We study the dynamics of two concrete inflationary models, namely Spontaneous Symmetry Breaking Inflation as well as Loop Inflation. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results of last year, and we give predictions for the duration of reheating as well as for the reheating temperature after inflation. Our numerical results show that baryogenesis via leptogenesis may be realized within the inflationary models considered in this work.
Reheating connects the inflationary universe to the radiation-dominated evolution of standard Big Bang cosmology. Due to the lack of direct observations, we rely on indirect bounds on this phase from the Cosmic Microwave Background (CMB) data. Using reheating constraints to arrive at additional constraints on inflationary models is prevalent in the literature. In this work, we develop a formalism to analyze the reheating constraints for the general case of single field canonical slow-roll inflation without dealing with a specific inflationary model. We find that using the lower bound on reheat…
We study the two-phase scenario following inflation, where the initial step is preheating, accompanied by a step of perturbative reheating at which inflaton field decays transferring all of its energy to create relativistic particles, the interaction of these particles will evolve towards a state of thermal equilibrium with a temperature Tre called the reheating temperature. It is observed that the scenario of reheating normally predicts the maximum reheating temperature that corresponds to an almost instantaneous transition from inflation to the radiation domination era. This will naturally l…
We investigate the influence on the inflationary predictions from the reheating processes characterized by the $e$-folding number $N_{\mathrm{reh}}$ and the effective equation-of-state parameter $w_{\mathrm{reh}}$ during the reheating phase. For the first time, reheating processes can be constrained in the $N_{\mathrm{reh}}\!-\!w_{\mathrm{reh}}$ plane from Planck 2015. We find that for Higgs inflation with a nonminimal coupling to gravity, the predictions are insensitive to the reheating phase for current CMB measurements. We also find that the spontaneously broken SUSY inflation and axion mon…
For the subclass of Horndeski theory of gravity, we investigate the effects of reheating on the predictions of natural inflation. In the presence of derivative self-interaction of a scalar field and its kinetic coupling to the Einstein tensor, the gravitational friction to inflaton dynamics is enhanced. As a result, the tensor-to-scalar ratio $r$ is suppressed. We place the observational constraints on a natural inflation model and show that the model is now consistent with the observational data for some plausible range of the model parameter $Δ$, mainly due to the suppressed tensor-to-scalar…
We study the effects of perturbative reheating on the evolution of the curvature perturbation ζ, in two-field inflation models. We use numerical methods to explore the sensitivity of f_NL, n_s and r to the reheating process, and present simple qualitative arguments to explain our results. In general, if a large non-Gaussian signal exists at the start of reheating, it will remain non zero at the end of reheating. Unless all isocurvature modes have completely decayed before the start of reheating, we find that the non-linearity parameter, f_NL, can be sensitive to the reheating timescale, and th…
Recently, a combined model of the primordial inflation and the present cosmic acceleration has been proposed in the context of f(R) gravity. This model is composed of the late-time acceleration term and an R2 term, which enables the model to avoid high curvature singularity and describe a quasi-de Sitter inflationary phase in the early Universe. An interesting feature of this model is that the reheating dynamics after the inflation is significantly modified, in contrast to the original R2 model, and affects the shape of a gravitational wave background (GWB) spectrum. Here we investigate the pr…
We investigate a new possible solution to the Hubble constant tension. we propose a simple resolution to the problem assuming that a first-order phase transition related to H0 transition occurred in the early Universe. The early evolution of the Universe is a result of hybrid inflation that has lasted for a specific period until symmetry breaking takes place. Fitting our model to measurements from Planck and SH0ES data provides a key explanation of discrepancies of H0 measurements. The quantum fluctuations calculated in this model have significant results on the reheating parameters Nre and Tr…
In a logamediate inflationary universe model we introduce the curvaton field in order to bring this inflationary model to an end. In this approach we determine the reheating temperature. We also outline some interesting constraints on the parameters that describe our models. Thus, we give the parameter space in this scenario.
