Primordial perturbations and inflation in holographic cosmology
Nicolas R. Bertini, Neven Bilic, Davi C. Rodrigues
备注：
20 pages, 1 figure. The field equations are corrected by adding a new term which vanishes for a conformally flat background metric. The resulting change of perturbed field equations does not affect the results and conclusions. The corrections match the Erratum published in PRD
发表信息：
Phys. Rev. D 102, 123505 (2020); Phys. Rev. D 105, 129901 (2022) (Erratum)
We consider an inflationary scenario in the holographic braneworld with a cosmological fluid occupying the 3+1 dimensional brane located at the holographic boundary of an asymptotic ADS$_5$ bulk. The contribution of the boundary conformal field can be represented as a modification of Einstein's equations on the boundary. Using these effective Einstein equations we calculate the cosmological perturbations and derive the corresponding power spectra assuming a general $k$-essence type of inflaton. We find that the braneworld scenario affects the scalar power spectrum only in the speed of sound dependence on the slow-roll parameters whereas there is no change in the tensor power spectrum. This implies that the changes in the spectral indices appear at the second order in the slow-roll parameter expansion.
We study the inflation via logarithmic entropy-corrected holographic dark energy LECHDE model with future event horizon, particle horizon and Hubble horizon cut-offs, and compare the results with those of obtained in the study of inflation by holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in HDE model. Moreover, the consistency with the observational data in LECHDE model of inflation, constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and t…
The increasing interest in studying the role of holographic dark energy in the evolution of the very early universe motivates us to study it for the scenario of warm inflation. Due to this scenario, the holographic dark energy, which now drives inflation, has an interaction with the radiation. The case of interacting dark energy also has received increasing interest in studying the late time cosmology. The Infrared cutoff is taken as the Hubble length and all corrections are assumed to be exhibited by the parameter $c$, which appears in the holographic dark energy. By comparing the predictions…
In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose \emph{inflaton} is a non-canonical scalar field of the tachyon-type. The respective background field equations for an inverse-square potential produce a power-law inflation, and it is explicitly shown that for such a potential the power spectrum tends to be scale-independent for highly accelerated regimes in the inflationary expansion.
We investigate the origin and evolution of primordial electric and magnetic fields in the early universe, when the expansion is governed by a cosmological constant $Λ_0$. Using the gravitoelectromagnetic inflationary formalism with $A_0=0$, we obtain the power of spectrums for large-scale magnetic fields and the inflaton field fluctuations during inflation. A very important fact is that our formalism is {\em naturally non-conformally invariant}.
In the present paper, we use the holographic approach to describe the early-time acceleration and the late-time acceleration eras of our Universe in a unified manner. Such ``holographic unification'' is found to have a correspondence with various higher curvature cosmological models with or without matter fields. The corresponding holographic cut-offs are determined in terms of the particle horizon and its derivatives, or the future horizon and its derivatives. As a result, the holographic energy density we propose is able to merge various cosmological epochs of the Universe from a holographic…
I consider a semiclassical expansion of the scalar field in the warm inflation scenario. I study the evolution for the fluctuations of the metric around the Friedmann-Robertson-Walker one. The formalism predicts that, in the power-law expansion universe, the fluctuations of the metric decreases with time.
The scenario of constant-roll inflation is investigated assuming that it is caused by holographic dark energy with energy density $3M_p^2 c^2 / L^2$. The energy density with varying $c$ parameter and Hubble radius as infrared cutoff provides a proper description for the late time acceleration expansion. This motivates us to study the role of the same holographic dark energy in the scenario of constant-roll inflation. One of the main features of constant-roll inflation is that the second slow-roll parameter is constant which is not necessarily small. This feature brings a differential equation …
The gravitationally enhanced friction can reduce the speed of the inflaton to realize an ultra-slow-roll inflation, which will amplify the curvature perturbations. The amplified perturbations can generate a sizable amount of primordial black holes (PBHs) and induce simultaneously a significant background gravitational waves (SIGWs). In this paper, we investigate the primordial non-Gaussianity of the curvature perturbations in the inflation with gravitationally enhanced friction. We find that when the gravitationally enhanced friction plays a role in the inflationary dynamics, the non-Gaussiani…
The application of holographic principle in very early time is studied. The consideration of the principle in the late-time evolution will be a good motivation to study its role at the time of inflation. Since the length scale is expected to be small during inflation, the resulted energy density form the holographic principle is expected to be large enough to drive inflation. The entropy of the system is the main part of the holographic principle, in which modifying entropy will leads to a modified energy density. Here, instead of the original entropy, we are going to apply a modified entropy,…
The basic motivation of this work is to attempt to explain the rapid primordial inflation and the observed slow late-time inflation by using the Brans-Dicke theory of gravity. We show that the ratio of these two inflation parameters is proportional to the square root of the Brans-Dicke parameter $% ω$ $(ω\gg1) $. We also calculate the Hubble parameter $% H$ and the time variation of the time dependent Newtonian gravitational constant $G$ for both regimes. The variation of the Hubble parameter predicted by Brans-Dicke cosmology is shown to be consistent with recent measurements: The value of $H…
Chaotic inflation is inconsistent with the observational constraint at 68\% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model $V(ϕ)=V_0ϕ^{1/3}$ satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature pert…
A scenario where inflation emerges as a response to protect the holographic principle is described. A two fluid model in a closed universe inflation picture is assumed, and a possible explanation for secondary exponential expansion phases as those currently observed is given.
