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.
Cosmological perturbations of massive higher-spin fields are generated during inflation, but they decay on scales larger than the Hubble radius as a consequence of the Higuchi bound. By introducing suitable couplings to the inflaton field, we show that one can obtain statistical correlators of massive higher-spin fields which remain constant or decay very slowly outside the Hubble radius. This opens up the possibility of new observational signatures from inflation.
We reconsider magnetogenesis in the context of three-form inflation, and its backreaction. In particular, we focus on first order perturbation theory during inflation and subsequent radiation era: we discuss the consistency of the perturbative approach, and elaborate on the possible non-Gaussian signatures of the model.
The large-scale power deficit in the cosmic microwave background fluctuations might be relevant with the physics of pre-inflation, a bounce, or a superinflationary phase preceding slow-roll inflation, which can provide a singular-free realization of inflation. We investigate the primordial perturbations from such pre-inflationary evolutions, which generally may consist of multiple phases with different background dynamics, and give a universal formula for the power spectrum of primordial perturbations in terms of the recursive Bogoliubov coefficients. We also apply our formula to corresponding…
We investigate a fluid description of inflationary cosmology. It is shown that the three observables of the inflationary universe: the spectral index of the curvature perturbations, the tensor-to-scalar ratio of the density perturbations, and the running of the spectral index, can be compatible with the Planck analysis. In addition, we reconstruct the equation of state (EoS) for a fluid from the spectral index of the curvature perturbations consistent with the Planck results. We explicitly demonstrate that the universe can gracefully exit from inflation in the reconstructed fluid models. Furth…
We consider first order perturbation theory for a non-minimally coupled inflaton field without assuming an adiabatic equation of state. In general perturbations in non-minimally coupled theory may be non-adiabatic. However under the slow-roll assumptions the perturbation theory may look like adiabatic one. We show in the frame-work of perturbation theory, that our results of spectral index and bound on no-minimal coupling parameter agree with the results obtained using the adiabatic equation of state by the earlier authors.
We examine the generation of primordial perturbations during an inflationary epoch in generalised theories of gravity when the equations of motion are derived using the Palatini variational principle. Both f(R) and Scalar-Tensor theories are considered and we compare our results with those obtained under the conventional metric formalism. Non-linear generalisations of the action lead to different theories under the two variational choices and we obtain distinct results for scalar and tensor spectral indices and their ratio. We find the following general result; inflation driven solely by f(R) …
We investigate one-loop quantum corrections to the power spectrum of adiabatic perturbation from entropy modes/adiabatic mode cross-interactions in multiple DBI inflationary models. We find that due to the non-canonical kinetic term in DBI models, the loop corrections are enhanced by slow-varying parameter $ε$ and small sound speed $c_s$. Thus, in general the loop-corrections in multi-DBI models can be large. Moreover, we find that the loop-corrections from adiabatic/entropy cross-interaction vertices are IR finite.
This article reviews the properties of the quantum state of inflationary perturbations. After a brief description of the inflationary background, the wavefunction of the Mukhanov-Sasaki variable is calculated and shown to be that of a strongly squeezed state. The corresponding Wigner function and density matrix, which are convenient tools to characterize the properties of a quantum state, are also evaluated. Finally, the issue of definite outcomes for inflation is discussed.
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related…
Recently, there are several reports that the cosmic magnetic fields on Mpc scale in void region is larger than $\sim 10^{-15}$G with an uncertainty of a few orders from the current blazar observations. On the other hand, in inflationary magnetogenesis models, additional primordial curvature perturbations are inevitably produced from iso-curvature perturbations due to generated electromagnetic fields. We explore such induced curvature perturbations in a model independent way and obtained a severe upper bound for the energy scale of inflation from the observed cosmic magnetic fields and the obse…
We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index $n_s$ and the tensor-to-scalar ratio $r$. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the …
We generalize former findings regarding quantum-gravitational corrections arising from a canonical quantization of a perturbed FLRW universe during inflation by considering an initial state for the scalar and tensor perturbations that generalizes the adiabatic vacuum state and allows us to consider the scenario that the perturbation modes start their evolution in an excited state. Our result shows that the quantum-gravitationally corrected power spectra get modified by pre-factors including the excitation numbers.
Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $ρ$…
We estimate fermion loop corrections to the two-point correlation function of primordial tensor perturbations in a slow-roll inflationary background. We particularly compute an explicit term of one-loop correction from a massless fermion, and then extend to the complete Interaction Hamiltonian. After that, we study one-loop corrections contributed by a massive fermion to primordial tensor fluctuations. The loop correction arisen from a massless fermion field contains logarithms and thus may constrain the validity of perturbation theory in inflationary cosmology, but the situation could be rela…
We study the infrared divergences arising from gravitational loops in the standard cosmological perturbation theory. We provide a simple solution to the problem at all orders of cosmological perturbation theory by redefining the perturbation theory in terms of a local observer. We propose to reformulate the standard perturbations in the in-in formalism, and obtain an infrared safe perturbation theory. Our results do not depend on any infrared cutoffs or similar parameters. We then present an explicit example of graviton one-loop corrections, and briefly discuss non-gaussianities.
