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 inflation, with the specific cut-off of Nojiri and Odintsov, and holographic inflation is proven.
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 manuscript, we present a generalization of the interacting holographic dark energy model using the viscous generalized Chaplygin gas. We also study the model by considering a dynamical Newton's constant $G$. Then we reconstruct the potential and the dynamics of the scalar field which describe the viscous Chaplygin cosmology.
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.
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…
We investigate bounce cosmological models in the presence of a viscous fluid, making use of generalized holographic cutoffs introduced by Nojiri and Odintsov (2017). We consider both an exponential, a power-law, and a double exponential form for the scale factor. By use of these models we calculate expressions for infrared cutoffs analytically, such that they correspond to the particle horizon at the bounce. Finally we derive the energy conservation equation, from the holographic point of view. In that way the relationship between the viscous fluid bounce and the holographic bounce is demonstr…
We study the entropy-corrected version of the holographic dark energy (HDE) model in the framework of modified FRW cosmology. We consider a non-flat universe filled with an interacting viscous entropy-corrected HDE (ECHDE) with dark matter. We also include the case of variable gravitational constant G in our model. We obtain the equation of state and the deceleration parameters of the interacting viscous ECHDE. Moreover, we reconstruct the potential and the dynamics of the quintessence, tachyon, K-essence and dilaton scalar field models according to the evolutionary behavior of the interacting…
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.
The theory of holographic space-time (HST) generalizes both string theory and quantum field theory. It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of non-commutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite dimensional unitary representations of super- algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-P…
We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.
This article is devoted to the application of the holographic principle to describe Rip brane cosmological models in the presence of a bulk viscosity. We make use of the generalized infrared-cutoff holographic dark energy, introduced by Nojiri and Odintsov We consider various examples: Rip brane cosmology corresponding to the Little Rip case, asymptotic de Sitter theory, and the so-called Big Freeze theory leading to a singularity. Analytical expressions for infrared cutoffs, as well as the particle and the future horizons at the brane, are obtained. The equations for energy conservation on th…
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.
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.
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 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…
It is well known that, in single clock inflation, the curvature perturbation $ζ$ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of $ζ$ follows from the cut-off independence of correlators of the energy momentum …
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…
In this article we apply the holographic principle for describing in a unifying way the early and the late-time universe, when the general equation of state contains a bulk viscosity. We use the idea of a generalized cut-off holographic dark energy introduced by Nojiri and Odintsov (2006,2017), and study the evolution of the universe when the equation of state has two power-law asymptotes. Analytical expressions for the infrared cut-offs in terms of the particle horizon are obtained. The energy conservation laws as derived from the holographic point of view, are given for various forms of the …
In this paper, we investigate inhomogeneous viscous fluid cosmology for inflation. Several toy models are presented in the attempt to analyze how inflation can be realized according with cosmological data by making use of an inhomogeneous EoS parameter for the fluid and/or by introducing a viscosity to have a graceful exit from inflation. The results will be compared with the ones of scalar field representation and discussed. We will pay attention on the possibility to recover the reheating and therefore the Friedmann universe.
We consider a universe with a bulk viscous cosmic fluid, in a flat Friedmann-Lemaitre-Robertson-Walker geometry. We derive the conditions for the existence of inflation, and those which at the same time prevent the occurrence of self-reproduction. Our theoretical model gives results which are in perfect agreement with the most recent data from the PLANCK surveyor.
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.
