Abstract
We consider a generalized Starobinski inflationary model. We present a method for computing solutions as generalized asymptotic expansions, both in the kinetic dominance stage (psi series solutions) and in the slow roll stage (asymptotic expansions of the separatrix solutions). These asymptotic expansions are derived in the framework of the Hamilton-Jacobi formalism where the Hubble parameter is written as a function of the inflaton field. They are applied to determine the values of the inflaton field when the inflation period starts and ends as well as to estimate the corresponding amount of inflation. As a consequence, they can be used to select the appropriate initial conditions for determining a solution with a previously fixed amount of inflation.
Highlights
We consider a generalized Starobinski inflationary model
We have analysed the asymptotic properties of the solutions of a generalization of the Starobinski inflationary model determined by the potential (4)
We have considered both the kinetic dominance and the slow roll periods within the Hamilton-Jacobi formalism, which provides a natural framework to determine generalized asymptotic expansions of the Hubble parameter as a function of the inflaton field
Summary
Let us begin with the Hamilton Jacobi formulation of the inflationary models (1). Due to (7) the parameter c3 is defined as c3 = c1 λ c2 μ c1 λ (12). In this work we use Plank units ( G = c = h = 1). We have that (see for example [15]) Λ4 = 10−10 m2Pl , so the coefficients c j , j = 1, 2, 3 are of order 10−10
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