  We present some features of early universe cosmology in terms of Hankel
functions index ($\nu$). Actually, the recent data from observational cosmology
indicate that our universe was nearly de Sitter space-time in the early times
which results in an approximate scale-invariant spectrum. This imposes some
constrains on index $\nu$ [1]. These constrains stimulate us to use general
solution of inflaton field equation for $\nu\neq{\frac{3}{2}}$. To obtain the
general solution for the inflationary background, we use asymptotic expansion
of Hankel functions up to non-linear order of $\frac{1}{k\eta}$. We consider
the non-linear modes as the fundamental modes for early universe during the
inflation. In this paper, we obtain the general form of the inflationary modes,
scale factor expansion, equation of state and some non-linear corrections of
power spectrum in terms of index \nu. These results are general and in the
quasi-de Sitter and de Sitter limit confirm the conventional results.