A model of inflation produced by a viscous fluid is investigated and its compatibility with the holographic principle at the very early universe (as recently formulated for the holographic universe with a holographic cut-off radius) is demonstrated. Specifically, ensuing from the model, the corresponding scale factor and infrared cut-off are analytically calculated, which are taken to be the particle and future event horizon for inflation, respectively. Using them, the energy conservation law, in the holographic point of view, is obtained. In this way, total equivalence of viscous fluid inflat…
After a brief introduction to the AdS/CFT holography a tachyon inflation will be discussed in the framework of holographic cosmology. The model is based on a holographic braneworld scenario with an effective tachyon field on a D3-brane located at the holographic bound of an asymptotic ADS$_5$ bulk.
In this paper, we suppose that the universe begins in a holographic thermal equilibrium phase with the diverged correlation length, and the phase transition to the radiation phase of standard cosmology goes with the abrupt reducing of correlation length. In this case, the primordial perturbations may be induced by thermal fluctuations in this holographic phase. We calculate the spectra of this holographic primordial perturbations, and find that the scalar spectrum has a slightly red tilt and the tensor perturbation amplitude has a moderate ratio, which may be tested in coming observations. The…
A model where the inflationary phase emerges as a response to protect the Fischler-Susskind holographic bound is described. A two fluid model in a closed universe inflation picture is assumed, and a discussion on conditions under which is possible to obtain an additional exponential expansion phase as those currently observed is given.
We apply the holographic principle during the inflationary stage of our universe. Where necessary, we illustrate the analysis in the case of new and extended inflation which, together, typify generic models of inflation. We find that in the models of extended inflation type, and perhaps of new inflation type also, the holographic principle leads to a lower bound on the density fluctuations.
It is shown that in a number of scalar potentials with an unstable local maximum at the origin chaotic inflation is followed by new inflation if model parameters are appropriately chosen. In this model density fluctuation can have a large-amplitude peak on the comoving Hubble scale at the onset of the slow-roll new inflation and can result in formation of appreciable amount of primordial black holes on astrophysically interesting mass scales.
Recently, Verlinde conjectured that gravity may be an entropic force, arising from thermodynamics on the holographic screen. We investigate the implications of the entropic force formalism for inflationary cosmology. We find the background dynamics of inflation can be dually described in the holographic language. At the perturbation level, two kinds of novel scale invariant scalar fluctuations arise from thermal fluctuations on the holographic screen. These fluctuations can be responsible for CMB anisotropy and structure formation.
