Amplitude Of Curvature Perturbations Research Articles

Defying eternal inflation in warm inflation with a negative running

It was pointed out previously [1] that a sufficiently negative running of the spectral index of curvature perturbations from (ordinary i.e. cold) inflation is able to prevent eternal inflation from ever occurring. Here, we reevaluate those original results, but in the context of warm inflation, in which a substantial radiation component (produced by the inflaton) exists throughout the inflationary period. We demonstrate that the same general requirements found in the context of ordinary (cold) inflation also hold true in warm inflation; indeed an even tinier amount of negative running is sufficient to prevent eternal inflation. This is particularly pertinent, as models featuring negative running are more generic in warm inflation scenarios. Finally, the condition for the existence of eternal inflation in cold inflation — that the curvature perturbation amplitude exceed unity on superhorizon scales — becomes more restrictive in the case of warm inflation. The curvature perturbations must be even larger, i.e. even farther out on the potential, away from the part of the potential where observables, e.g. in the Cosmic Microwave Background, are produced.

From inflation to reheating and their dynamical stability analysis in Gauss–Bonnet gravity

We investigate the inflation and reheating phenomenology in scalar-Einstein-Gauss–Bonnet theory of gravity where a scalar field non-minimally couples with the Gauss-Bonnet (GB) curvature term. Regarding the inflationary phenomenology, we find – (1) the inflation starts with a quasi de-Sitter phase and has an exit at a finite e-fold, which is indeed consistent with the resolution of horizon and flatness problems, (2) the scalar and tensor perturbations prove to be ghost free and do not suffer from gradient instability, (3) the curvature perturbation amplitude as well as its tilt and the tensor-to-scalar ratio turn out to be simultaneously compatible with the recent Planck data for suitable values of the parameters which also results to the inflationary energy scale ∼1012GeV. After the inflation ends, the scalar field starts to decay to radiation with a constant decay width. For our considered scalar potential and the GB coupling function, the model results to an analytic power law solution of the Hubble parameter and a logarithmic solution of the scalar field during the reheating era, where the exponent of the Hubble parameter determines the effective EoS parameter (weff) during the same. The stability of such reheating dynamics is examined by dynamical analysis which ensures that weff can go beyond unity and reach up-to the maximum value of max(weff)=1.56. The scenario with weff>1 proves to be purely due to the presence of the GB coupling function, which in turn may have important consequences on enhancing the primordial gravitational waves’ amplitude observed today. The inflationary e-fold number (Nf) gets further constrained by the input of the reheating stage, and we critically examine the constraint of Nf coming from both the inflation and reheating phenomenology. We finally construct the complete forms of scalar potential (V(ϕ)) and the GB coupling function (ξ(ϕ)) that smoothly transits from inflation to reheating, and numerically solve the Hubble parameter and the scalar field for such complete forms of V(ϕ) and ξ(ϕ). Such numerical solutions match with analytic ones in the respective regime. After the reheating ends, the GB term gets decouple from the theory and the radiation energy density dominates the energy budget of the universe, which in turn produces the standard radiation era of the universe.

Threshold of primordial black hole formation in nonspherical collapse

We perform (3+1)-dimensional simulations of primordial black hole (PBH) formation starting from the spheroidal super-horizon perturbations. We investigate how the ellipticity (prolateness or oblateness) affects the threshold of PBH formation in terms of the peak amplitude of curvature perturbation. We find that, in the case of the radiation-dominated universe, the effect of ellipticity on the threshold is negligibly small for the large amplitude of perturbations expected for PBH formation.

Higgs-squark-slepton inflation from the MSSM

The inflation within the MSSM is proposed, where the inflaton field is a combination of the Higgs, squark and slepton states. While the inflationary phase is fully governed by the electron Yukawa superpotential coupling, the fields' condensates float along the flat $D$-term trajectory. This predicts the MSSM parameter $\tan \beta \simeq 13.1$ determined via the value of the curvature perturbation amplitude. The values of the scalar spectral index and the tensor-to-scalar ratio are predicted to be $n_s\simeq 0.966$ and $r=0.00118$. The postinflation reheating of the Universe proceeds by the radiative decay of the inflaton to the two gluons ($\phi \to gg$) with the reheating temperature $T_r\simeq 1.4\cdot 10^7$ GeV.