The reheating dynamics after the inflation induced by $R^2$-corrected $f(R)$ model is considered. To avoid the complexity of solving the fourth order equations, we analyze the inflationary and reheating dynamics in the Einstein frame and its analytical solutions are derived. We also perform numerical calculation including the backreaction from the particle creation and compare the results with the analytical solutions. Based on the results, observational constraints on the model are discussed.
We present a simple formula that allows to calculate the value of the inflaton field, denoted by $ϕ$, at the scale with wavenumber mode $k$. In the extreme case of instantaneous reheating $ϕ_k$ is calculated exactly and all inflationary observables and quantities of interest follow. This formula, together with the fact that the scale factor $a_p$ at the pivot scale wavenumber $k_p=0.05/Mpc$ lies in the radiation era, allows the development of a diagrammatic approach to study the evolution of the universe. This scheme is complementary to the usual analytical method and some interesting results,…
The epochs of reheating and preheating are studied in a simple extension of the Starobinsky inflationary model, which consists of an $R^2$--correction to the Einstein--Hilbert action and an additional scalar field. We find that if the $R^2$--correction at the end of inflation is dynamically important, it affects the expansion rate and as a consequence the reheating and preheating processes. While we find that the reheating temperature and duration of reheating are only slightly affected, the effect has to be taken into account when comparing the theory to data. In the case of preheating, the g…
The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to …
With the growing consensus on simple power law inflation models not being favored by the PLANCK observations, dynamics for the non-standard inflation gain significant interest in the recent past. In this paper, we analyze in detail a class of supergravity inspired phenomenological inflationary models with non-polynomial potential based on Maity (Nucl.Phys. B919 (2017) 560), and compare the model predictions with the currently most favored Starobinsky and its generalized $α$-attractor models in the ($n_s$ , $r$) plane constrained by PLANCK. Importantly for a wide range of parameter space, our m…
Among primordial magnetogenesis models, inflation is a prime candidate to explain the current existence of cosmological magnetic fields. Assuming conformal invariance to be restored after inflation, their energy density decreases as radiation during the decelerating eras of the universe, and in particular during reheating. Without making any assumptions on inflation, on the magnetogenesis mechanism and on how the reheating proceeded, we show that requiring large scale magnetic fields to remain subdominant after inflation gives non-trivial constraints on both the reheating equation of state par…
We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced in cite{hap, hap2}, we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data cite{Ade, Planck, bicep2} is only possible for reheating temperatures that range between $1$ GeV and $10^4$ GeV. On the other hand, when the universe reheats via the production of massless particles, the viability of the model is only possible when those particles are ne…
We study cosmological inflation and its dynamics in the framework of the Randall-Sundrum II brane model. In particular, we analyze in detail four representative small-field inflationary potentials, namely Natural inflation, Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each characterized by two mass scales. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results. Furthermore, we investigate whether or not those models in brane cosmology are consistent with the recently proposed Swampland Criteria, and give predicti…
Inflation has long been the accepted paradigm for understanding the early universe. Most models of inflation have a scalar field acting as the inflaton particle which decays after inflation during a process called reheating into standard model (SM) particles. In this work, we consider a fermion as the inflaton field. Noether symmetry arguments show that an exponentially expanding universe is possible with a fermion if it is coupled non-minimally to gravity. We use such a scenario in this model to study both inflation and reheating. We find relations between the various parameters involved in t…
We study $α$-attractor models with both E-model and T-model potential in an extended Non-Minimal Derivative (NMD) inflation where a canonical scalar field and its derivatives are non-minimally coupled to gravity. We calculate the evolution of perturbations during this regime. Then by adopting inflation potentials of the model we show that in the large N and small $α$ limit, value of the scalar spectral index ns and tensor to scalar ratio r are universal. Next, we study reheating after inflation in this formalism. We obtain some constraints on the model's parameter space by adopting the results…
