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 ratio show good consistency with observations.
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 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 …
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 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.
We study the seemingly duality between large and small $η_H$ for the constant-roll inflation with the second slow-roll parameter $η_H$ being a constant. In the previous studies, only the constant-roll inflationary models with small $η_H$ are found to be consistent with the observations. The seemingly duality suggests that the constant-roll inflationary models with large $η_H$ may be also consistent with the observations. We find that the duality between the constant-roll inflation with large and small $η_H$ does not exist because both the background and scalar perturbation evolutions are very …
The slow roll approximation is studied for cosmological models in Hyperextended Scalar-Tensor Theories of Gravity. A procedure to obtain slow roll solutions in non-minimally coupled gravity is outlined and some examples are provided. An integral condition over the functional form of the non-minimal coupling is imposed in order to obtain intermediate inflationary behavior.
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.
We consider the classical wave equation with a thermal and Starobinsky-Vilenkin noise which in a slow-roll and long wave approximation describes the quantum fluctuations of the graviton-inflaton system in an expanding metric. We investigate the resulting consistent stochastic Einstein-Klein-Gordon system in the slow-roll regime. We show in some models that the slow-roll requirements (of the negligence of $\partial_{t}^{2}ϕ$) can be satisfied in the probabilistic sense for the stochastic system with quantum and thermal noise for arbitrarily large time and an infinite range of fields. We calcula…
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…
We study power law inflation in the context of non-minimally coupled to the scalar curvature. We analyze the inflationary solutions under an exact analysis and also in the slow roll approximation. In both solutions, we consider the recent data from Planck and BICEP2 data to constraint the parameter in our model. We find that the slow roll approximation is disfavored in the presence of non-minimal couplings during the power law expansion of the Universe.
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 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.
The slow-roll approximation is the usual starting point to study the constraints imposed on the inflaton potential parameters by the observational data. We show that, for a potential exhibiting at least two extrema and giving rise to a limited inflationary period, slow-roll does not have to be taken as an additional hypothesis and is in fact forced by the constraints on the number of e-foldings.
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…
Slow roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the last few years there has been growing interest in a new class of inflationary models known as Constant-Roll Inflation. Constant roll solutions are a generalization of "ultra-slow roll" dynamics, where the first slow roll parameter is small, but the second slow roll parameter $η$ is larger than unity. In Ultra-slow Roll Inflation, the large-$η$ solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant roll generalization, rece…
We investigate the slow-roll inflation in the nonminimal derivative coupling (NDC) model with exponential, quadric, and quartic potentials. It was known that this model provides an enhanced slow-roll inflation induced by gravitationally enhanced friction even for a steep exponential potential. In the phase portrait, the inflationary attractor is described by the slow-roll equation. Introducing the autonomous form, the inflation is regarded as an emergence from the saddle point and it leaves this fixed point along the slow-roll equation. We show explicitly that if one uses the NDC with potentia…
The minimal warm inflation model was constructed as a warm inflation setup with direct interaction between inflaton and (non-Abelian) gauge fields. The model was shown to be compatible with observation for some forms of potential. As a result of direct analysis of CMB data, the model presents a reasonable phase-space of its parameter compatible with observation and the Trans-planckian censorship conjecture (TCC).
We discuss under which conditions multi-field cold and warm inflationary models with canonical kinetic energy terms are compatible with the swampland conjectures about the emergence of de Sitter solutions in string theory. We find that under quite general conditions the slow-roll conditions for multi-field cold inflation are at odds with the swampland conjectures for an arbitrary number of scalar fields driving inflation. However, slow-roll conditions can be reconciled with the swampland conjectures in the strong dissipative regime of warm inflation.
For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio up to the first order by using the method of Bessel function approximation. The derived $n_s-r$ results for the constant-roll inflation are also compared with the observations, we find that only one constant-roll inflation is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflat…
Warm inflation in the non minimal derivative coupling model with a general dissipation coefficient is considered. We investigate conditions for the existence of the slow roll approximation and study cosmological perturbations. The spectral index, and the power spectrum are calculated and the temperature of the universe at the end of the slow roll warm inflation is obtained.