Feebly interacting dark matter particle as the inflaton

We present a scenario where a $Z_2$-symmetric scalar field $\phi$ first drives cosmic inflation, then reheats the Universe but remains out-of-equilibrium itself, and finally comprises the observed dark matter abundance, produced by particle decays \`{a} la freeze-in mechanism. We work model-independently without specifying the interactions of the scalar field besides its self-interaction coupling, $\lambda\phi^4$, non-minimal coupling to gravity, $\xi\phi^2R$, and coupling to another scalar field, $g\phi^2\sigma^2$. We find the scalar field $\phi$ serves both as the inflaton and a dark matter candidate if $10^{-9}\lesssim \lambda\lesssim g\lesssim 10^{-7}$ and $3 \rm{keV} \lesssim m_{\rm \phi}\lesssim 85 \rm{MeV}$ for $\xi=\mathcal{O}(1)$. Such a small value of the non-minimal coupling is also found to be of the right magnitude to produce the observed curvature perturbation amplitude within the scenario. We also discuss how the model may be distinguished from other inflationary models of the same type by the next generation CMB satellites.

On post-inflation validity of perturbation theory in Horndeski scalar-tensor models

By using the newtonian gauge, we re-confirm that, as in the minimal case, the re-scaled Mukhanov-Sasaki variable is conserved leading to a constraint equation for the Newtonian potential. However, conversely to the minimal case, in Horndeski theories, the super-horizon Newtonian potential can potentially grow to very large values after inflation exit. If that happens, inflationary predictability is lost during the oscillating period. When this does not happen, the perturbations generated during inflation can be standardly related to the CMB, if the theory chosen is minimal at low energies. As a concrete example, we analytically and numerically discuss the new Higgs inflationary case. There, the Inflaton is the Higgs boson that is non-minimally kinetically coupled to gravity. During the high-energy part of the post-inflationary oscillations, the system is anisotropic and the Newtonian potential is largely amplified. Thanks to the smallness of today's amplitude of curvature perturbations, however, the system stays in the linear regime, so that inflationary predictions are not lost. At low energies, when the system relaxes to the minimal case, the anisotropies disappear and the Newtonian potential converges to a constant value. We show that the constant value to which the Newtonian potential converges is related to the frozen part of curvature perturbations during inflation, precisely like in the minimal case.

Evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: Indications for a no-go theorem in single field matter bounce cosmologies

Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of curvature perturbations due to the nontrivial background evolution, this growth is very limited because of the conservation of curvature perturbations on super-Hubble scales. We further perform a general analysis of the evolution of primordial non-Gaussianities through the bounce phase. By studying the general form of the bispectrum we show that the non-Gaussianity parameter ${f}_{\mathrm{NL}}$ (which is of order unity before the bounce phase) is enhanced during the bounce phase if the curvature fluctuations grow. Hence, in such nonsingular bounce models with matter given by a single scalar field, there appears to be a tension between obtaining a small enough tensor-to-scalar ratio and not obtaining a value of ${f}_{\mathrm{NL}}$ in excess of the current upper bounds. This conclusion may be considered as a ``no-go'' theorem that rules out any single field matter bounce cosmology starting with vacuum initial conditions for the fluctuations.

Negative running can prevent eternal inflation

Current data from the Planck satellite and the BICEP2 telescope favor, at around the 2 σ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running α < 0, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on nS from Planck, this corresponds to an upper bound of the running α < −9 × 10−5, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In single-field inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as 104 e-folds.

Effects of variable Newton constant during inflation

In this paper the effects of a time-dependent Newton constant $G$ during inflation are studied. We present the formalism of curvature perturbations in an inflationary system with a time-dependent Newton constant. As an example we consider a toy model in which $G$ undergoes a sudden change during inflation. By imposing the appropriate matching conditions the imprints of this sharp change in $G$ on the curvature perturbation power spectrum are studied. We show that if $G$ increases (decreases) during the transition the amplitude of curvature perturbations on large scales decreases (increases). In our model with a sudden change in $G$ continuous sinusoidal modulations on the curvature power spectrum is induced. However, in a realistic scenario in which the change in $G$ has some finite time scale we expect these sinusoidal modulations to be damped on short scales. The generated features may be used to explain the observed glitches on the CMB power spectrum. This puts a bound on $\ensuremath{\Delta}G$ during inflation of roughly the same order as current bounds on $\ensuremath{\Delta}G$ during the entire observed age of the universe.