We investigate the matter creation processes during the reheating period at the end of inflation in the early Universe, by using the irreversible thermodynamic of open systems. The matter content of the Universe is assumed to consist of the inflationary scalar field, which, through its decay, generates relativistic matter, and pressureless dark matter, respectively. At the early stages of reheating the inflationary scalar field transfers its energy to the newly created matter particles, with the field energy decreasing to near zero. The general equations governing the irreversible matter creat…
We show how to constrain inflationary models and reheating by using mixed constraints. In particular we study the physics of the reheating phase after inflation from observational constraints to the inflationary stage. We show that it is possible to determine $ω$, the equation of state during reheating, by using the reported values of the spectral index and the {\it full} number of $e$-folds $N(n_s,ω)= N_H(n_s)+N_{re}(n_s,w)\approx 60$, which includes the accelerated expansion and the reheating phase. We show that the reheating number of $e$-folds $N_{re}$ is quite sensitive to this equation o…
We consider the 3-form field, which has been considered as a candidate for realizing inflation, coupled to a scalar field which models the relativistic matter particles produced during the reheating epoch. We have investigated the stability conditions for this theory and found that introducing such a coupling does not lead to any ghosts or Laplacian instabilities. We have also investigated the reheating temperature and the production of particles due to parametric resonances. We have found that this process is more efficient in this theory compared to the result of the standard-scalar-field in…
We have tested some simple $Λ$CDM (the same test is also valid for quintessence) inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success.
We study reheating in some one and two field realizations of {\it Fibre Inflation}. We find that reheating begins with a phase of preheating in which long wavelength fluctuation modes are excited. In two field models there is a danger that the parametric amplification of infrared fluctuations in the second scalar field - associated with an entropy mode - might induce an instability of the curvature fluctuations. We show that, at least in the models we consider, the entropy mode has a sufficiently large mass to prevent this instability. Hence, from the point of view of reheating the models we c…
We study observational viability of Natural Inflation with a tachyon field as inflaton. By obtaining the main perturbation parameters in this model, we perform a numerical analysis on the parameter space of the model and in confrontation with $68\%$ and $95\%$ CL regions of Planck2015 data. By adopting a warped background geometry, we find some new constraints on the width of the potential in terms of its height and the warp factor. We show that the Tachyon Natural Inflation in the large width limit recovers the tachyon model with a $ϕ^{2}$ potential which is consistent with Planck2015 observa…
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.
We study particle production at the end of inflation in kinetically driven G-inflation model and show that, in spite of the fact that there are no inflaton oscillations and hence no parametric resonance instabilities, the production of matter particles due to a coupling to the evolving inflaton field can be more efficient than pure gravitational Parker particle production.
The curvaton was introduced recently as a distinct inflationary mechanism for generating adiabatic density perturbations. Implicit in that scenario is that the curvaton offers a new mechanism for reheating after inflation, as it is a form of energy density not diluted by the inflationary expansion. We consider curvaton reheating in the context of a braneworld inflation model, {\em steep inflation}, which features a novel use of the braneworld to give a new mechanism for ending inflation. The original steep inflation model featured reheating by gravitational particle production, but the ineffic…
In this work we address the reheating issue in the context of $F(R)$ gravity, for theories that the inflationary era does not obey the slow-roll condition but the constant-roll condition is assumed. As it is known, the reheating era takes place after the end of the inflationary era, so we investigate the implications of a constant-roll inflation era on the reheating era. We quantify our considerations by calculating the reheating temperature for the constant-roll $R^2$ model and we compare to the standard reheating temperature in the context of $F(R)$ gravity. As we demonstrate, the new reheat…
Reheating is the the epoch which connects inflation to the subsequent hot Big-Bang phase. Conceptually very important, this era is however observationally poorly known. We show that the current Planck satellite measurements of the Cosmic Microwave Background (CMB) anisotropies constrain the kinematic properties of the reheating era for most of the inflationary models. This result is obtained by deriving the marginalized posterior distributions of the reheating parameter for about 200 models taken in Encyclopaedia Inflationaris. Weighted by the statistical evidence of each model to explain the …
