Super-horizon Curvature Perturbations Research Articles

Superhorizon Curvature Perturbations Are Protected against One-Loop Corrections.

We examine one-loop corrections from small-scale curvature perturbations to the superhorizon-limit ones in single-field inflation models, which have recently caused controversy. We consider the case where the Universe experiences transitions of slow-roll (SR)→intermediate period→SR. The intermediate period can be an ultra-slow-roll period or a resonant amplification period, either of which enhances small-scale curvature perturbations. We assume that the superhorizon curvature perturbations are conserved at least during each of the SR periods. Within this framework, we show that the superhorizon curvature perturbations during the first and the second SR periods coincide at one-loop level in the slow-roll limit.

Thermal curvature perturbations in thermal inflation

We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature T c, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for T > T c. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below T c, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.

Cancellation of quantum corrections on the soft curvature perturbations

We study the cancellation of quantum corrections on the superhorizon curvature perturbations from subhorizon physics beyond the single-clock inflation from the viewpoint of the cosmological soft theorem. As an example, we focus on the transient ultra-slow-roll inflation scenario and compute the one-loop quantum corrections to the power spectrum of curvature perturbations taking into account nontrivial surface terms in the action. We find that Maldacena’s consistency relation is satisfied and guarantees the cancellation of contributions from the short-scale modes. As a corollary, primordial black hole production in single-field inflation scenarios is not excluded by perturbativity breakdown even for the sharp transition case in contrast to some recent claims in the literature. We also comment on the relation between the tadpole diagram in the in-in formalism and the shift of the elapsed time in the stochastic-δN formalism. We find our argument is not directly generalisable to the tensor perturbations.

Scale invariant curvature perturbations from a spontaneously decaying scalar field

The evolution of superhorizon curvature perturbations in a two-component interacting Universe is considered. It is found that adiabatic modes conserve the total curvature perturbation , unless there are stages in which the rate of dissipation of one component into another is not constant. Moreover, our result shows that when the rate is varying it is possible for ‘isocurvature’ perturbations generated during reheating to alter the amplitude of an adiabatic curvature mode even when the mode is outside the horizon. Specifically, if an indefinitely large rate Γ for massive particles decaying into photons develops rapidly amid vanishingly small initial values (before decay) of the total curvature and Newtonian potential , such that the product and become a pair of finite and universal constants for all superhorizon scales afterwards, Harrison–Zel’dovich scale-invariant power spectrum could be synthesized from a homogeneous state without inflation at all.

Constraints on ultraslow-roll inflation from the third LIGO-Virgo observing run

The nonattractor evolution in ultra-slow-roll (USR) inflation results in the amplification of superhorizon curvature perturbations and then induces a strong and detectable stochastic gravitational wave background. In this letter, we search for such a stochastic gravitational wave background in data from the third LIGO-Virgo observing run and place constraints on the USR inflationary models. The $e$-folding number of the USR phase are constrained to be $\Delta N \lesssim 2.9$ at the 95% confidence level and the power spectrum of curvature perturbations amplified during the USR phase is constrained to be $\log_{10}P_{R\mathrm{p}}<-1.7$ at the scales $2.9\times10^5 ~\mathrm{pc^{-1}} \lesssim k \lesssim 1.7\times10^{11}~\mathrm{pc^{-1}}$. Besides, we forecast the ability of future experiments to constrain USR inflation, and find $P_{R\mathrm{p}}\lesssim 10^{-3.6}$ for LISA and Taiji, $P_{R\mathrm{p}}\lesssim 10^{-3.3}$ for Cosmic Explore and Einstein Telescope, $P_{R\mathrm{p}}\lesssim 10^{-5.5}$ for DECIGO and Big Bang Observer and $P_{R\mathrm{p}}\lesssim 10^{-5.2}$ for Square Kilometre Array.

Constraining First-Order Phase Transitions with Curvature Perturbations.