We propose a new single field inflation model in which the usual slow-roll inflation is joined to a new period of slow-climb and slow-roll inflation through a short intermediate non-inflationary phase. We then show that primordial curvature perturbations can be enhanced at small scales, a sizable amount of primordial black holes (PBHs) can be produced which make up most of dark matter, the gravitational waves (GWs) induced by scalar metric perturbations that accompany with the formation of PBHs can be detectable by future GW experiments, and last but not least, our model is compatible with the…
Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models predicting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{\mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{\mathrm{NL}}$ becomes large at the scales before the power spectrum reaches …
There are at least three cosmic backgrounds of primordial gravitational waves coming from inflation: those produced during inflation and associated with the stretching of quantum modes; those produced at the violent stage of preheating after inflation; and those associated with the self-ordering of Goldstone modes if inflation ends via a global symmetry breaking scenario, like in hybrid inflation. Each background has its own characteristic spectrum with specific features. We describe in detail the origin of extra peaks in the PGW background from preheating in the case in which inflation ends w…
We investigate observational constraints on inflationary parameters in the context of an holographic cosmology with an induced gravity correction. We consider two situations where a universe is firstly filled with a scalar field and secondly with a tachyon field. Both cases are investigated in a slow-roll regime. We adopt a quadratic potential and an exponential potential for the scalar and the tachyon inflation respectively. In this regard, the standard background and perturbative parameters characterizing the inflationary era are modified by correction terms. We show a good agreement between…
In this letter we study a model of inflation in which the inflationary regimen comes from a type of holographic energy density. In particular, we consider the Granda-Oliveros proposal for the holographic energy density, which contains two free dimensionless parameters, $α$ and $β$. This holographic energy density is associated to the so-called Granda-Oliveros infrared cutoff (G-O cutoff). Additionally, since in the inflationary regimen the energy scales are very high, it is necessary to modify the G-O cutoff taking into account a correction due to the ultraviolet cutoff. In this way, we obtain…
Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it is necessary to go beyond linear perturbation theory. Stochastic inflation provides a way to take the leading non-linear effects into account. In this contribution, I discuss recent progress in numerical computations of stochastic inflation. A numerical approach can include more of the non-linearities than an analytical calculation, and can be applied to sin…
The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar-tensor inflation, Gauss-Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fra…
We investigate the primordial power spectra for general kinetic inflation models that support a period of kinetic dominance in the case of curved universes. We present derivations of the Mukhanov-Sasaki equations with a nonstandard scalar kinetic Lagrangian which manifests itself through the inflationary sound speed $c_s^2$. We extend the analytical approximations exploited in Contaldi et al [1] and Thavanesan et al [2] to general kinetic Lagrangians and show the effect of $k$-inflation on the primordial power spectra for models with curvature. In particular, the interplay between sound speed …
We study the emission of neutral massless $(1, 2)\hbar$-spin bosons during power-law inflation using unified spinor field theory. We shows that during inflation gravitons and photons were emitted with wavelengths (on physical coordinates) that increase as the Hubble radius: $λ_{Ph} \sim a/H$. The quantised action related to these bosons is calculated and results to be a fraction of the Planck constant.
We compute the spectral index for scalar perturbations generated in a primordial inflationary model. In this model, the transition of the inflationary phase to the radiative era is achieved through the decay of the cosmological term leading a second order phase transition and the characteristics of the model allow to implement a set of initial conditions where the perturbations display a thermal spectrum when they emerge from the horizon. The obtained value for the spectral index is equal to 2, a result that depends very weakly on the various parameters of the model and on the initial conditio…
We investigate the corrections of the holographic dark energy to inflation paradigm. We study the evolution of the holographic dark energy in the inflationary universe in detail, and carry out a model-independent analysis on the holographic dark energy correction to the primordial scalar power spectrum. It turns out that the corrections generically make the spectrum redder. To be consistent with the experimental data, there must be a upper bound on the reheating temperature. We also discuss the corrections due to different choices of the infrared cutoff.
Depending on various assumptions on the energy scale of inflation and assuming a primordial power spectrum of a Broken Scale Invariance (BSI) type, we explore the possibility for Primordial Black Holes (PBH) and Planck relics to contribute substantially to cold dark matter in the Universe. A recently proposed possibility to produce planck relics in 4-dimensional string gravity is considered. Possible experimental detection through gravitational waves is further explored. We stress that inflation with a low energy scale, and also possibly when Planck relics are produced, leads unavoidably to re…
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 present a simple derivation of an upper bound on the average size of the true vacuum bubbles at the end of inflation, in models of extended inflation type. The derivation uses the inequality that the total energy inside a given volume must be less than its linear dimensions. The above bound is the same as that obtained earlier, by applying the holographic principle according to Fischler-Susskind prescription. Such a bound leads to a lower bound on the denisty fluctuations.
We study a double inflation model (a hybrid inflation + a new inflation) in supergravity and discuss the formation of primordial black holes (PBHs) with mass \sim 10^{-20}-10^{5}M_{\odot}. We find that in a wide range of parameter space, we obtain PBHs which amount to Ω\simeq 1, i.e., PBH dark matter. Also, we find a set of inflation parameters which produces PBHs evaporating now. Those PBHs may be responsible for antiproton fluxes observed by the BESS experiment.
A model of tachyon inflation is proposed in the framework of holographic cosmology. The model is based on a holographic braneworld scenario with a D3-brane located at the holographic boundary of an asymptotic ADS$_5$ bulk. The tachyon field that drives inflation is represented by a DBI action on the brane. We solve the evolution equations analytically in the slow-roll regime and solve the exact equations numerically. We calculate the inflation parameters and compare the results with Planck 2018 data.
