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We investigate a constraint on reheating followed by alpha-attractor-type inflation (the E-model and T-model) from an observation of the spectral index n_s. When the energy density of the universe is dominated by an energy component with the cosmic equation-of-state parameter w_{re} during reheating, its e-folding number N_{re} and the reheating temperature T_{re} are bounded depending on w_{re}. When the reheating epoch consists of two phases, where the energy density of the universe is dominated by uniform inflaton field oscillations in the first phase and by relativistic non-thermalised particles in the second phase, we find a constraint on the e-folding number of the first oscillation phase, N_{sc}, depending the parameters of the inflaton potential. For the simplest perturbative reheating scenario, we find the lower bound for a coupling constant of inflaton decay in the E-model and T-model depending on the model parameters. We also find a constraint on the $alpha$ parameter, alphasimgt 0.01, for the T-model and E-model when we assume a broad resonance reheating scenario.
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We study the evolution of the Universe at early stages, we discuss also preheating in the framework of hybrid braneworld inflation by setting conditions on the coupling constants $lambda $ and $g$ for effective production of $chi$-particles. Considering the phase between the time observable CMB scales crossed the horizon and the present time, we write reheating and preheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in terms of the scalar spectral index $n_{s}$, and prove that, unlike the reheating case, the preheating duration does not depend on the values of the equation of state $omega ^{ast }$. We apply the slow-roll approximation in the high energy limit to constrain the parameters of D-term hybrid potential. We show also that some inflationary parameters, in particular, the spectral index $n_{s}$ demand that the potential parameter $alpha$ is bounded as $alpha geq 1$ to be consistent with $Planck$s data, while the ratio $r$ is in agreement with observation for $ alpha leq 1 $ considering high inflationary e-folds. We also propose an investigation of the brane tension effect on the reheating temperature. Comparing our results to recent CMB measurements, we study preheating and reheating parameters $N_{re}$, $T_{re}$ and $N_{pre}$ in the Hybrid D-term inflation model in the range $0.8leq alphaleq 1.1$, and conclude that $T_{re}$ and $N_{re}$ require $alpha leq 1$, while for $N_{pre}$ the condition $alpha leq 0.9$ must be satisfied, to be compatible with $Planck$s results.
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 Kahler Moduli Inflation. In addition, we extend the de-facto analysis generally done only for the pivot scale to all the observable scales which crossed the Hubble radius during inflation. We study how the maximum number of e-folds varies for different scales, and the effect of the equation of state and potential parameters.
In this paper, we apply reconstruction techniques to recover the potential parameters for a particular class of single-field models, the $alpha$-attractor (supergravity) models of inflation. This also allows to derive the inflaton vacuum expectation value at horizon crossing. We show how to use this value as one of the input variables to constrain the postaccelerated inflationary phase. We assume that the tensor-to-scalar ratio $r$ is of the order of $10^{-3}$ , a level reachable by the expected sensitivity of the next-generation CMB experiments.
We present constraints on the reheating era within the string Fibre Inflation scenario, in terms of the effective equation-of-state parameter of the reheating fluid, $w_{reh}$. The results of the analysis, completely independent on the details of the inflaton physics around the vacuum, illustrate the behavior of the number of $e$-foldings during the reheating stage, $N_{reh}$, and of the final reheating temperature, $T_{reh}$, as functions of the scalar spectral index, $n_s$. We analyze our results with respect to the current bounds given by the PLANCK mission data and to upcoming cosmological experiments. We find that large values of the equation-of-state parameter ($w_{reh}>1/3$) are particularly favored as the scalar spectral index is of the order of $n_ssim 0.9680$, with a $sigma_{n_s}sim 0.002$ error. Moreover, we compare the behavior of the general reheating functions $N_{reh}$ and $T_{reh}$ in the Fibre Inflation scenario with that extracted by the class of the $alpha$-attractor models with $alpha=2$. We find that the corresponding reheating curves are very similar in the two cases.
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. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.
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