Reheating after R^2 inflation proceeds through gravitational particle production of conformally noninvariant fields. We argue that the nonvanishing expectation value of flat directions generic in supersymmetric theories break conformal invariance of the fields coupled to them in a position-dependent manner due to quantum fluctuations. As a result modulated reheating can occur after the supergravity R^2-inflation. The resultant curvature fluctuation is a mixture of the one produced during inflation and that produced by modulated reheating. The spectral index takes a value between n_s=0.960 and …
We have tested some simple quintessential inflation models, imposing that they match with the recent observational data provided by the BICEP and Planck's team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success. Moreover, for the models coming from supergravity one needs to demand low temperatures in order to avoid problems such as the gravitino overproduction or the gravitational production of moduli fields, which are obtained only when the reheating temperature is due to the production of mas…
We consider the scale-invariant inflationary model studied in [1]. The Lagrangian includes all the scale-invariant operators that can be built with combinations of $R$, $R^2$ and one scalar field. The equations of motion show that the symmetry is spontaneously broken after an arbitrarily long inflationary period and a fundamental mass scale is generated. Upon symmetry breaking, and in the Jordan frame, both Hubble function and the scalar field undergo damped oscillations that can eventually amplify Standard Model fields and reheat the Universe. In the present work, we study in detail inflation…
We investigate the dependence of the gravitational wave spectrum from quintessential inflation on the reheating process. We consider two extreme reheating processes. One is the gravitational reheating by particle creation in the expanding universe in which the beginning of the radiation dominated epoch is delayed due to the presence of the epoch of domination of the kinetic energy of the inflaton (kination). The other is the instant preheating considered by Felder et al. in which the Universe becomes radiation dominated soon after the end of inflation. We find that the spectrum of the gravitat…
We investigate the feasibility of models of inflation with a large Gauss-Bonnet coupling at late times, which have been shown to modify and prevent the end of inflation. Despite the potential of Gauss-Bonnet models in predicting favourable power spectra, capable of greatly lowering the tensor-to-scalar-ratio compared to now-disfavoured models of standard chaotic inflation, it is important to also understand in what context it is possible for post-inflationary (p)reheating to proceed and hence recover an acceptable late-time cosmology. We argue that in the previously-studied inverse power law c…
The curvaton reheating in a non-oscillatory inflationary universe model is studied in a Jordan-Brans-Dicke theory. For different scenarios, the temperature of reheating is computed. The result tells us that the reheating temperature becomes practically independent of the Jordan-Brans-Dicke parameter $w$. This reheating temperature results to be quite different when compared with that obtained from Einstein`s theory of gravity.
We study the cosmological inflation and reheating in a teleparallel model of gravity. Reheating is assumed to be due to the decay of a scalar field to radiation during its rapid oscillation. By using cosmological perturbations during inflation, and subsequent evolutions of the Universe, we calculate the reheating temperature as a function of the spectral index and the power spectrum.
In the present work, we study slow-roll inflation in scalar-tensor gravity theories in the presence of both the non-minimal coupling between the scalar field and curvature, and the Galileon self-interaction of the scalar field. Furthermore, we give predictions for the duration of reheating as well as for the reheating temperature after inflation. After working out the expressions for the power spectra of scalar and tensor perturbations in the case of a general non-minimal coupling function that depends solely on the scalar field and a general scalar potential, we focus on the special cases of …
The end of inflation is connected to the standard cosmological scenario through reheating. During reheating, the inflaton oscillates around the minimum of the potential and thus decays into the daughter particles that populate the Universe at later times. Using cosmological evolution for observable CMB scales from the time of Hubble crossing to the present time, we translate the constraint on the spectral index $n_s$ from Planck data to the constraint on the reheating scenario in the context of Kähler Moduli Inflation. In addition, we extend the de-facto analysis generally done only for the pi…
We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt.…