In this work we study the imprints of bubble nucleation on primordial inflationary perturbations. We assume that the bubble is formed via the tunneling of a spectator field from the false vacuum of its potential to its true vacuum. We consider the configuration in which the observable CMB sphere is initially outside of the bubble. As the bubble expands, more and more regions of the exterior false vacuum, including our CMB sphere, fall into the interior of the bubble. The modes which leave the horizon during inflation at the time when the bubble wall collides with the observable CMB sphere are …
We investigate the implication of Trans-Planckian Censorship Conjecture (TCC) for the initial state of primordial perturbations. It is possible to set the state of perturbation modes in the infinite past as the Minkowski vacuum, only if the pre-inflationary era is past-complete. We calculate the evolution of the perturbation modes in such a pre-inflationary era and show that at the beginning of inflation the perturbation modes with wavelengths much shorter than the Hubble scale (but still larger than the Planck length scale) will behave as they are in the Bunch-Davis state. Therefore, a past-c…
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.
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the Schwinger-Dyson hierarchy of in-out quantum field theory. We extend this approach to the complete set of momentum space correlation functions. A formal solution can be obtained using raytracing techniques adapted from geometrical optics. We reformulate inflationary perturbation theory in this language, and show that raytracing reproduces the familiar "delta N" Tay…
We report on a new class of fast-roll inflationary models. In a huge part of its parameter space, inflationary perturbations exhibit quite unusual phenomena such as scalar and tensor modes freezing out at widely different times, as well as scalar modes reentering the horizon during inflation. In another, narrower range of parameters, this class of models agrees with observations. One specific point in parameter space is characterized by extraordinary behavior of the scalar perturbations. Freeze-out of scalar perturbations as well as particle production at horizon crossing are absent. Also the …
We investigate the scalar perturbation produced at the pre-inflationary stage driven by a massive scalar field in Eddington-inspired Born-Infeld gravity. The scalar power spectrum exhibits a peculiar rise for low $k$-modes. The tensor-to-scalar ratio can be significantly lowered compared with that in the standard chaotic inflation model in general relativity. This result is very affirmative considering the recent dispute on the detection of the gravitational wave radiation between PLANCK and BICEP2.
In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescripti…
Based on the effective field theory (EFT) of nonsingular cosmologies, we build a stable model, without the ghost and gradient instabilities, of bounce inflation (inflation is preceded by a cosmological bounce). We perform a full simulation for the evolution of scalar perturbation, and find that the perturbation spectrum has a large-scale suppression (as expected), which is consistent with the power deficit of the cosmic microwave background (CMB) TT-spectrum at low multipoles, but unexpectedly, it also shows itself one marked lower valley, which actually provides a better fit to the dip at mul…
We discuss the impact of adiabatic renormalization on the power spectrum of scalar and tensor perturbations from inflation. We show that adiabatic regularization is ambiguous as it leads to very different results, for different adiabatic subtraction schemes, both in the range $v\equiv k/(aH) \gsim 0.1$ and in the infrared regime. All these schemes agree in the far ultraviolet, $v\gg 1$. Therefore, we argue that in the far infrared regime, $v\ll 1$, the adiabatic expansion is no longer valid, and the unrenormalized spectra are the physical, measurable quantities. These findings cast some doubt …
We study non-linear contributions to the power spectrum of the curvature perturbation on super-horizon scales, produced during slow-roll inflation driven by a canonical single scalar field. We find that on large scales the linear power spectrum completely dominates and leading non-linear corrections remain totally negligible, indicating that we can safely rely on linear perturbation theory to study inflationary power spectrum. We also briefly comment on the infrared and ultraviolet behaviour of the non-linear corrections.
