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Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method

Abstract:

The phase-integral approximation devised by Fröman and Fröman is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform-approximation methods. © 2009 The American Physical Society.