The randomness of the quantum tunneling process induces superhorizon curvature perturbations during cosmological first-order phase transitions. We for the first time utilize curvature perturbations to constrain the phase transition parameters, and find that the observations of the cosmic microwave background spectrum distortion and the ultracompact minihalo abundance can give strict constraints on the phase transitions below 100GeV, especially for the low-scale phase transitions and some electroweak phase transitions. The current constraints on the phase transition parameters are largely extended by the results of this work, therefore provide an novel approach to probe related new physics.

Limits on primordial magnetic fields from primordial black hole abundance

Primordial magnetic field (PMF) is one of the feasible candidates to explain observed large-scale magnetic fields, for example, intergalactic magnetic fields. We present a new mechanism that brings us information about PMFs on small scales based on the abundance of primordial black holes (PBHs). The anisotropic stress of the PMFs can act as a source of the super-horizon curvature perturbation in the early universe. If the amplitude of PMFs is sufficiently large, the resultant density perturbation also has a large amplitude, and thereby, the PBH abundance is enhanced. Since the anisotropic stress of the PMFs is consist of the square of the magnetic fields, the statistics of the density perturbation follows the non-Gaussian distribution. {Assuming Gaussian distributions and delta-function type power spectrum for PMFs, based on a Monte-Carlo method, we obtain an approximate probability density function of the density perturbation, and it is an important piece to relate the amplitude of PMFs with the abundance of PBHs.} Finally, we place the strongest constraint on the amplitude of PMFs as a few hundred nano-Gauss on 102 Mpc-1 ⩽ k ⩽ 1018 Mpc-1 where the typical cosmological observations never reach.

Secondary isocurvature perturbations from acoustic reheating

The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.

On the initial regime of pre-big bang cosmology

The production of a background of super-horizon curvature perturbations with the appropriate (red) spectrum needed to trigger the cosmic anisotropies observed on large scales is associated, in the context of pre-big bang inflation, with a phase of growing string coupling. The extension towards the past of such a phase is not limited in time by the dynamical backreaction of the quantum perturbations of the cosmological geometry and of its sources. A viable, slightly red spectrum of scalar perturbations can thus be the output of an asymptotic, perturbative regime which is well compatible with an initial string-vacuum state satisfying the postulate of "Asymptotic Past Triviality".

Constraints on variations in inflaton decay rate from modulated preheating

Modulated (p)reheating is thought to be an alternative mechanism for producing super-horizon curvature perturbations in CMB. But large non-gaussianity and iso-curvature perturbations produced by this mechanism rule out its acceptability as the sole process responsible for generating CMB perturbations. We explore the situation where CMB perturbations are mostly generated by usual quantum fluctuations of inflaton during inflation, but a modulated coupling constant between inflaton and a secondary scalar affects the preheating process and produces some extra curvature perturbations. If the modulating scalar field is considered to be a dark matter candidate, coupling constant between the fields has to be unnaturally fine tuned in order to keep the local-form non-gaussianity and the amplitude of iso-curvature perturbations within observational limit; otherwise parameters of the models have to be tightly constrained. Those constraints imply that the curvature perturbations generated by modulated preheating should be less than 15% of the total observed CMB perturbations. On the other hand if the modulating scalar field is not a dark matter candidate, parameters of the models could not be constrained, but the constraints on the maximum amount of the curvature perturbations coming from modulated preheating remain valid.

Adiabatic regularization of functional determinants in cosmology and radiative corrections during inflation

We express the in-in functional determinant giving the one-loop effective potential for a scalar field propagating in a cosmological spacetime in terms of the mode functions specifying the vacuum of the theory and then apply adiabatic regularization to make this bare potential finite. In this setup, the adiabatic regularization offers a particular renormalization prescription that isolates the effects of the cosmic expansion. We apply our findings to determine the radiative corrections to the classical inflaton potentials in scalar field inflationary models and also we derive an effective potential for the superhorizon curvature perturbation \zeta\ encoding its scatterings with the subhorizon modes. Although the resulting modifications to the cosmological observables like nongaussianity turn out to be small, they distinctively appear after horizon crossing.

