Inflaton Fluctuations Research Articles

Stochastic emergence of inflaton fluctuations in a SdS primordial universe with large-scale repulsive gravity from a 5D vacuum

We develop a stochastic approach to study scalar field fluctuations of the inflaton field in an early inflationary universe with a black-hole (BH), which is described by an effective 4D SdS metric. Considering a 5D Ricci-flat SdS static metric, we implement a planar coordinate transformation, in order to obtain a 5D cosmological metric, from which the effective 4D SdS metric can be induced on a 4D hypersurface. We found that at the end of inflation, the squared fluctuations of the inflaton field are not exactly scale independent and becomes sensitive with the mass of the BH.

Preheating after small-field inflation

Whereas preheating after chaotic and hybrid inflation models has been abundantly studied in the literature, preheating in small field inflation models, where the curvature of the inflaton potential is negative during inflation, remains less explored. In these models, a tachyonic instability at the end of inflation leads to a succession of exponentially large increases and \emph{decreases} of the inflaton fluctuations as the inflaton condensate oscillates around the minimum of its potential. The net effect is a competition between low-momentum modes which grow and decrease significantly, and modes with higher momenta which grow less but also decrease less. We develop an analytical description of this process, which is analogous to the quantum mechanical problem of tunneling through a volcano-shaped potential. Depending on the parameters, preheating may be so efficient that it completes in less than one oscillation of the inflaton condensate. Preheating after small field inflation may also be followed by a long matter-dominated stage before the universe thermalizes, depending on the energy scale of inflation and the details of the inflaton interactions. Finally, another feature of these models is that the spectrum of the inflaton fluctuations at the end of preheating may be peaked around the Hubble scale. In fact, because preheating starts when the second slow-roll parameter $|\eta|$ becomes of order unity while the first slow-roll parameter $\epsilon$ is still much smaller than one, the universe is still inflating during preheating and the modes amplified by the initial tachyonic instability leave the Hubble radius. This may lead to an abundant production of primordial black holes and gravitational waves with frequencies today which are naturally small enough to fall into the range accessible by high-sensitivity interferometric experiments.

Large Non-Gaussianity in Axion Inflation

The inflationary paradigm has enjoyed phenomenological success; however, a compelling particle physics realization is still lacking. Axions are among the best-motivated inflaton candidates, since the flatness of their potential is naturally protected by a shift symmetry. We reconsider the cosmological perturbations in axion inflation, consistently accounting for the coupling to gauge fields cΦFF, which is generically present in these models. This coupling leads to production of gauge quanta, which provide a new source of inflaton fluctuations, δΦ. For c≥10(2)M(p)(-1), these dominate over the vacuum fluctuations, and non-Gaussianity exceeds the current observational bound. This regime is typical for concrete realizations that admit a UV completion; hence, large non-Gaussianity is easily obtained in minimal and natural realizations of inflation.

Phenomenology of a pseudo-scalar inflaton: naturally large nongaussianity

Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars ϕ are naturally coupled to gauge fields through cϕFF̃. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the ``vacuum'' perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological signatures are highly distinctive: large nongaussianity of (nearly) equilateral shape, in addition to detectably large values of both the scalar spectral tilt and tensor-to-scalar ratio (both being typical of large field inflation). The WMAP bound on nongaussianity implies that the coupling c of the pseudo-scalar inflaton to any gauge field must be smaller than about 102 Mp−1.

Remarks on non-Gaussian fluctuations of the inflaton and constancy ofζoutside the horizon

We point out that the non-gaussianity arising from cubic self interactions of the inflaton field is proportional to \xi N_e where \xi ~ V"' and N_e is the number of e-foldings from horizon exit till the end of inflation. For scales of interest N_e = 60, and for models of inflation such as new inflation, natural inflation and running mass inflation \xi is large compared to the slow roll parameter \epsilon ~ V'^{2}. Therefore the contribution from self interactions should not be outrightly ignored while retaining other terms in the non-gaussianity parameter f_{NL}. But the N_e dependent term seems to imply the growth of non-gaussianities outside the horizon. Therefore we briefly discuss the issue of the constancy of correlations of the curvature perturbation \zeta outside the horizon. We then calculate the 3-point function of the inflaton fluctuations using the canonical formalism and further obtain the 3-point function of \zeta_k. We find that the N_e dependent contribution to f_{NL} from self interactions of the inflaton field is cancelled by contributions from other terms associated with non-linearities in cosmological perturbation theory.