We consider the space-condensate inflation model to study the primordial gravitational waves generated in the early Universe. We calculate the energy spectrum of gravitational waves induced by the space-condensate inflation model for full frequency range with assumption that the phase transition between two consecutive regimes to be abrupt during evolution of the Universe. The suppression of energy spectrum is found in our model for the decreasing frequency of gravitational waves depending on the model parameter. To realize the suppression of energy spectrum of the primordial gravitational wav…
A macroscopic universe may emerge naturally from a Planck cell fluctuation by unfolding through a stage of exponential expansion towards a homogeneous cosmological background. Such primordial inflation requires a large and presumably infinite degeneracy at the Planck scale, rooted in the unbounded negative gravitational energy stored in conformal classes. This complex Planck structure is consistent with a quantum tunneling description of the transition from the Planck scale to the inflationary era and implies, in the limit of vanishing Planck size, the Hartle-Hawking no-time boundary condition…
We argue that primordial gravitational waves have a spectral break and its information is quite useful for exploring the early universe. Indeed, such a spectral break can be a fingerprint of the end of inflation, and the amplitude and the frequency at the break can tell us the energy scale of inflation and the reheating temperature simultaneously. In order to investigate the spectral break, we give an analytic formula for evolution of the Hubble parameter around the end of inflation where the slow roll approximation breaks down. We also evaluate the spectrum of primordial gravitational waves a…
The large enhancement of the primordial power spectrum of the curvature perturbation can seed the formation of primordial black hole, that can play as a dark matter component in the Universe. In multi-filed inflation models, the curved trajectory of the scalar fields in the field space can generate a peak in the power spectrum on small scales due to the existence of the isocurvature perturbation. Here we show that a potential can be reconstructed from a given power spectrum, which is made of a scale-invariant one on large scales and the other function with a peak on small scales. In multi-fiel…
We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology.
In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis-Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et. al [Class. Quant. Grav. 30 (2013) 12] for these Berry phases, which is resolved to yield agreement with our results.
We study slow-roll inflation and the generation of primordial fluctuations in $F(T)$ gravity's rainbow. We obtain the second order action for scalar and tensor perturbations and then calculate the primordial power spectrum for them. Thus, after calculating the inflationary observables up to first order in slow-roll approximation, namely the scalar spectral index $n_{s}$ and the tensor-to scalar ratio $r$, we confront the predictions of the model with the current PLANCK and BICEP/Keck data.
In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
We use holographic techniques to compute inflationary non-Gaussianities for general single-field inflation, including models with a non-trivial sound speed. In this holographic approach, the inflationary dynamics is captured by a relevant deformation of the dual conformal field theory (CFT) in the UV, while the inflationary correlators are computed by conformal perturbation theory. In this paper, we discuss the effects of higher derivative operators, such as $(\partial_μϕ\partial^μϕ)^{m}$, which are known to induce a non-trivial sound speed and source potentially large non-Gaussianities. We co…
We study primordial gravitational waves from inflation in Randall-Sundrum braneworld model. The effect of small change of the Hubble parameter during inflation is investigated using a toy model given by connecting two de Sitter branes. We analyze the power spectrum of final zero-mode gravitons, which is generated from the vacuum fluctuations of both initial Kaluza-Klein modes and zero-mode. The amplitude of fluctuations is confirmed to agree with the four-dimensional one at low energies, whereas it is enhanced due to the normalization factor of zero-mode at high energies. We show that the five…
We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the …
We apply the holographic principle at the early universe, obtaining an inflation realization of holographic origin. Such a consideration has equal footing with its well-studied late-time application, and moreover the decrease of the horizons at early times naturally increases holographic energy density at inflationary scales. Taking as Infrared cutoff the particle or future event horizons, and adding a simple correction due to the Ultraviolet cutoff, whose role is non-negligible at the high energy scales of inflation, we result in a holographic inflation scenario that is very efficient in inco…
In numerical calculations of the primordial power spectrum of perturbations produced during inflation, for very little wavenumber $k$s, to implement the initial conditions required of the perturbation mode functions consistently, we must let the universe experience more e-foldings of inflation than that required of it to solve the horizon, flatness and other pre-inflation problems. However, if the number of e-foldings of inflation has an upper bound, then for perturbations at scales greater than some critical value, the initial conditions required of the mode functions cannot be implemented ph…