Warm inflation dynamics is reviewed. Results on dissipative scalar field dynamics relevant to warm inflation are examined and estimates of radiation production are given.
The bispectrum of scalar mode density perturbations is analysed for the strong regime of warm inflationary models. This analysis generalises previous results by allowing damping terms in the inflaton equation of motion that are dependent on temperature. A significant amount of non-gaussianity emerges with constant (or local) non-linearity parameter $f_{NL}\sim 20$, in addition to the terms with non-constant $f_{NL}$ which are characteristic of warm inflation.
We propose a new approach to constant-roll warm inflation as a generalization of constant-roll inflation. Based on the $β$-function formalism, it is shown that constant-roll warm inflation models with a natural end fall into universality classes defined by three different types of $β$-functions, under the assumption that radiation energy density is quasi-stable. Given that warm inflation is completely specified by the $β$-function and dissipation coefficient ratio, we investigate whether or not the inflation can physically be realized for enough number of e-foldings at the background level for…
Inflation predicts the generation of cosmological perturbations. Usually, the power spectra for the scalar and tensor modes are calculated with help of the slow roll approximation. In the case of power law inflation an exact result is available. We compare the predictions for the cosmic microwave background anisotropies from the slow roll approximation with the exact results from power law inflation. We find that the so-called consistency check from the slow roll approximation, $C_2^T/C_2^S \approx -6.93 n_T$, may differ considerably from the exact result.
Ideas borrowed from renormalization group are applied to warm inflation to characterize the inflationary epoch in terms of flows away from the de Sitter regime. In this framework different models of inflation fall into universality classes. Furthermore, for warm inflation this approach also helps to characterise when inflation can smoothly end into the radiation dominated regime. Warm inflation has a second functional dependence compared to cold inflation due to dissipation, yet despite this feature, it is shown that the universality classes defined for cold inflation can be consistently exten…
Constant-roll warm inflation is introduced in this work. A novel approach to finding an exact solution for Friedman equations coupled to scalar field equation of motion is presented for cold inflation and is extended to warm inflation with the constant dissipative parameter $Q=\fracΓ{3H}$. The evolution of the primordial inhomogeneities of a scalar field in a thermal bath is also studied. The $1σ$ consistency between the theoretical predictions of the model and observational constraints has been proven for a range of $Q$ and $β=\frac{\ddotϕ}{3Hϕ}$ (constant rate of inflaton roll). In addition,…
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.
Warm inflation, its different particle physics model implementations and the implications of dissipative particle production for its cosmology are reviewed. First, we briefly present the background dynamics of warm inflation and contrast it with the cold inflation picture. An exposition of the space of parameters for different well-motivated potentials, which are ruled out, or severely constrained in the cold inflation scenario, but not necessarily in warm inflation, is provided. Next, the quantum field theory aspects in realizing explicit microscopic models for warm inflation are given. This …
By extending the potential, we propose a mechanism for the end of the constant-roll inflation and the subsequent reheating phase in the FLRW space-time. Based on astrophysical data, we estimate the Universe reheating temperature.
In warm inflation scenarios, radiation always exists, so that the radiation energy density is also assumed to be finite when inflation starts. To find out the origin of the non-vanishing initial radiation energy density, we revisit thermodynamic analysis for a warm inflation model and then derive an effective Stefan-Boltzmann law which is commensurate with the temperature-dependent effective potential by taking into account the non-vanishing trace of the total energy-momentum tensors. The effective Stefan-Boltzmann law shows that the zero energy density for radiation at the Grand Unification e…
By using the relations between the slow-roll parameters and the power spectrum for the single field slow-roll inflation, we derive the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ for the constant slow-roll inflation and obtain the constraint on the slow-roll parameter $η$ from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the $…
In the cold inflation scenario, the slow roll inflation and reheating via coherent rapid oscillation, are usually considered as two distinct eras. When the slow roll ends, a rapid oscillation phase begins and the inflaton decays to relativistic particles reheating the Universe. In another model dubbed warm inflation, the rapid oscillation phase is suppressed, and we are left with only a slow roll period during which the reheating occurs. Instead, in this paper, we propose a new picture for inflation in which the slow roll era is suppressed and only the rapid oscillation phase exists. Radiation…