A naturally large four-point function in single field inflation

Non-Gaussianities of the primordial density perturbations have emerged as a very powerful possible signal to test the dynamics that drove the period of inflation. While in general the most sensitive observable is the three-point function in this paper we show that there are technically natural inflationary models where the leading source of non-Gaussianity is the four-point function. Using the recently developed Effective Field Theory of Inflation, we are able to show that it is possible to impose an approximate parity symmetry and an approximate continuos shift symmetry on the inflaton fluctuations that allow, when the dispersion relation if of the form ω ∼ csk, for a unique quartic operator, while approximately forbidding all the cubic ones. The resulting shape for the four-point function is unique. In the models where the dispersion relation is of the form ω ∼ k2/M a similar construction can be carried out and additional shapes are possible.

Stochastic growth of quantum fluctuations during slow-roll inflation

We compute the growth of the mean square of quantum fluctuations of test fields with small effective mass during a slowly changing, nearly de Sitter stage which took place in different inflationary models. We consider a minimally coupled scalar with a small mass, a modulus with an effective mass $ \propto H^2$ (with $H$ as the Hubble parameter) and a massless non-minimally coupled scalar in the test field approximation and compare the growth of their relative mean square with the one of gauge-invariant inflaton fluctuations. We find that in most of the single field inflationary models the mean square gauge invariant inflaton fluctuation grows {\em faster} than any test field with a non-negative effective mass. Hybrid inflationary models can be an exception: the mean square of a test field can dominate over the gauge invariant inflaton fluctuation one on suitably choosing parameters. We also compute the stochastic growth of quantum fluctuation of a second field, relaxing the assumption of its zero homogeneous value, in a generic inflationary model; as a main result, we obtain that the equation of motion of a gauge invariant variable associated, order by order, with a generic quantum scalar fluctuation during inflation can be obtained only if we use the number of e-folds as the time variable in the corresponding Langevin and Fokker-Planck equations for the stochastic approach. We employ this approach to derive some bounds in the case of a model with two massive fields.

Semiclassical gravitoelectromagnetic inflation in a Lorentz gauge: Seminal inflaton fluctuations and electromagnetic fields from a 5D vacuum state

Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. The difference with other previous works is that in this one we use a Lorentz gauge. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of magnetic field modes during the early inflationary epoch of the universe on cosmological scales.

PILOT-WAVE SCALAR FIELD THEORY IN DE SITTER SPACE: LATTICE SCHRÖDINGER PICTURE

In the lattice Schrödinger picture, we find the de Broglie–Bohm quantum trajectories for the eigenstates of a generically coupled free real scalar field in de Sitter space. For the massless minimally coupled scalar field which has exact quantum trajectory, we evaluate both the time evolution of vacuum state and the possible effects of initial quantum nonequilibrium on the power spectrum of the primordial inflaton and curvature fluctuations in the slow-roll approximation. We reproduce the results that were already presented by Valentini who considered only the massless minimal coupling case. In addition we cover both massive minimal and massive non-minimal coupling cases which are the extension of Valentini's work. Finally we discuss the difference between de Broglie's first-order dynamics and Bohm's second-order dynamics in finding the quantum trajectories.

Non‐Gaussianity from Particle Production during Inflation

In a variety of models the motion of the inflaton may trigger the production of some non‐inflaton particles during inflation, for example via parametric resonance or a phase transition. Such models have attracted interest recently for a variety of reasons, including the possibility of slowing the motion of the inflaton on a steep potential. In this review we show that interactions between the produced particles and the inflaton condensate can lead to a qualitatively new mechanism for generating cosmological fluctuations from inflation. We illustrate this effect using a simple prototype model for the interaction between the inflaton, ϕ, and iso‐inflaton, χ. Such interactions are quite natural in a variety of inflation models from supersymmetry and string theory. Using both lattice field theory and analytical calculations, we study the production of χ particles and their subsequent rescatterings off the condensate ϕ(t), which generates bremsstrahlung radiation of light inflaton fluctuations δϕ. This mechanism leads to observable features in the primordial power spectrum. We derive observational constraints on such features and discuss their implications for popular models of inflation. Inflationary particle production also leads to a very novel kind of nongaussian signature which may be observable in future missions.

Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data

Using the recently developed effective field theory of inflation, we argue that the size and the shape of the non-Gaussianities generated by single-field inflation are generically well described by two parameters: fNLequil, which characterizes the size of the signal that is peaked on equilateral configurations, and fNLorthog, which instead characterizes the size of the signal which is peaked both on equilateral configurations and flat-triangle configurations (with opposite signs). The shape of non-Gaussianities associated with fNLorthog is orthogonal to the one associated to fNLequil, and former analysis have been mostly blind to it. We perform the optimal analysis of the WMAP 5-year data for both of these parameters. We find no evidence of non-Gaussianity, and we have the following constraints: −125 ⩽ fNLequil ⩽ 435, −369 ⩽ fNLorthog ⩽ 71 at 95% CL. We show that both of these constraints can be translated into limits on parameters of the Lagrangian of single-field inflation. For one of them, the speed of sound of the inflaton fluctuations, we find that it is either bounded to be cs ⩾ 0.011 at 95% CL. or alternatively to be so small that the higher-derivative kinetic term dominate at horizon crossing. We are able to put similar constraints on the other operators of the inflaton Lagrangian.

