INFLATON POTENTIAL RECONSTRUCTION AND GENERALIZED EQUATIONS OF STATE

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Abstract
We extend a previous analysis concerning cosmological fluids with generalized equations of state in order to study inflationary scenarios. In the framework of the slow-roll approximation we find the expressions for the perturbation parameters ε, η and the density perturbation spectra in terms of the adiabatic index γ(a) as a function of the universe scale factor. This connection allows one to find straightforwardly γ(a) corresponding, for example, to the simplest chaotic model and to the Harrison-Zeldovich potential and shows its capability to be applied to more complicated situations. Finally, we use this description to develop a new approach to the early universe dynamics, based on a 1/N expansion, where N is the e-fold number. To this end, we introduce a set of suitable dimensionless variables and show that at the zeroth order in /1N, an improved slow-roll approximation is obtained.
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