本文提出温暴胀的精确解方法，可推广 Del Campo 的修正 Friedmann 方法并在特定极限下退化为 Hamilton-Jacobi 形式，进而用于研究 Tsallis 熵修正 Friedmann 宇宙中的温暴胀及其扰动谱。
摘要：
近年来，宇宙暴胀理论因其对早期宇宙的惊人预言而受到大量应有的关注。除了通常的冷暴胀范式之外，温暴胀在现代暴胀研究中获得了巨大关注。其独特特征以及特别是与冷暴胀不同的预言，已经催生了大量相关文献。在温暴胀框架下，各种修正宇宙学场景也已被研究。在这项工作中，我们引入温暴胀的精确解方法。该方法允许人们在各种修正宇宙学场景中直接研究温暴胀阶段。我们首先概述我们的方法，并证明它推广了 Del Campo 的修正 Friedmann 方法，并在特定极限下退化为著名的暴胀 Hamilton-Jacobi 形式。我们还求出了早期宇宙中标量和张量扰动的扰动谱，然后将我们的方法应用于研究 Tsallis 熵修正 Friedmann 宇宙中的温暴胀。我们在论文结尾就本工作的适用范围给出一些总结性评论。
英文摘要：
The theory of cosmic inflation has received a great amount of deserved attention in recent years due to it's stunning predictions about the early universe. Alongside the usual cold inflation paradigm, warm inflation has garnered a huge amount of interest in modern inflationary studies. It's peculiar features and specifically different predictions from cold inflation have led to a substantial amount of literature about it. Various modified cosmological scenarios have also been studied in the warm inflationary regime. In this work, we introduce the exact solution approach for warm inflation. This approach allows one to directly study warm inflationary regime in a variety of modified cosmological scenarios. We begin by outlining our method and show that it generalizes the modified Friedmann approach of Del Campo , and reduces to the well known Hamilton-Jacobi formalism for inflation in particular limits. We also find the perturbation spectra for cosmological and tensor perturbations in the early universe, and then apply our method to study warm inflation in a Tsallis entropy modified Friedmann universe. We end our paper with some concluding remarks on the domain of applicability of our work.
We extend the k-inflation which is a type of kinetically driven inflationary model under the standard inflationary scenario to a possible warm inflationary scenario. The dynamical equations of this warm k-inflation model are obtained. We rewrite the slow-roll parameters which are different from the usual potential driven inflationary models and perform a linear stability analysis to give the proper slow-roll conditions in the warm k-inflation. Two cases, a power-law kinetic function and an exponential kinetic function, are studied, when the dissipative coefficient $Γ=Γ_0$ and $Γ=Γ(ϕ)$, respect…
It is presumed that thermal fluctuations present during inflationary epoch can make inflaton scalar field to interact with other fields resulting in the existence of a thermal component during the inflationary period. The presence of this thermal component assists structure formation and reduces reheating dependence as in the contemporary inflationary paradigm. This is known as warm inflation. In 1990 J . D. Barrow \cite{25} considered a scenario of inflation with matter field having a phenomenological equation of state of the type $p+ρ=γρ^λ,~γ\neq 0$ and $λ$ constant. He called such inflation…
This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient $Γ=Γ_0$ and $Γ=Γ(ϕ)$, respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by …
In this work, we investigate the Higgs-Starobinsky (HS) model in the context of warm inflation scenario. The dissipative parameter as a linear form of temperature of warm inflation is considered with strong and weak regimes. We study the HS model in the Einstein frame with the slow-roll inflation framework. We compute the inflationary observables and then compare with the Plank 2018 data. With the sizeable number of e-folds and proper choices of parameters, we discover that the predictions of warm HS model present in this work are in very good agreement with the latest Planck 2018 results. Mor…
The present work deals with a non-equilibrium thermodynamics that is associated with the scenario of warm inflation. The premise is that an adiabatic radiation production process holds exactly i.e. the radiation dilution is exactly counterbalanced by a dissipation term. Under this hypothesis, it is found that radiation particle number, temperature, radiation energy density and pressure are all conserved -- a contradiction to the very nature of the warm inflation dynamics. However, such exact adiabatic radiation production process never happens in any realistic analysis of warm inflation. In th…
A fundamental prediction of inflation is a nearly scale-invariant spectrum of gravitational wave. The features of such a signal provide extremely important information about the physics of the early universe. In this paper, we focus on several topics about warm inflation. First, we discuss the stability property about warm inflation based on nonequilibrium statistical mechanics, which gives more fundamental physical illustrations to thermal property of such model. Then, we calculate the power spectrum of gravitational waves generated during warm inflation, in which there are three components c…
