported in very steep potentials if it is generated by rapidly turning fields, which can be natural in negatively curved field spaces. The curvature perturbation, $ζ$, of these models undergoes an exponential, transient amplification around the time of horizon crossing, but can still be compatible with observations at the level of the power spectrum. However, a recent analysis (based on a proposed single-field effective theory with an imaginary speed of sound) found that the trispectrum and other higher-order, non-Gaussian correlators also undergo similar exponential enhance…
High-scale string inflationary models are in well-known tension with low-energy supersymmetry. A promising solution involves models where the inflaton is the volume of the extra dimensions so that the gravitino mass relaxes from large values during inflation to smaller values today. We describe a possible microscopic origin of the scalar potential of volume modulus inflation by exploiting non-perturbative effects, string loop and higher derivative perturbative corrections to the supergravity effective action together with contributions from anti-branes and charged hidden matter fields. We also…
For primordial perturbations, deviations from Gaussian statistics on the tail of the probability distribution can be associated with non-perturbative effects of inflation. In this paper, we present some particular examples in which the tail of the distribution becomes highly non-Gaussian although the statistics remains almost Gaussian in the perturbative regime. We begin with an extension of the ultra-slow-roll inflation that incorporates a transition process, where the inflaton climbs up a tiny potential step at the end of the non-attractor stage before it converges to the slow-roll attractor…
We calculate one-loop correction to the two-point functions of curvature perturbation in single-field inflation generated by cubic self-interaction. Incorporating the observed red-tilted spectrum of curvature perturbation, the relevant one-loop correction takes a finite value and inversely proportional to the spectral tilt. Requiring one-loop correction to be much smaller than the tree-level contribution leads to an upper bound on primordial non-Gaussianity. While observationally allowed region of non-Gaussian parameter space is found to be entirely included by the region, where one-loop corre…
We consider warm inflation with a Dirac-Born-Infeld (DBI) kinetic term in which both the nonequilibrium dissipative particle production and the sound speed parameter slow the motion of the inflaton field. We find that a low sound speed parameter removes, or at least strongly suppresses, the growing function appearing in the scalar of curvature power spectrum of warm inflation, which appears due to the temperature dependence in the dissipation coefficient. As a consequence of that, a low sound speed helps to push warm inflation into the strong dissipation regime, which is an attractive regime f…
Combining the stochastic and $δN$ formalisms, we derive non perturbative analytical expressions for all correlation functions of scalar perturbations in single-field, slow-roll inflation. The standard, classical formulas are recovered as saddle-point limits of the full results. This yields a classicality criterion that shows that stochastic effects are small only if the potential is sub-Planckian and not too flat. The saddle-point approximation also provides an expansion scheme for calculating stochastic corrections to observable quantities perturbatively in this regime. In the opposite regime…
The simplest two-field completion of natural inflation has a regime in which both fields are active and in which its predictions are within the Planck 1-$σ$ confidence contour. We show this for the original model of natural inflation, in which inflation is achieved through the explicit breaking of a U(1) symmetry. We consider the case in which the mass coming from explicit breaking of this symmetry is comparable to that from spontaneous breaking, which we show is consistent with a hierarchy between the corresponding energy scales. While both masses are comparable when the observable modes left…
