According to a Barrow solution for the scale factor of the universe, the main properties of the tachyon inflation model in the framework of the RSII braneworld are studied. Within this framework the basic slow-roll parameters are calculated analytically. We compare this inflationary scenario to the latest observational data. The predicted spectral index and the tensor-to-scalar fluctuation ratio are in excellent agreement with those of Planck 2015. The current predictions are consistent with those of viable inflationary models.
The set up and motivationThe standard model of inflation is driven by a scalar inflaton (quanta of the inflationary field) field can be traced back to early efforts to solve the basic problems of the Big-Bang cosmology, namely horizon, flatness and monopole [1,2] problems. The nominal inflationary paradigm contains two mainly different segments: the slow-roll and the (p)reheating regimes. In the slow-roll phase the kinetic part of energy (which has the canonical form here) of the scalar field is negligible with respect to the potential part of energy V (φ), which implies a nearly de Sitter expansion of the universe. However, after the slow-roll epoch the kinetic energy becomes comparable to the potential energy and thus the inflaton field oscillates around the minimum at the (p)reheating phase and progressively the universe is filled by radiation [3,4]. In order to achieve inflation one can use tachyon scalar fields for which the kinetic term does not follow the canonical form (kinflation [5]). It has been found that tachyon fields which are associated with unstable D-branes [6] may be responsible for the cosmic acceleration phase in early times [5,7,8]. Notice that the tachyon potential has the following two properties: the maximum of the potential occurs when φ → 0, while a