We study and analyze the dynamic properties of both canonical and noncanonical warm inflationary models with dissipative effects. We consider different models of canonical warm inflation with different dissipative coefficients and prove that the behavior at infinity of quadratic dissipative model distinctly differs from that of the constant dissipative model, which means that quadratic dissipative coefficient increases the possibility of the occurrence of inflation. We also show that the different choice of combination of the parameters in noncanonical warm inflation exhibits dramatically diff…
In this paper, $k$-inflation is analyzed in warm braneworld scenario. A general class of $k$-essence models with power-law kinetic term is investigated and weak and strong dissipation regimes are studied. Scalar perturbations and spectral index are derived. The results are discussed and applied to specific examples.
In this paper we introduce the "warm vector inflation" scenario. In warm inflation scenario radiation is produced during the inflation epoch and reheating is avoided. Slow-roll and perturbation parameters of this model are presented. We develop our model using intermediate inflation model. In this case, the model is compatible with observational data. We also study the model using another exact cosmological solution, named logamediate scenario. We present slow-roll and Hubble parameters, power spectrum and tensor-scalar ratio in terms of inflaton. The model is compatible with WMAP7 and Planck …
In this paper, we discuss the warm inflation model with both a Langevin equation and a generalized Langevin equation scenario. As a brief picture to illustrate the basic properties of stochastic differential equation in warm inflation, this paper is started from a simple condition with constant dissipative coefficient. In this model, we prove the perturbed inflaton field exhibits a stationary process on large scale, so the perturbed field has a scale-invariant power spectrum. Then we study the warm inflation with a generalized Langevin equation scenario. The perturbed field in such model also …
The framework of a kind of noncanonical warm inflation is introduced, and the dynamical equations of this scenario are presented. We propose the slow roll approximations and give some redefining slow roll parameters in this scenario which remain dimensionless. Performing systemic stability analysis, we calculate the slow roll conditions to guarantee that slow roll approximations hold. The slow roll conditions suggest slow roll inflation in general noncanonical warm inflationary scenario can still exist, and in addition, the slow roll approximations are more easily to be satisfied. Then, a conc…
We investigate the warm inflation condition in loop quantum cosmology. In our consideration, the system is described by a tachyon field interacted with radiation. The exponential potential function, $V(ϕ)=V_0 e^{-αϕ}\label{exp-p}$, with the same order parameters $V_0$ and $α$, is taken as an example of this tachyon warm inflation model. We find that, for the strong dissipative regime, the total number of e-folds is less than the one in the classical scenario, and for the weak dissipative regime, the beginning time of the warm inflation will be later than the tachyon (cool) inflation.
In this paper, we investigate a class of Horndeski scalar-tensor theory of gravity for warm inflation. We present some models where the early-time acceleration is realized in the weak and in the strong dissipation regime. Cosmological perturbations are analyzed.
Inhomogeneous fluid models for warm inflation are investigated. The early-time acceleration is supported by inhomogeneous fluid whose coupling with radiation leads to the radiation dominated era after inflation. Several examples are analyzed, strong dissipation regime is discussed, and the viability of the models respect to the last Planck data is verified.
Starting from a gauge invariant treatment of perturbations an analytical expression for the spectrum of long wavelength density perturbations in warm inflation is derived. The adiabatic and entropy modes are exhibited explicitly. As an application of the analytical results, we determined the observational constraint for the dissipation term compatible with COBE observation of the cosmic microwave radiation anisotropy for some specific models. In view of the results the feasibility of warm inflation is discussed.