Non-Gaussianity as a signature of thermal initial condition of inflation

We study non-Gaussianities in the primordial perturbations in single field inflation where there is radiation era prior to inflation. Inflation takes place when the energy density of radiation drops below the value of the potential of a coherent scalar field. We compute the thermal average of the two, three and four point correlation functions of inflaton fluctuations. The three point function is proportional to the slow roll parameters and there is an amplification in $f_{NL}$ by a factor of 65 to 90 due to the contribution of the thermal bath, and we conclude that the bispectrum is in the range of detectability with the 21-cm anisotropy measurements. The four point function on the other hand appears in this case due to the thermal averaging and the fact that thermal averaging of four-point correlation is not the same as the square of the thermal averaging of the two-point function. Due to this fact $\tau_{NL}$ is not proportional to the slow-roll parameters and can be as large as -42. The non-Gaussianities in the four point correlation of the order 10 can also be detected by 21-cm background observations. We conclude that a signature of thermal inflatons is a large trispectrum non-Gaussianity compared to the bispectrum non-Gaussianity.

Study of the spectrum of inflaton perturbations

We examine the spectrum of inflaton fluctuations resulting from any given long period of exponential inflation. Infrared and ultraviolet divergences in the inflaton dispersion summed over all modes do not appear in our approach. We show how the scale invariance of the perturbation spectrum arises. We also examine the spectrum of scalar perturbations of the metric that is created by the inflaton fluctuations that have left the Hubble sphere during inflation and the spectrum of density perturbations that they produce at reentry after inflation has ended. When the inflaton dispersion spectrum is renormalized during the expansion, we show (for the case of the quadratic inflaton potential) that the density perturbation spectrum approaches a mass-independent limit as the inflaton mass approaches zero, and remains near that limiting value for masses less than about 1/4 of the inflationary Hubble constant. We show that this limiting behavior does not occur if one only makes the Minkowski space subtraction, without the further adiabatic subtractions that involve time derivatives of the expansion scale factor a(t). We also find a parametrized expression for the energy density produced by the change in a(t) as inflation ends. If the end of inflation were sufficiently abrupt, then the temperaturemore » corresponding to this energy density could be very significant. We also show that fluctuations of the inflaton field that are present before inflation starts are not dissipated during inflation and could have a significant observational effect today. The mechanism for this is caused by the initial fluctuations through stimulated emission from the vacuum.« less

Primordial non-Gaussianity in models with dark matter isocurvature fluctuations

We investigate primordial non-Gaussianity and dark matter isocurvature fluctuations in the modulated reheating and the curvaton scenarios. In these scenarios, a large non-Gaussianity can be generated; on the other hand, depending on how dark matter is produced, too large isocurvature fluctuations can also arise, which is inconsistent with current observations. In this paper, we study this issue in a mixed scenario where the curvature fluctuations can also be produced from the inflaton fluctuations as well as those from a light scalar field such as the modulus and the curvaton. We show that primordial fluctuations can be highly non-Gaussian without conflicting with the current constraint on isocurvature fluctuations for such mixed scenarios. However, if the constraint on isocurvature fluctuations becomes severer as expected by the Planck satellite, ${f}_{\mathrm{NL}}$, a nonlinearity parameter for adiabatic fluctuations, should be very small as ${f}_{\mathrm{NL}}\ensuremath{\lesssim}3$, which would give interesting implications for the generation mechanism of dark matter. Non-Gaussianity from isocurvature fluctuations is also discussed in these scenarios.

Cosmological constraints on rapid roll inflation

We obtain cosmological constraints on models of inflation which exhibit rapid rollsolutions. Rapid roll attractors exist for potentials with large mass terms andare thus of interest for inflationary model building within string theory. Weconstrain a general ansatz for the power spectrum arising from rapid rollinflation that, in the small field limit, can be associated with tree level hybrid potentials with variable mass termsand nonminimal gravitational coupling ξRϕ2. We consider perturbations generated throughmodulated reheating and/or curvaton mechanisms in place of the observationallyunacceptable primary spectra generated by inflaton fluctuations in these models.The lack of a hierarchy amongst higher-order k-dependencies of the power spectrumresults in models with potentially large runnings, allowing us to impose tight constraints on such models usingCMB and LSS data. In particular, we find ns < 1 and |α| < 0.01. We conclude with a concrete realization of rapid roll inflationwithin warped throat brane inflation that is in good agreement with current data.