Strong coupling problem with time-varying sound speed

For a single scalar field with unit sound speed minimally coupled to Einstein gravity, there are exactly three distinct cosmological solutions which produce a scale invariant spectrum of curvature perturbations in a dynamical attractor background, assuming vacuum initial conditions: slow-roll inflation; a slowly contracting adiabatic ekpyrotic phase, described by a rapidly-varying equation of state; and an adiabatic ekpyrotic phase on a slowly expanding background. Of these three, only inflation remains weakly coupled over a wide range of modes, while the other scenarios can produce at most 12 e-folds of scale invariant and Gaussian modes. In this paper, we investigate how allowing the speed of sound of fluctuations to evolve in time affects this classification. While in the presence of a variable sound speed there are many more scenarios which are scale invariant at the level of the two-point function, they generically suffer from strong coupling problems similar to those in the canonical case. There is, however, an exceptional case with superluminal sound speed, which suppresses non-Gaussianities and somewhat alleviates strong coupling issues. We focus on a particular realization of this limit and show these scenarios are constrained and only able to produce at most 28 e-folds of scale invariant and Gaussian perturbations. A similar bound should hold more generally---the condition results from the combined requirements of matching the observed amplitude of curvature perturbations, demanding that the Hubble parameter remain sub-Planckian and keeping non-Gaussianities under control. We therefore conclude that inflation remains the unique cosmological scenario, assuming a single degree of freedom on an attractor background, capable of producing arbitrarily many scale invariant modes while remaining weakly coupled. Alternative mechanisms must inevitably be unstable or rely on multiple degrees of freedom.

Amplification of curvature perturbations in cyclic cosmology

We analytically and numerically show that through the cycles with nonsingular bounce the amplitude of curvature perturbation on large scale will be amplified and the power spectrum will be redden. In some sense, this amplification will eventually destroy the homogeneity of background, which will lead to the ultimate end of cycles of global universe. We argue that for the model with increasing cycles, it might be possible that a fissiparous multiverse will emerge after one or several cycles, in which the cycles will continue only at corresponding local regions.

DBI-curvaton

In this Letter, we study a curvaton model described by a Dirac–Born–Infeld-like action. We calculate the spectrum of curvature perturbation induced by DBI-curvaton and estimate its non-Gaussianity. We find that in the limit of low sound speed the amplitude of curvature perturbation is enhanced more than that in DBI inflation. This result also means that the inflationary scale with DBI-curvaton may be lower than that in usual curvaton model. In addition, we also find that under same conditions the local non-Gaussianity level in DBI-curvaton is generally about 10 times larger than that in usual curvaton model, which is interesting for current observations. This work in some sense explores a new application of brane-cosmology in inflation.

The Classical and Quantum Inflaton: the Precise Inflationary Potential and Quantum Inflaton Decay after WMAP

We clarify classical inflaton models by considering them as effective field theories à la Ginzburg-Landau. In this approach, the WMAP statement excluding the pure ϕ 4 potential implies the presence of an inflaton mass term at the scale m ∼ 10 13 GeV . Chaotic, new and hybrid inflation models are studied in an unified manner. In all cases the inflaton potential takes the form V ( ϕ ) = m 2 M P l 2 v ( ϕ M P l ) , where all coefficients in the polynomial v ( ϕ ) are of order ( m / M P l ) 0 . If such potential corresponds to supersymmetry breaking, the corresponding susy breaking scale is m M P l ∼ 10 16 GeV which turns out to coincide with the grand unification (GUT) scale. The inflaton mass is therefore given by a see-saw formula m ∼ M GUT 2 / M P l . For red tilted spectrum, the potential which fits the best the present data ( | 1 − n s | ≲ 0.1 , r ≲ 0.1 ) and which best prepares the way for the forthcoming data is a trinomial polynomial with negative quadratic term (new inflation). For blue tilted spectrum, hybrid inflation turns to be the best choice. In both cases, we find an analytic formula relating the inflaton mass with the ratio r of tensor to scalar perturbations and the spectral index n s of scalar perturbations: 10 6 m M P l = 127 r | 1 − n s | where the numerical coefficient is fixed by the WMAP amplitude of adiabatic perturbations. Implications for string theory are discussed. We then review quantum phenomena during inflation which contribute to relevant observables in the CMB anisotropies and polarization and we focus on inflaton decay . The deviation from the scale invariant power spectrum measured by a small parameter Δ turns to be crucial, Δ regulates the infrared too. In slow roll inflation, Δ is a simple function of the slow roll parameters. We find that quantum fluctuations can self-decay as a consequence of the inflationary expansion through processes which are forbidden in Minkowski space-time. We compute the self-decay of the inflaton quantum fluctuations during slow roll inflation: for wavelengths deep inside the Hubble radius the decay is enhanced by the emission of ultrasoft collinear quanta, i.e. bremsstrahlung radiation of superhorizon quanta which becomes the leading decay channel for physical wavelengths H ≪ k p h ( η ) ≪ H / ( η V − ε V ) . The decay of short wavelength fluctuations hastens as the physical wave vector approaches the horizon. Superhorizon fluctuations decay with a power law η Γ in conformal time where Γ is expressed in terms of the amplitude of curvature perturbations Δ R 2 , the scalar spectral index n s , the tensor to scalar ratio r and slow roll parameters. The behavior of the growing mode η η V − ε V + Γ / η features a new scaling dimension Γ. We discuss the implications of these results for scalar and tensor perturbations as well as for non-gaussianities in the power spectrum. The recent WMAP data suggests Γ ≳ 3.6 × 10 −9 .