We study the main properties of the warm inflationary model based on Barrow's solution for the scale factor of the universe. Within this framework we calculate analytically the basic slow roll parameters for different versions of warm inflation. We test the performance of this inflationary scenario against the latest observational data and we verify that the predicted spectral index and the tensor-to-scalar fluctuation ratio are in excellent agreement with those of {\it Planck 2015}. Finally, we find that the current predictions are consistent with those of viable inflationary models.
We investigate the non-minimally Higgs inflaton (HI) model in the context of warm inflation scenario. Warm little inflaton (WLI) model considers the little Higgs boson as inflaton. The concerns of warm inflation model can be eliminated in WLI model. There is a special case of dissipation parameter in WLI model $Γ=Γ_0 T$. Using this parameter, we study the potential of HI in Einstein frame . Finally we will constrain the parameters of our model using current Planck observational data.
Warm inflationary universe models in the context of logamediate expansion are studied. General conditions required for these models to be realizable and discussed. This study is done in the weak and strong dissipative regimes. The parameters of our models are constrained from the observational data.
Warm inflationary universe model in a tachyon field theory is studied in the weak dissipative regime. We develop our model for an exponential potential and the dissipation parameter $Γ=Γ_0$=constant. We describe scalar and tensor perturbations for this scenario.
A warm inflationary universe in the context of Galileon model or G-model is studied. Under a general formalism we study the inflationary dynamics and the cosmological perturbations considering a coupling of the form $G(ϕ,X)=g(ϕ)\,X$. As a concrete example, we consider an exponential potential together with the cases in which the dissipation and Galilean coefficients are constants. Also, we study the weak regime given by the condition $R<1+3gH\dotϕ$, and the strong regime in which $1<R+3gH\dotϕ$.Additionally, we obtain constraints on the parameters during the evolution of G-warm inflation, assu…
We extend the warm inflationary scenario to the case of the noncanonical scalar fields. The equation of motion and the other basic equations of this new scenario are obtained. The Hubble damped term is enhanced in noncanonical inflation. A linear stability analysis is performed to give the proper slow-roll conditions in warm noncanonical inflation. We study the density fluctuations in the new picture and obtain an approximate analytic expression of the power spectrum. The energy scale at the horizon crossing is depressed by both noncanonical effect and thermal effect, and so is the tensor-to-s…
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.
A warm intermediate inflationary model in the context of Generalized Chaplygin Gas is investigated. We study this model in the weak and strong dissipative regimes, considering a generalized form of the dissipative coefficient $Γ=Γ(T,ϕ)$, and we describe the inflationary dynamics in the slow-roll approximation. We find constraints on the parameters in our model considering the Planck 2015 data, together with the condition for warm inflation $T>H$, and the conditions for the weak and strong dissipative regimes.
We investigate warm intermediate scenario of the cosmological inflation in $F(T)$ gravity in the limit of high dissipation. The inflationary expansion is driven by the scalar inflaton while the gravitational dynamics follow from the $F(T)$ gravity. We calculate the relevant inflationary observables such as scalar-tensor ratio, power-spectrum indices of density perturbations and gravitational waves and the e-folding parameter. We obtain a ratio of slow-roll parameters to be constant. Our calculations support the warm-intermediate inflationary scenario in a spacetime with torsion. Moreover our r…
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…
The warm inflation scenario is an alternative mechanism which can explain the isotropic and homogeneous Universe which we are living in. In this work I extend a previously introduced formalism, without the restriction of slow - roll regime. Quantum to classical transition of the fluctuations is studied by means of the "transition function" here introduced. I found that the fluctuations of radiation energy density decrease with time and the thermal equilibrium at the end of inflation holds.
A second-order expansion for the quantum fluctuations of the matter field was considered in the framemork of the warm inflation scenario. The friction and Hubble parameters were expanded by means of a semiclassical approach. The fluctuations of the Hubble parameter generates fluctuations of the metric. These metric fluctuations produce an effective term of curvature. The power spectrum for the metric fluctuations can be calculated on the infrared sector.
