Perturbations in some models of tachyonic inflation

In the present work an inflationary tachyon field model of the early universe is considered. Several cosmological effects produced by a particular potential in this tachyonic era are studied, under the approximation of slow-roll inflation. In particular, the evolution of the spectral index $n_s$ with time is obtained. The equations for the cosmological scalar perturbations are analytically solved in order to show that the power spectrum for small $k$ values is $P_ζ\sim 1/k^{\frac{1}{2}+ν_2}$, where $ν_2$ depends on the barotropic index $γ_0$. For large $k$ values we find that the power spectrum is well approximated by the standard inflation model. Additionally, the three-point correlation function is calculated in order to get the primordial non-Gaussianity of the perturbation. The result is that $f_{NG} \simeq 0$ so the non-gaussianities generated by this tachyon field are negligible.

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