We present predictions of the Kähler moduli inflation model for the spectral tilt by parametrising the reheating epoch by an effective equation-of-state parameter and the number of e-foldings of reheating; and taking into account the post-inflationary history of the model. This model has an epoch in which the energy density of the universe is dominated by cold moduli particles. We compare our results with data from the PLANCK mission and find that exotic reheating (with effective equation of state $w_{\rm re}$ greater than 1/3) is required to match the observations. For canonical reheating cas…
We discuss the possibility of explaining the recent NANOGrav results by inflationary gravitational waves (IGWs) with a blue-tilted primordial spectrum. Although such IGWs can account for the NANOGrav signal without contradicting the upper bound on the tensor-to-scalar ratio at the cosmic microwave background scale, the predicted spectrum is in strong tension with the upper bound on the amplitude of the stochastic gravitational wave background by big-bang nucleosynthesis (BBN) and the second LIGO-Virgo observation run. However, the thermal history of the Universe, such as reheating and late-tim…
A new model for inflation using modified gravity in the Palatini formalism is constructed. Here non-minimal coupling of scalar field h with the curvature R as a general function f(R,h) is considered. Explicit inflation models for some choices of f(R,h) are developed. By writing an equivalent scalar-tensor action for this model and going over to Einstein frame, slow roll parameters are constructed. There exists a large parameter space which satisfies values of n_s and limits on r compatible with Planck 2018 data. Further, we calculate reheating temperature and the number of e-folds at the end o…
In this work we study one of the most appealing string theory-motivated models, we present a tachyonic inflationary model in the recently proposed symmetric teleparallel framework, and examine constraints on tachyon inflation with the exponential potential along with the reheating for a chosen $f(Q)$ gravity model. Considering a reheating phase parametrized by a number of e-folds $N_{re},$ a temperature $T_{re}$, and an equation of state $ω_{re}$, we relate the reheating parameters as functions of the exponential tachyon potential, $f(Q)$ model, and\ the spectral index $n_{s}$ parameters. We a…
Current measurements of the Higgs boson mass and top Yukawa coupling suggest that the effective Higgs potential develops an instability below the Planck scale. If the energy scale of inflation is as high as the GUT scale, inflationary quantum fluctuations of the Higgs field can easily destabilize the standard electroweak vacuum and produce a lot of AdS domains. This destabilization during inflation can be avoided if a relatively large nonminimal Higgs-gravity or inflaton-Higgs coupling is introduced. Such couplings generate a large effective mass term for the Higgs, which can raise the effecti…
Reheating is a transition era after the end of inflation, during which the inflaton is converted into the particles that populate the Universe at later times. No direct cosmological observables are normally traceable to this period of reheating. Indirect bounds can however be derived. One possibility is to consider cosmological evolution for observable CMB scales from the time of Hubble crossing to the present time. Depending upon the model, the duration and final temperature after reheating, as well as its equation of state, may be directly linked to inflationary observables. For single-field…
We study the impact of perturbative reheating on primordial observables in models of multiple-field inflation. By performing a sudden decay calculation, we derive analytic expressions for the local-type non-linearity parameter $f_{\rm NL}^{\rm local}$, the scalar spectral index $n_ζ$, and the tensor-to-scalar ratio $r_T$ as functions of the decay rates of the inflationary fields. We compare our analytic results to a fully numerical classical field theory simulation, finding excellent agreement. We find that the sensitivity of $f_{\rm NL}$, $n_ζ$, and $r_T$ to the reheating phase depends heavil…
As additional perturbative degrees of freedom, it is known that magnetic fields of inflationary origin can source curvature perturbations on super-Hubble scales. By requiring the magnetic generated curvature to remain smaller than its inflationary adiabatic counterpart during inflation and reheating, we derive new constraints on the maximal field value today, the reheating energy scale and its equation of state parameter. These bounds end up being stronger by a few order of magnitude than those associated with a possible backreaction of the magnetic field onto the background. Our results are r…
In this paper, we consider a model of quintessential inflation based upon inverse hyperbolic potential. We employ curvaton mechanism for reheating which is more efficient than gravitational particle production; the mechanism complies with nucleosynthesis constraint due to relic gravity waves. We obtain a lower bound on the coupling constant $g$ that governs the interaction of curvaton with matter fields. We study curvaton decay before domination and decay after domination and plot the allowed region in the parameter space in both cases.
