Slow-roll parameters in extended RSII model
The inflation theory proposes a period of extremely rapid (exponential) expansion of the universe during the very early stage of the universe. Although inflationary cosmology has successfully complemented the Standard Model, the process of inflation, primarily the way it begins, is still largely unknown.
A popular class of the inflationary cosmological models introduce a scalar field with nonstandard tachyonic Lagrangian of the Dirac-Born-Infeld (DBI) type. Our research is motivated by the second Randall-Sundrum (RSII) cosmological model. In this work, we study a tachyon cosmological model based on the dynamics of a 3-brane in the RSII model extended to include matter in the bulk. The presence of matter modifies the RSII cosmology and tachyon potential. We study different types tachyonic potential (inverse power law, exponential and inverse cosh) in the context of the braneworld cosmology.
The slow-roll approximation is used only to estimate the initial conditions. The solutions for the dynamics of inflation is calculated numerically. The results are used to calculate the Hubble parameter, as well as the observational parameters for random values of the free parameters in a given range and the corresponding initial conditions.
The results obtained for observational cosmological inflation parameters: the scalar spectral index n_s and the tensor-to-scalar ratio r for a braneworld inflationary scenarios will be presented. The calculated numerical values of observational parameters are compared with the latest results of observations obtained by the Planck Collaboration (2018).