Deriving super-horizon curvature perturbations from the dynamics of preheating

We present a framework for calculating super-horizon curvature perturbation from the dynamics of preheating, which gives a reasonable match to the lattice results. Hubble patches with different initial background field values evolve differently. From the bifurcation of their evolution trajectories we find curvature perturbation using Lyapunov theorem and δ N formulation. In this way we have established a connection between the finer dynamics of preheating and the curvature perturbation produced in this era. From the calculated analytical form of the curvature perturbation we have derived the effective super-horizon curvature perturbation smoothed out on large scales of CMB. The order of the amount of local form non-gaussianity generated in this process has been calculated and problems regarding the precise determination of it have been pointed out.

Cosmological perturbations through a non-singular ghost-condensate/Galileon bounce

We study the propagation of super-horizon cosmological perturbations in a non-singular bounce spacetime. The model we consider combines a ghost condensate with a Galileon term in order to induce a ghost-free bounce. Our calculation is performed in harmonic gauge, which ensures that the linearized equations of motion remain well-defined and non-singular throughout. We find that, despite the fact that near the bounce the speed of sound becomes imaginary, super-horizon curvature perturbations remain essentially constant across the bounce. In fact, we show that there is a time close to the bounce where curvature perturbations of all wavelengths are required to be momentarily exactly constant. We relate our calculations to those performed in other gauges, and comment on the relation to previous results in the literature.

Asymmetric sky from the long mode modulations

The observed dipole asymmetry in Cosmic Microwave Background radiation may have originated from the modulations of super-horizon long wavelength modes. In this work we unveil different aspects of asymmetries generated from the long wavelength mode modulations. We show that the same mechanism which leads to the observed CMB power spectrum dipole asymmetry from the long mode modulations also yields dipole asymmetry in (a): tensor perturbations power spectrum and (b): the halo bias parameter. These are different phenomena relevant to different cosmological histories but both share the same underlying mechanism in generating asymmetries in the sky. We obtain the set of consistency conditions relating the amplitude of dipole asymmetries generated on tensor perturbations and halo bias parameter to the amplitude of dipole asymmetry generated on CMB power spectrum. In addition, we show that this mechanism does not produce dipole asymmetry in acceleration expansion in $\Lambda CDM$ universe because the super-horizon curvature perturbation is conserved in this background.

Self-consistent initial conditions for primordial black hole formation

For an arbitrarily strong, spherically symmetric super-horizon curvature perturbation, we present analytic solutions of the Einstein equations in terms of the asymptotic expansion over the ratio of the Hubble radius to the length-scale of the curvature perturbation to set initial conditions for numerical computations of primordial black hole formation. To obtain this solution we develop a recursive method of quasi-linearization which reduces the problem to a system of coupled ordinary differential equations for the Nth order terms in the asymptotic expansion with sources consisting of a non-linear combination of the lower order terms.

Fully nonlinear equivalence ofδNand covariant formalisms

We explicitly show the fully nonlinear equivalence of the $\ensuremath{\delta}\mathrm{N}$ and the covariant formalisms for the superhorizon curvature perturbations, which enables us to safely evaluate the non-Gaussian quantities of the curvature perturbation in either formalism. We also discuss isocurvature perturbations in the covariant formalism and clarify the relation between the fully nonlinear evolution of the curvature covector and that of the curvature perturbation for multiple interacting fluids.

