The constant-roll inflation is studied where the inflaton is taken as a tachyon field. Based on this approach, the second slow-roll parameter is taken as a constant which leads to a differential equation for the Hubble parameter. Finding an exact solution for the Hubble parameter is difficult and leads us to a numerical solution for the Hubble parameter. On the other hand, since in this formalism the slow-roll parameter $\eta$ is constant and could not be assumed to be necessarily small, the perturbation parameters should be reconsidered again which, in turn, results in new terms appearing in the amplitude of scalar perturbations and the scalar spectral index. Utilizing the numerical solution for the Hubble parameter, we estimate the perturbation parameter at the horizon exit time and compare it with observational data. The results show that, for specific values of the constant parameter $\eta$, we could have an almost scale-invariant amplitude of scalar perturbations. Finally, the attractor behavior for the solution of the model is presented, and we determine that the feature could be properly satisfied.

We investigate warm inflationary scenario in which the accelerated expansion of the early Universe is driven by chameleon-like scalar fields. Due to the non-minimal coupling between the scalar field and the matter sector, the energy-momentum tensor of each fluid component is not conserved anymore, and the generalized balance equation is obtained. The new source term in the energy equation can be used to model warm inflation. On the other hand, if the coupling function varies slowly, the model reduces to the standard model used for the description of cold inflation. To test the validity of the warm chameleon inflation model, the results for warm inflationary scenarios are compared with the observational Planck2018 Cosmic Microwave Background data. In this regard, the perturbation parameters such as the amplitude of scalar perturbations, the scalar spectral index and the tensor-to-scalar ratio are derived at the horizon crossing in two approximations, corresponding to the weak and strong dissipative regimes. As a general result it turns out that the theoretical predictions of the chameleon warm inflationary scenario are consistent with the Planck 2018 observations.

In this study, the scenario of a two-component warm tachyon inflation is considered, where the tachyon field plays the role of the inflaton by driving the inflation. During inflation, the tachyon scalar field interacts with the other component of the Universe, which is assumed to be photon gas, i.e., radiation. The interacting term contains a dissipation coefficient, and the study is modeled based on two different and familiar choices of the coefficient that were studied in the literature. By employing the latest observational data, the acceptable ranges for the free parameters of the model are obtained. For any choice within the estimated ranges, there is an acceptable concordance between the theoretical predictions and observations. Although the model is established based on several assumptions, it is crucial to verify their validity for the obtained values of the free parameters of the model. It is found that the model is not self-consistent for all values of the ranges, and for some cases, the assumptions are violated. Therefore, to achieve both self-consistency and agreement with the data, the parameters of the model must be constrained. Subsequently, we consider the recently proposed swampland conjecture, which imposes two conditions on the inflationary models. These criteria rule out some inflationary models; however, warm inflation is among those that successfully satisfy the swampland criteria. We conduct a precise investigation, which indicates that the proposed warm tachyon inflation cannot satisfy the swampland criteria for some cases. In fact, for the first case of the dissipation coefficient, in which, there is dependency only on the scalar field, the model agrees with observational data. However, it is in direct tension with the swampland criteria. Nevertheless, for the second case, wherein the dissipation coefficient has a dependency on both the scalar field and temperature, the model exhibits acceptable agreement with observational data, and suitably satisfies the swampland criteria.

The ACT data shows an enhancement in the value of the scalar spectral index, as n_s = 0.9743 ± 0.0034, leading to disfavoring many inflationary models, including the Starobinsky model. To satisfy the constraint made by ACT, we will investigate the Starobinsky potential within the Einstein-Gauss-Bonnet(EGB) gravity theory. EGB gravity is motivated by the higher-dimensional theory, which includes quadratic curvature correction terms and a coupling between the scalar field and the GB term that modifies the dynamical equations. The model is considered by using the slow-roll approximation method and the exact numerical approach for two different coupling functions. The results indicate that the model is in good agreement with the data and the results stand in 1σ of the ACT r-n_s plane. Considering the running of the scalar spectral index also implies the consistency of the model with data. In addition, the parametric space of the free parameters of the EGB coupling is explored, where we find the acceptable region of the parameters in which the resulting n_s and r stay in 1σ of the ACT data. Next, the reheating phase is considered. It is determined that the model can simultaneously satisfy the constraint of ACT data and the reheating temperature constraints.

The Hamilton-Jacobi formalism as a powerful method is being utilized to reconsider the warm inflationary scenario, where the scalar field as the main component driving inflation interacts with other fields. Separating the context into strong and weak dissipative regimes, the goal is followed for two popular functions of $\mathrm{\Gamma }$. Applying slow-rolling approximation, the required perturbation parameters are extracted and, by comparing to the latest Planck data, the free parameters are restricted. The possibility of producing an acceptable inflation is studied where the result shows that for all cases the model could successfully suggest the amplitude of scalar perturbation, scalar spectral index, its running, and the tensor-to-scalar ratio.

The scenario of constant-roll inflation in the framework of a noncanonical inflaton model is studied. Both of these modifications lead to the appearance of some differences in the slow-roll parameters besides the Friedmann equations, resulting in a better justification of theoretical predictions compared to observations. Phenomenologically, by assuming a constant $\eta$, i.e., a second slow-roll parameter, and recalculating the related perturbation equations, obviously there should appear some modification in the scalar spectral index and amplitude of scalar perturbations. It is shown that finding an exact solution for the Hubble parameter is one of the main advantages and triumphs of this approach. Also, whereas making a connection between subhorizon and super-horizon regions has a crucial role in inflationary studies, the main perturbation parameters are obtained at the horizon crossing time. To examine the accuracy of our results, we consider the Planck 2018 results as a confident criterion. To do so by virtue of the $r-n_s$ diagram, the acceptable ranges of the free parameters of the model are illustrated. As a result, it is found that the second slow-roll parameter should be a positive constant and smaller than unity. By constraining the free parameters of the model, also, an energy scale of inflation is estimated that is of order ${10}^{-2}$. Even more, by investigating the attractor behavior of the model, it is clear that the aforementioned properties can be appropriately satisfied.