Constraining inflationary models using cosmological observables

In the present thesis, we attempt to find the constraints imposed by recent observational data on two widely-used inflationary models, including non-minimal inflation and Starobinsky inflation. The first part of the manuscript is dedicated to introducing some theoretical and observational foundations of cosmology which are necessary for the research chapters and the second part is devoted to present the results obtained by my published papers. In the first part, we start by introducing the principles of Einstein's gravity and the field equations as the foundation of the standard cosmology. Then, we study the dynamical universe for different single-component cases and also the present time. The thermal history of the universe is examined in detail based on the temperature and time of the universe in each stage. Then, we review the observational proofs and also shortcomings of the Hot Big Bang model. We introduce the idea of cosmic inflation and show how inflation can remove the mentioned defects of the Hot Big Bang model. In the following, we go dipper into cosmic inflation by presenting the standard inflationary formalism and some common inflationary models. Moreover, the reheating process and the primordial perturbations generated during the inflationary era are discussed in detail. The thesis is followed by dedicating a chapter to study the physics of cosmic microwave background radiation as the main source of inflationary observables. Particularly, we study the primary temperature and polarization anisotropies of cosmic background photons generated by inflationary perturbations in the early universe and also express how can we use the observables to constraint our inflationary models. The second part of the thesis is devoted to the research works carried out during my Ph.D. course about finding the observational constraints on inflationary models. The main purpose of the first research work is finding the cosmic microwave background anisotropies constraints on parameters space of power-law inflationary potentials in the context of non-minimal coupling of gravity and inflaton. Also, we study the effects of the presence of the non-minimal coupling term on the predicted amount of gravitational waves in such models. We carry out the inflationary analysis for the power-law potentials with the non-minimal coupling term in the Einstein frame as the easier frame which is conformally connected to the Jordan frame as the non-minimal frame. We consider two main classes of large field potentials, e.g., n=4 and n eq4 with integer and fractional values. The inflationary parameters in both cases are calculated up to the first order of the slow-roll parameters, where we are assured that the results of the two frames are the same. In order to use the observational data, we use a model-depended analysis method in which N and \xi as the independent parameters driven by modified CosmoMC code can be randomly sampled in a given range and to calculate the inflationary parameters of the model. Finally, we provide the final results by the corresponded plots and tables. Our second research work is dedicated to finding constraints on inflationary parameters using a set of recent cosmic microwave background data and under the assumption of the Starobinski model. Also, we consider a particular class of inflationary models that generalize Starobinsky inflation and the possibility of an extension to LambdaCDM described by the A_lens parameter. We present the inflationary analysis for the generalized form of the Starobinsky model and use the conformal transformation to mapping to the Einstein frame as the conformal frame. Then, we follow the inflationary analysis in the presence of a new scalar field, which is called scaleron, created due to using the conformal transformation. We calculate the inflationary parameters up to the first order of the slow-roll parameters for two main classes, p=1 or Starobinsky model and p eq1 for a generalized case. Similar to the previous model, we use a model-depended analysis method wherein N and p as the independent parameters driven by modified CosmoMC code, can be randomly sampled in a given range and to calculate the inflationary parameters of the model. Lastly, we examine the final results by the corresponded plots and tables.