Università degli Studi di Ferrara（费拉拉大学）；INFN, Sezione di Ferrara（意大利国家核物理研究所费拉拉分部）；Università di Padova（帕多瓦大学）；INFN Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；INAF-Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
We compute the inflationary perturbation spectra and the quantity $r+8n_{T}$ to the next-to-next-to-leading log order in quantum gravity with purely virtual particles (which means the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). The spectra are functions of the inflationary running coupling $α(1/k)$ and satisfy the cosmic renormalization-group flow equations, which determine the tilts and the running coefficients. The tensor fluctuations receive contributions from the spin-2 fakeon $χ_{μν}$ at every order of the expansion in powers of $α\sim 1/115$. The dependen…
We study the quantum mechanical evolution of the tensor perturbations during inflation with non-linear tensor interactions. We first obtain the Lindblad terms generated by non-linear interactions by tracing out unobservable sub-horizon modes. Then we calculate explicitly the reduced density matrix for the super-horizon modes, and show that the probability of maintaining the unitarity of the squeezed state decreases in time. The decreased probability is transferred to other elements of the reduced density matrix including off-diagonal ones, so the evolution of the reduced density matrix describ…
In this paper we study the generation of primordial perturbations in a cosmological setting of bigravity during inflation. We consider a model of bigravity which can reproduce the $Λ$CDM background and large scale structure and a simple model of inflation with a single scalar field and a quadratic potential. Reheating is implemented with a toy-model in which the energy density of the inflaton is entirely dissipated into radiation. We present analytic and numerical results for the evolution of primordial perturbations in this cosmological setting. We find that the amplitude of tensor perturbati…
We show that in single field inflationary models the super-horizon evolution of curvature perturbations on comoving slices $\mathcal{R}$, which can cause the production of primordial black holes (PBH), is not due to entropy perturbations, but to the background evolution effect on the conversion between entropy and curvature perturbations. We derive a general relation between the time derivative of comoving curvature perturbations and entropy perturbations, in terms of a conversion factor depending on the background evolution. Contrary to previous results derived in the uniform density gauge as…
We study the primordial tensor perturbation produced from the double inflationary scenario with an intermediate break stage. Because of the transitions, the power spectrum deviates from the vacuum one and there will appear oscillatory behavior. In the case of a scalar-type curvature perturbation, it is known that the amplitude of these oscillations may be enhanced to result in the power spectrum larger than the one for the vacuum case. One might expect the similar enhancement for the tensor perturbation as well. Unfortunately, it is found that when the equation of state (EOS) parameter $w=p/ρ$…
We review the recent progress regarding the loop corrections to the correlation functions in the inflationary universe. A naive perturbation theory predicts that loop corrections generated during inflation suffer from various infrared (IR) pathologies. Introducing an IR cutoff by hand is not only unsatisfactory but also does not fix the problem of secular growth, which may ruin the predictive power of inflation models if the inflation lasts sufficiently long. We discuss the origin of the IR divergences and explore the regularity conditions of loop corrections for the adiabatic perturbation, th…
We extend the formalism of time-sliced perturbation theory (TSPT) for cosmological large-scale structure to include non-Gaussian initial conditions. We show that in such a case the TSPT interaction vertices acquire new contributions whose time-dependence factorizes for the Einstein-de Sitter cosmology. The new formulation is free from spurious infrared (IR) enhancements and reveals a clear IR structure of non-Gaussian vertices. We use the new technique to study the evolution of oscillating features in primordial statistics and show that they are damped due to non-linear effects of large bulk f…
Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize c…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known gauge-invariant quadratic action for scalar and tensor perturbations, and determine the interactions to arbitrary order. This approach does not require the explicit solution of the energy and momentum constraints, a novel feature which simplifies the determination of the interaction vertices. The constraints and the necessary imposition of gauge conditions is reflected in…
The effective field theory (EFT) of inflation provides a natural framework to study the new physical effects on primordial perturbations. Recently a healthy extension of the EFT of inflation with high-order operators has been proposed, which avoids ghosts and meanwhile leads to a nonlinear dispersion relation of the scalar perturbations. This paper is devoted to studying the effects of these high-order operators by using the uniform asymptotic approximation method. In particular, we first construct the approximate analytical solution to the mode function of the scalar perturbations. Because of…
We review several related investigations of the effects of the quantum stress tensor of a conformal field in inflationary cosmology. Particular attention will be paid to the effects of quantum stress tensor fluctuations as a source of density and tensor perturbations in inflationary models. These effects can possibly depend upon the total expansion factor during inflation, and hence be much larger than one might otherwise expect. They have the potential to contribute a non-scale invariant and non-Gaussian component to the primordial spectrum of perturbations, and might be observable.
Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the…
A gauge-invariant, linear cosmological perturbation theory of an almost homogeneous and isotropic universe with dynamically evolving Newton constant G and cosmological constant $Λ$ is presented. The equations governing the evolution of the comoving fractional spatial gradients of the matter density, G and $Λ$ are thus obtained. Explicit solutions are discussed in cosmologies, featuring an accelerated expansion, where both G and $Λ$ vary according to renormalization group equations in the vicinity of an ultraviolet fixed point. Finally, a similar analysis is carried out in the late universe reg…
We extend the δN formalism so that it gives all of the stochastic properties of the primordial curvature perturbation ζif the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation \fnl of the bispectrum of ζ, which is the main signal of non-gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained.