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…
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…
We compare two holographic arguments that impose especially strong bounds on the amount of inflation. One comes from the de Sitter Equilibrium cosmology and the other from the work of Banks and Fischler. We find that simple versions of these two approaches yield the same bound on the number of e-foldings. A careful examination reveals that while these pictures are similar in spirit, they are not necessarily identical prescriptions. We apply the two pictures to specific cosmologies which expose potentially important differences and which also demonstrate ways these seemingly simple proposals ca…
In a holographic description of inflation, cosmological time evolution in the bulk is expected to correspond to the renomalization group (RG) flow in a dual boundary theory. Here, we analyze this expectation by computing the correlation functions of the curvature perturbation $ζ$ holographically. For this purpose, we use a deformed conformal field theory at the boundary, with a single deformation operator. In standard single field models of inflation, $ζ$ is known to be conserved at large scales under very general conditions. However, we find that this is not generically the case in the dual d…
In a class of recently proposed models, the early universe is strongly coupled and described holographically by a three-dimensional, weakly coupled, super-renormalizable quantum field theory. This scenario leads to a power spectrum of scalar perturbations that differs from the usual empirical LCDM form and the predictions of generic models of single field, slow roll inflation. This spectrum is characterized by two parameters: an amplitude, and a parameter g related to the coupling constant of the dual theory. We estimate these parameters, using WMAP and other astrophysical data. We compute Bay…
Holographic considerations may provide a glimpse of quantum gravity beyond what is currently accessible by other means. Here we apply holography to inflationary cosmology. We argue that the appropriate holographic bound on the total entropy in the inflationary perturbations is given by the {\it difference} of the area of the apparent horizon in the slow-roll approximation and its exact value near the end of inflation. This implies that the effective field theory of the inflaton weakly coupled to gravity requires modifications below the Planck scale. For a conventional model of inflation this s…
The inflationary expansion of our early-time universe is considered in terms of the van der Waals equation, as equation of state for the cosmic fluid, where a bulk viscosity contribution is assumed to be present. The corresponding gravitational equations for the energy density in a homogeneous and isotropic Friedmann-Lema\^ıtre-Robertson-Walker universe are solved, and an analytic expression for the scale factor is obtained. Attention is paid, specifically, to the role of the viscosity term in the accelerated expansion; the values of the slow-roll parameters, the spectral index, and the tensor…
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…
Warm inflation model with bulk viscous pressure in the context of "intermediate inflation" where the cosmological scale factor expands as $a(t)=a_0\exp(At^f)$, is studied. The characteristics of this model in slow-roll approximation and in high dissipative regime are presented in two cases: 1- Dissipative parameter $Γ$ as a function of scalar field $ϕ$ and bulk viscous coefficient $ζ$ as a function of energy density $ρ$. 2- $Γ$ and $ζ$ are constant parameters. Scalar, tensor perturbations and spectral indices for this scenario are obtained. The cosmological parameters appearing in the present …
The review of basic cosmological properties of four-dimensional F(R)-gravity, including FRW equations of motion and its accelerating solutions, generalized fluid and scalar-tensor representation of the theory is done. Cosmological reconstruction equation is written and conditions for stability of cosmological solution are discussed. The overview of realistic F(R)-models unifying inflation with dark energy epoch is made. The avoidance of finite-time future singularities in such theories via the introduction of R^2-term is studied. New realistic non-singular F(R)-gravity unifying early-time infl…
The results of the paper of Verlinde [hep-th/0008140], discussing the holographic principle in a radiation dominated universe, are extended when allowing the cosmic fluid to possess a bulk viscosity. This corresponds to a non-conformally invariant theory. The generalization of the Cardy-Verlinde entropy formula to the case of a viscous universe seems from a formal point of view to be possible, although we question on physical grounds some elements in this kind of theory, especially the manner in which the Casimir energy is evaluated. Our discussion suggests that for non-conformally invariant t…
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.
In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inflation is realized--- is highly constrained, with use of the Hamilton--Jacobi equations. In multi-field holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wavefunctions contain no oscillatory phases independent of the momenta). We show that this result is exact, independe…
We obtain conditions for the existence of an attractor in the system of equations describing a tachyon warm inflationary model with bulk viscosity taken into account. When these conditions are met the evolution approaches slow-roll regime. We present the primordial power spectrum for the tachyon field by considering a dissipation coefficient depending on the scalar field and temperature.