Temporal enhancement of super-horizon curvature perturbations from decays of two curvatons and its cosmological consequences

If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10^{-5}. The traces of the enhancement may be left as higher order correlation functions, that is, as non-Gaussianity, the stochastic gravitational waves that are sourced by scalar-scalar mode couplings, as well as the primordial black holes that are formed by the gravitational collapse of the enhanced curvature perturbations. We first confirm that such a temporal enhancement indeed occurs by solving the linearized perturbation equations both numerically and analytically. We then derive an analytic expression of the full-order curvature perturbation which does not rely on the frequently used sudden decay approximation and is exact on super-horizon scales. By using this analytic formula, we provide expressions of the non-linearity parameters f_nl, tau_nl and g_nl. If both two curvatons contribute to the final curvature perturbations, the strong non-Gaussianity appears in the trispectrum rather than in the bispectrum. We also find a unique consistency relation between tau_nl and g_nl without f_nl. By using the second-order perturbation theory, we numerically show that the spectrum of the induced gravitational waves has a plateau corresponding to duration of the enhancement and such gravitational waves can be probed by ultimate-DECIGO and space-based atomic interferometers. We finally calculate the abundance of the primordial black holes and put a constraint on the amplitude of the enhanced curvature perturbations.

Full nonlinear growing and decaying modes of superhorizon curvature perturbations

We clarify the behavior of curvature perturbations in a nonlinear theory in case the inflaton temporarily stops during inflation. We focus on the evolution of curvature perturbation on superhorizon scales by adopting the spatial gradient expansion and show the nonlinear theory, called the beyond $\ensuremath{\delta}N$ formalism, for a general single scalar field as the next-leading order in the expansion. Both the leading order in the expansion ($\ensuremath{\delta}N$ formalism) and our nonlinear theory include the solutions of full-nonlinear orders in the standard perturbative expansion. Additionally, in our formalism, we can deal with the time evolution in contrast to $\ensuremath{\delta}N$ formalism, where curvature perturbations remain just constant, and show decaying modes do not couple with growing modes as similar to the case with the linear theory. We can conclude that, although the decaying mode diverges when $\stackrel{\ifmmode \dot{}\else \textperiodcentered \fi{}}{\ensuremath{\phi}}$ vanishes, there appears no trouble for both the linear and nonlinear theory since these modes will vanish at late times.

Non-Gaussianity of superhorizon curvature perturbations beyond δ N formalism

We develop a theory of nonlinear cosmological perturbations onsuperhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by O(ϵm), where ϵ = 1/(HL) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations. We obtain the general solution for a full nonlinear versionof the curvature perturbation valid up through second-order in ϵ (m = 2). We find the solution satisfies a nonlinear second-order differentialequation as an extension of the equation for the linear curvatureperturbation on the comoving hypersurface.Then we formulate a general method to match a perturbative solution accurate to n-th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order (m = 2) inthe gradient expansion on scales slightly greater than the Hubble radius.The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called δNformalism or separate universe approach which is equivalentto leading order (m = 0) in the gradient expansion.In particular, it can deal with the case when there isa temporary violation of slow-roll conditions.As an application of our formalism, we consider Starobinsky's model, which is a single field model having a temporary non-slow-roll stage due to a sharp change inthe potential slope. We find that a large non-Gaussianity can be generated even on superhorizonscales due to this temporary suspension of slow-roll inflation.

Scale-invariant cosmological perturbations from Hořava-Lifshitz gravity without inflation

Based on the renormalizable theory of gravitation recently proposed by Hořava, we present a simple scenario to generate almost scale-invariant, super-horizon curvature perturbations. The anisotropic scaling with dynamical critical exponent z = 3 implies that the amplitude of quantum fluctuations of a free scalar field generated in the early epoch of the expanding universe is insensitive to the Hubble expansion rate and, thus, scale-invariant. Those fluctuations are later converted to curvature perturbations by the curvaton mechanism or/and the modulated decay of heavy particles/oscillating fields. This scenario works, for example, for power law expansion a∝t p with p>1/3 and, thus, does not require inflation. Also, this scenario does not rely on any additional assumptions such as the detailed balance condition.