Non-Gaussianity generated in inflation can be contributed by two parts. The first part, denoted by $f_{NL}^{δN}$, is the contribution from four-point correlation of inflaton field which can be calculated using $δN$ formalism, and the second part, denoted by $f_{NL}^{int}$, is the contribution from the three-point correlation function of the inflaton field. We consider the two contributions to the non-Gaussianity in noncanonical warm inflation throughout (noncanonical warm inflation is a new inflationary model which is proposed in \cite{Zhang2014}). We find the two contributions are complementa…
Warm inflation is extended from the canonical field to the noncanonical field with a general Lagrangian density having coupling form of kinetic and potential terms. We develop the motion equation of the noncanonical inflaton field, and notice the motion equation has an annoying coupling term $\mathcal{L}_{Xφ}\dotφ^2$, which makes the inflation difficult to solve. It is found that a special field redefinition exists, making the motion equation of inflaton uncoupled. Then we can solve inflation in the special field representation for convenience. The relation of field redefinition between the sp…
A second-order expansion for the quantum fluctuations of the matter field was considered in the framework of the warm inflation scenario. The friction and Hubble parameters were expended by means of a semiclassical approach. The fluctuations of the Hubble parameter generates fluctuations of the metric. These metric fluctuations produce an effective term of curvature. The power spectrum for the metric fluctuations can be calculated on the infrared sector.
A warm inflationary Universe in the Randall-Sundrum II model during intermediate inflation is studied. For this purpose, we consider a general form for the dissipative coefficient $Γ(T,ϕ)=C_ϕ\,\frac{T^{m}}{ϕ^{m-1}}$, and also analyze this inflationary model in the weak and strong dissipative regimes. We study the evolution of the Universe under the slow-roll approximation and find solutions to the full effective Friedmann equation in the brane-world framework. In order to constrain the parameters in our model, we consider the recent data from the BICEP2-Planck 2015 data together with the neces…
We investigate the observational signatures of quantum cosmology in the Cosmic Microwave Background data provided by Planck collaboration. We apply the warm inflationary paradigm with a tachyon scalar field to the loop quantum cosmology. In this context, we first provide the basic cosmological functions in terms of the tachyon field. We then obtain the slow-roll parameters and the power spectrum of scalar and tensor fluctuations respectively. Finally, we study the performance of various warm inflationary scenarios against the latest Planck data and we find a family of models which are in agree…
I consider the COBE data coarse-grained field that characterize the now observable universe for a model of warm inflation which takes into account the thermal coupled fluctuations of the scalar field with the thermal bath. The power spectrum for both, matter and metric fluctuations are analyzed. I find that the amplitude for the fluctuations of the metric when the horizon entry, should be very small for the expected values of temperature.
The present work examines the possibility of warm inflationary paradigm in the modified gravity theory with fractal geometry. By choosing the normal fluid as radiation fluid and the effective fluid (with the extra term in modified field equation) as the inflaton field both strong and weak dissipative regimes have been studied using slow roll approximation with quasi-stable criteria for radiation. Finally, using the Planck data set, the present model has been analyzed for various choices of the fractal function and the dissipation parameter.
Using some ideas of Modern Kaluza-Klein theory, we examine the evolution of entropy on a 4D Friedmann-Robertson-Walker (FRW) brane from a 5D vacuum state, which is defined on a 5D background Riemann-flat metric. We found that entropy production is sufficiently important during inflation: $S > 10^{90}$, for all the initial values of temperature $T_0 < T_{GU}$.
I consider a new semiclassical expansion for the inflaton field in the framework of warm inflation scenario. The fluctuations of the matter field are considered as thermally coupled with the particles of the thermal bath. This coupling parameter depends on the temperature of the bath. The power spectrum remains invariant under this new semiclassical expansion for the inflaton. However, I find that the thermal component of the amplitude for the primordial field fluctuations should be very small at the end of inflation.