We consider the inflation produced by two coupled fluids in the flat Friedmann-Robertson-Walker universe. Different cosmological models for describing inflation by use of an inhomogeneous equation of state for the fluid are investigated. The gravitational equations for energy and matter are solved, and analytic representations for the Hubble parameter and the energy density are obtained. Corrections in the energy density for matter inducing the inflation and the coupling with energy are discussed. We analyze the description of inflation induced by non-constant equation-of-state parameters from…
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 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,…
In a recently proposed scenario for primordial inflation, where the Standard Model (SM) Higgs boson plays a role of the inflation field, an effective field theory (EFT) approach is the most convenient for working out the consequences of breaking of perturbative unitarity, caused by the strong coupling of the Higgs field to the Ricci scalar. The domain of validity of the EFT approach is given by the ultraviolet (UV) cutoff, which, roughly speaking, should always exceed the Hubble parameter in the course of inflation. On the other hand, applying the trusted principles of quantum gravity to a loc…
This paper is a major revision of our previous work on the HST model of inflation. We identify the local fluctuations of the metric with fluctuations of the mass and angular momentum of black holes, and show that the consistency conditions in HST for a single trajectory to see more and more of a homogeneous distribution of black holes, imply that the system outside the horizon is undergoing inflation: small systems of equal entropy, are not in causal contact. Homogeneity then requires that the initial trajectory underwent inflation that expanded the black hole radius into our current horizon. …
We present a holographic description of four-dimensional single-scalar inflationary universes in terms of a three-dimensional quantum field theory. The holographic description correctly reproduces standard inflationary predictions in their regime of applicability. In the opposite case, wherein gravity is strongly coupled at early times, we propose a holographic description in terms of perturbative QFT and present models capable of satisfying the current observational constraints while exhibiting a phenomenology distinct from standard inflation. This provides a qualitatively new method for gene…
In the present work we report a study on the viscous extended holographic Ricci dark energy (EHRDE) model under the assumption of existence of bulk viscosity in the linear barotropic fluid and the EHRDE in the framework of standard Eckart theory of relativistic irreversible thermodynamics and it has been observed that the non-equilibrium bulk viscous pressure is significantly smaller than the local equilibrium pressure. We have studied the equation of state (EoS) parameter and observed that the EoS behaves like "quintom" and is consistent with the constraints set by observational data sets fro…
We study the warm-tachyon inflationary universe model with viscous pressure in high-dissipation regime. General conditions which are required for this model to be realizable are derived in the slow-roll approximation. We present analytic expressions for density perturbation and amplitude of tensor perturbation in longitudinal gauge. Expressions of tensor-to-scalar ratio, scalar spectral index and its running are obtained. We develop our model by using exponential potential, the characteristics of this model are calculated for two specific cases in great details: 1- Dissipative parameter $Γ$ an…
We consider an action for gravity that, in addition to the Einstein-Hilbert term, contains a function of the Ricci scalar and the Gauss-Bonnet invariant. The specific form of the function considered is motivated by holographic cosmology. At background level the field equations imply modified Friedmann equations of the same form as those in the holographic cosmology. We calculate the cosmological perturbations and derive the corresponding power spectra assuming a general $k$-inflation. We find that the resulting power spectra differ substantially from those obtained in both holographic and stan…
The Holographic Space-time (HST) model of inflation has a potential explanation for dark matter as tiny primordial black holes. Motivated by a recent paper of Barrau\cite{barrau} we propose a version of this model where some of the Inflationary Black Holes (IBHs), whose decay gives rise to the Hot Big Bang, carry the smallest value of a discrete symmetry charge. The fraction $f$ of IBHs carrying this charge is difficult to estimate from first principles, but we fix it by requiring that the crossover between radiation and matter domination occurs at the correct temperature $T_{eq} \sim 1 eV = 1…
The incorporation of bulk viscosity process to General Relativity leads to the appearance of nonsingular backgrounds that, at early and late times, depict an accelerated universe. These backgrounds could be analytically calculated and mimicked, in the context of General Relativity, by a single scalar field whose potential could also be obtained analytically. We will show that, we can build viable backgrounds that, at early times, depict an inflationary universe leading to a power spectrum of cosmological perturbations which match with current observational data, and after leaving the inflation…
We investigate infrared logarithms in de Sitter space from holographic perspective. We employ a gravitational Fokker-Planck equation to investigate the time evolution of the de Sitter entropy $S=π/(G_N H^2)$, where $H$ is the Hubble parameter and $G_N$ is the Newton's constant. Under the Gaussian approximation, we obtain the dynamical $β$ function of $g=1/S$. It is asymptotically free toward the future. It also possesses the ultraviolet fixed point indicating that the Universe started the de Sitter expansion at the Planck scale. The pre-inflation era exists to prepare a special initial conditi…
We derive a Higgs inflationary model in the context of holographic cosmology, where we consider a universe filled with a Higgs field non-minimally coupled to gravity in a slow-roll regime. The amplitude of density (scalar) perturbations is calculated. In this regard, we show that the background and perturbative parameters characterising the inflationary era are related to the standard one through corrections terms. We found that for the e-fold number $N\sim 58$, the spectral index,$n_{r}$, and the tensor-to-scalar ratio,$r$, values are $0.965$ and $0.021$, respectively, which are in agreement …
In the global description of eternal inflation, probabilities for vacua are notoriously ambiguous. The local point of view is preferred by holography and naturally picks out a simple probability measure. It is insensitive to large expansion factors or lifetimes, and so resolves a recently noted paradox. Any cosmological measure must be complemented with the probability for observers to emerge in a given vacuum. In lieu of anthropic criteria, I propose to estimate this by the entropy that can be produced in a local patch. This allows for prior-free predictions.
