Approach to exact solutions of cosmological perturbations: Tachyon field
  inflation
  An inflationary universe scenario in the context of tachyon field is studied.
This study is done from an ansantz for the effective potential of cosmological
perturbations $U(\eta)$. We describe in great detail the analytical solutions
of the scalar and tensor perturbations for two different ansantz in the
effective potential of cosmological perturbations; the Easther's model and an
effective potential similar to power law inflation. Also we find from the
background equations that the effective tachyonic potential $V(\varphi)$, in
both models satisfy the properties of a tachyonic potential. We consider the
recent data from the Planck data to constrain the parameters in our effective
potential of cosmological perturbations.