I study a stochastic approach for warm inflation considering back - reaction of the metric with the fluctuations of matter field. This formalism takes into account the local inhomogeneities fo the spacetime in a globally flat Friedmann - Robertson - Walker metric. The stochastic equations for the fluctuations of the matter field and the metric are obtained. Finally, the dynamics for the amplitude of these fluctuations in a power - law expansion for the universe are examined.
We investigate the cosmological perturbation theory and calculate the perturbation spectra in the warm $k$-inflation. Unlike the scalar perturbations of $k$-inflation in the cold inflationary scenario, entropy perturbations should be considered in our model. We study how the entropy perturbations affect the evolution of curvature perturbation $\mathcal{R}$ on the comoving hypersurfaces and find the dissipation coefficient $Γ$ plays a central role in the entropy perturbations and the evolution equation of $\mathcal{R}$. In the weak dissipation condition, entropy perturbations on the large scale…
We study the bispectrum of the primordial curvature perturbation on uniform-density hypersurfaces generated by a kind of the noncanonical warm inflation, wherein the inflation is provided by a noncanonical scalar inflaton field that is coupled to radiation through a thermal dissipation effect. We obtain an analytic form for the nonlinear parameter $f_{NL}$ that describes the non-Gaussianity in first-order cosmological perturbation theory and analyse the magnitude of this nonlinear parameter. We make a comparison between our result and those of the standard inflation and the canonical warm infl…
In the present work we show that warm chaotic inflation characterized by a simple $\fracλ{4}ϕ^{4}$ self-interaction potential for the inflaton, excluded by current data in standard cold inflation, and by an inflaton decay rate proportional to the temperature, is in agreement with the latest Planck data. The parameters of the model are constrained, and our results show that the model predicts a negligible tensor-to-scalar ratio in the strong dissipative regime, while in the weak dissipative regime the tensor-to-scalar ratio can be large enough to be observed.
In the present work, we study the consequences of considering a recently proposed polynomial inflationary potential in the context of the generalized, modified, and generalized cosmic Chaplygin gas models. In addition, we consider dissipative effects by coupling the inflation field to radiation, i.e., the inflationary dynamics is studied in the warm inflation scenario. We take into account a general parametrization of the dissipative coefficient $Γ$ for describing the decay of the inflaton field into radiation. By studying the background and perturbative dynamics in the weak and strong dissipa…
We explore the homogeneous background dynamics and the evolution of generated perturbations of cosmological inflation that is driven by multiple scalar fields interacting with a perfect fluid.Then we apply the method to warm inflation driven by two scalar fields and a radiation fluid, and present general results about the evolution of the inflaton and radiation. After decomposing the perturbations into adiabatic and entropy modes, we give the equation of motion of adiabatic and entropy perturbations on large scales. Then, we give numerical results of background and perturbation equations in a …
This paper is devoted to study the warm inflation using vector fields in the background of locally rotationally symmetric Bianchi type I universe model. We formulate the field equations, slow-roll and perturbation parameters (scalar and tensor power spectra as well as their spectral indices) under slow-roll approximation. We evaluate all these parameters in terms of directional Hubble parameter during intermediate and logamediate inflationary regimes by taking the dissipation factor as a function of scalar field as well as a constant. In each case, we calculate the observational parameter of i…
In this article we study a constant-roll inflationary model in the context of brane-world cosmology caused by a quintessence scalar field for warm inflation with a constant dissipative parameter Q =$Γ$/3H. We determine the analytical solution for the Friedman equation coupled to the equation of motion of the scaler field. The evolution of the primordial scalar and tensor perturbations is also studied using the modified Langevin equation. To check the viability of the model we use numerical approaches and plot some figures. Our results for the scalar spectral index and the tensor to scaler rati…
A general form of warm inflation with the dissipative coefficient $Γ=Γ_0(ϕ/ϕ_0) ^n(T/τ_0) ^m$ in loop quantum cosmology is studied. In this case, we obtain conditions for the existence of a warm inflationary attractor in the context of loop quantum cosmology by using the method of stability analysis. The two cases when the dissipative coefficient is independent $(m=0)$ and dependent $(m\neq0)$ on temperature are analyzed specifically. In the latter case, we use the new power spectrum which should be used when considering temperature dependence in the dissipative coefficient. We find that the t…
In this note, we will introduce an action for warm inflation model with direct coupling between the pseudoscalar field and mass-less $SU(2)$ gauge fields. The potential of inflaton is protected against the thermal corrections in a thermal bath of gauge fields even with strong direct interaction between inflaton and light fields. The dissipation parameter of this model is approximately constant in the high-dissipative regime. In this regime, the model is compatible with observational data and non-Gaussianity is in order of Hubble slow-roll parameter $\frac{ε_ϕ}{1+Q}$ even in $f<M_p$ limit.