Primordial perturbations and non-Gaussianities from modulated trapping

We propose a new mechanism to generate primordial curvature perturbations, based on the resonant production of particles during inflation. It is known that this phenomenon can trap the inflaton for a fraction of e-fold. This effect is governed by the mass of the produced particles and by their coupling to the inflaton, parameters which can depend on the expectation value of other fields. If one of such additional fields—a modulaton—is light, then its fluctuations, acquired during the earlier stages of inflation, will induce a spatial modulation of the trapping, and thus of the end of inflation, corresponding to a curvature perturbation. We calculate the power spectrum, bispectrum and trispectrum of the curvature perturbations generated by this mechanism, taking into account the perturbations due to the inflaton fluctuations as well. We find that modulated trapping could provide the main contribution to the observed power spectrum and lead to detectable primordial non-gaussianities.

A confirmation of agreement of different approaches for scalar gauge-invariant metric perturbations during inflation

We revisit an extension of the well-known formalism for gauge-invariant scalar metric fluctuations to study the spectra for both the inflaton and gauge-invariant (scalar) metric fluctuations in the framework of a single-field inflationary model, in which the quasi-exponential expansion is driven by an inflaton which is minimally coupled to gravity. The proposal here examined is valid also for fluctuations with large amplitudes, but for cosmological scales, where vector and tensor perturbations can be neglected and the fluid is irrotacional.

Generation of fluctuations during inflation: Comparison of stochastic and field-theoretic approaches

We prove that the stochastic and standard field-theoretical approaches produce exactly the same results for the amount of light massive scalar field fluctuations generated during inflation in the leading order of the slow-roll approximation. This is true both in the case for which this field is a test one and inflation is driven by another field, and the case for which the field plays the role of inflaton itself. In the latter case, in order to calculate the mean square of the gauge-invariant inflaton fluctuations, the logarithm of the scale factor $a$ has to be used as the time variable in the Fokker-Planck equation in the stochastic approach. The implications of particle production during inflation for the second stage of inflation and for the moduli problem are also discussed. The case of a massless self-interacting test scalar field in de Sitter background with a zero initial renormalized mean square is also considered in order to show how the stochastic approach can easily produce results corresponding to diagrams with an arbitrary number of scalar field loops in the field-theoretical approach (explicit results up to four loops included are presented).

Reexamination of the Power Spectrum in De Sitter Inflation

We find that the amplitude of quantum fluctuations of the invariant de Sitter vacuum coincides exactly with that of the vacuum of a comoving observer for a massless scalar (inflaton) field. We propose redefining the actual physical power spectrum as the difference between the amplitudes of the above vacua. An inertial particle detector continues to observe the Gibbons-Hawking temperature. However, although the resulting power spectrum is still scale-free, its amplitude can be drastically reduced since now, instead of the Hubble's scale at the inflationary period, it is determined by the square of the mass of the inflaton fluctuation field.

Primordial curvature fluctuation and its non-Gaussianity in models with modulated reheating

We investigate non-Gaussianity in the modulated reheating scenario where fluctuations of the decay rate of the inflaton generate adiabatic perturbations, paying particular attention to the nonlinearity (NL) parameters ${f}_{\mathrm{NL}}$, ${\ensuremath{\tau}}_{\mathrm{NL}}$, and ${g}_{\mathrm{NL}}$ as well as the scalar spectral index and tensor-to-scalar ratio which characterize the nature of the primordial power spectrum. We also take into account the preexisting adiabatic perturbations produced from the inflaton fluctuations. It has been known that the nonlinearity between the curvature perturbations and the fluctuations of the decay rate can yield non-Gaussianity at the level of ${f}_{\mathrm{NL}}\ensuremath{\sim}\mathcal{O}(1)$, but we find that the nonlinearity between the decay rate and the modulus field which determines the decay rate can generate much greater non-Gaussianity. We also discuss a consistency relation among nonlinearity parameters which holds in the scenario and find that the modulated reheating yields a different one from that of the curvaton model. In particular, they both can yield a large positive ${f}_{\mathrm{NL}}$ but with a different sign of ${g}_{\mathrm{NL}}$. This provides a possibility to discriminate these two competitive models by looking at the sign of ${g}_{\mathrm{NL}}$. Furthermore, we work on some concrete inflation models and investigate in what cases models predict the spectral index and the tensor-to-scalar ratio allowed by the current data while generating large non-Gaussianity, which may have many implications for model buildings of the inflationary universe.