Large-scale curvature perturbations with spatial and time variations of the inflaton decay rate

We present a gauge-invariant formalism to study the evolution of the curvature and entropy perturbations in the case in which spatialand time variations of the inflaton decay rate into ordinarymatter are present. During the reheating stage after inflation, curvature perturbations can vary with time on super-horizon scales sourced by a gauge-invariant inflaton decay rate perturbation. We showthat the latter is a function not only of the spatial variationsof the decay rate generated during inflation, as envisagedin a recently proposed scenario, but also ofthe time variation of the inflaton decay rate during reheating. If only the second source is present, the final curvatureperturbation at the end of the reheating stage is proportionalto the curvature perturbation at the beginning of reheating, with a coefficient of proportionality which can be either smalleror larger than unity depending upon the underlyingphysics governing the time variation of the inflaton decay rate.As a consequence, we show that the standard consistency relation between the amplitude of curvature perturbations, the amplitude of tensor perturbations and the tensor spectral index of one-single-field models of inflation is violatedand there is the possibility that the tensor-to-curvature amplitude ratio is larger than in the standard case.

Enhancement of superhorizon scale inflationary curvature perturbations

We show that there exists a simple mechanism which can enhance the amplitude of curvature perturbations on superhorizon scales, relative to their amplitude at horizon crossing, even in some single-field inflation models. We give a criterion for this enhancement in general single-field inflation models; the condition for a significant effect is that the quantity $a\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\varphi}}/H$ become sufficiently small, as compared to its value at horizon crossing, for some time interval during inflation.

Super-horizon perturbations and preheating

It has recently been claimed by Bassett et al. that preheating after inflation may affect the amplitude of curvature perturbations on large scales, undermining the usual inflationary prediction. We analyze the simplest model, and confirm the results of Jedamzik and Sigl and of Ivanov that in linear perturbation theory the effect is negligible. However, the dominant effect is second order in the field perturbation and we show that this too is negligible, and hence conclude that preheating has no significant influence on large-scale perturbations in this model. We briefly discuss the likelihood of an effect in other models.

Origin of density fluctuations in extended inflation.

We calculate both the curvature and isocurvature density fluctuations that arise due to quantum fluctuations in a simple model of extended inflation based upon the Jordan-Brans-Dicke theory. The curvature fluctuations that arise due to quantum fluctuations in the Brans-Dicke field in general have a non-scale-invariant spectrum and an amplitude that is cosmologically acceptable and interesting without having to tune any coupling constant to a very small value. The curvature perturbations that arise due to the Higgs field are subdominant. If there are other massless fields in the theory, e.g., an axion or an ilion, then isocurvature fluctuations arise in these fields too. Production of gravitational waves and the massless particles associated with excitations of the Brans-Dicke field are also discussed. Several attempts at more realistic models of extended inflation are also analyzed. The importance of the Einstein conformal frame in calculating curvature fluctuations is emphasized. When viewed in this frame, extended inflation closely resembles slow-rollover inflation with an exponential potential, and the usual formula for the amplitude of curvature perturbations applies directly.