In this article, we examine the effects of anisotropy on a model of canonical warm inflation with the power-law potential. The results of this model are compared to Planck satellite observational data. Using a conventional local scalar fi?eld in the Bianchi type I metric, the slow-roll conditions and the suitable regions, where the free parameters of the model show a good agreement with Planck results, are investigated in detail. Following the usual calculations for warm inflationary approaches, the early universe in two different dissipative regimes, namely the weak dissipative and the strong…
A warm inflationary universe scenario on a warped Dvali-Gabadadze-Porrati brane during intermediate inflation is studied. We consider a general form for the dissipative coefficient $Γ(T,ϕ)\propto T^{m}/ϕ^{m-1}$, and also study this model in the weak and strong dissipative regimes. We analyze the evolution of the universe in the slow-roll approximation, and find the exact solutions to the equations of motion. In both regimes, we utilize recent data from the BICEP2 experiment and also from the Planck satellite to constrain the parameters in our model in accordance with the theory of cosmological…
In the present paper we study warm inflationary universe models in the context of a polytropic gas. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases, 1- For a constant dissipative parameter $Γ$. 2- $Γ$ as a function of scalar field $ϕ$. In these cases we will obtain exact solution for the scalar field and Hubble parameter. We will also obtain explicit expressions for the tensor-scalar ratio $R$, scalar spectrum index $n_s$ and its running $α_s$, in slow-roll approximation.
Warm inflation is an interesting possibility of describing the early universe, whose basic feature is the absence, at least in principle, of a preheating or reheating phase. Here we analyze the dynamics of warm inflation generalizing the usual slow-roll parameters that are useful for characterizing the inflationary phase. We study the evolution of entropy and adiabatic perturbations, where the main result is that for a very small amount of dissipation the entropy perturbations can be neglected and the purely adiabatic perturbations will be responsible for the primordial spectrum of inhomogenei…
The warm inflation scenario in view of the modified Chaplygin gas is studied. We consider the inflationary expansion is driven by a standard scalar field whose decay ratio $Γ$ has a generic power law dependence with the scalar field $ϕ$ and the temperature of the thermal bath $T$. By assuming an exponential power law dependence in the cosmic time for the scale factor $a(t)$, corresponding to the intermediate inflation model, we solve the background and perturbative dynamics considering that our model evolves according to (i) weak dissipative regime and (ii) strong dissipative regime. Specifica…
The aim of this paper is to explore warm inflation in the background of $f(\mathcal{G})$ theory of gravity using scalar fields for the FRW universe model. We construct the field equations under slow-roll approximations and evaluate the slow-roll parameters, scalar and tensor power spectra and their corresponding spectral indices using viable power-law model. These parameters are evaluated for a constant as well as variable dissipation factor during intermediate and logamediate inflationary epochs. We also find the number of e-folds and tensor-scalar ratio for each case. The graphical behavior …
Two models that unify warm inflation with dark matter and dark energy are proposed. In the models, a single scalar field is responsible for the early expansion of the universe through the process of dissipative warm inflation and then acts as both dark matter and dark energy in subsequent stages. The first model is based on a noncanonical field with the Lagrangian density $\mathcal{L}=F(X)-V(ϕ)$, where the potential is dominant at the slow-roll inflationary epoch and negligible in subsequent stages. The second model takes advantage of a $k$-essence Lagrangian density having the coupled form $\…
