The post Newtonian parameter is considered in the Chameleon-Brans-Dicke frame. In the first step, the general form of this parameter and also effective gravitational constant is obtained. An arbitrary function for f (Φ), which indicates the coupling between matter and scalar field, is introduced to investigate validity of solar system constraint. It is shown that Chameleon-Brans-Dicke model can satisfy the solar system constraint and gives us an ω parameter of order 10 4 , which is in comparable to the constraint which has been indicated in [19].

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

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.

Tachyon inflation is reconsidered by using the recent observational data obtained from Planck-2013 and BICEP2. The Hamilton-Jacobi formalism is picked out as a desirable approach in this work, which allows one to easily obtain the main parameters of the model. The Hubble parameter is supposed as a power-law and exponential function of the scalar field, and each case is considered separately. The constraints on the model, which come from observational data, are explained during the work. The results show a suitable value for tensor spectral index and an appropriate form of the potential.

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In this work, we are going to study the inflationary era of the Universe evolution by using second type of Randall-Sundrum model (RS-II) braneworld gravity. It is supposed that the Universe is dominated by scalar field with noncanonical kinetic terms. The kinetic term is supposed as a power-law function, and the work is performed for two typical cases. Using recent observations, the free parameters of the model are determined. It is shown that theoretical results are in acceptable agreement with observational data. Finally the time period of inflation is derived approximately, and it is found out that the inflation could occur after the five-dimensional Planck time.

Using Hamilton-Jacobi formalism, the scenario of warm inflation with viscous pressure is considered. The formalism gives a way of computing the slow-rolling parameter without extra approximation, and it is well-known as a powerful method in cold inflation. The model is studied in detail for three different cases of the dissipation and bulk viscous pressure coefficients. In the first case where both coefficients are taken as constant, it is shown that the case could not portray warm inflationary scenario compatible with observational data even it is possible to restrict the model parameters. For other cases, the results shows that the model could properly predicts the perturbation parameters in which they stay in perfect agreement with Planck data. As a further argument, r − n s and α s − n s are drown that show the acquired result could stand in acceptable area expressing a compatibility with observational data.

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