In this paper, we calculate corrections of scalar perturbations spectra resulting from excited-de Sitter modes as the nontrivial initial states. To obtain these modes, we consider the asymptotic expansion of the Hankel functions up to the higher order of 1 kτ . Actually the Planck and WMAP data impose some constrains on the Hankel function index. These observational constraints and back-reaction effects stimulate us to use excited-de Sitter modes. Finally, we nominate these nontrivial general solutions as the fundamental mode functions during inflation and we calculate the corrected form of scale-dependent power spectrum with trans-Planckian corrections, and in de Sitter space-time limit the results reduce to the scale-invariant power spectrum.

We use the auxiliary fields and (excited-) de Sitter solutions to study the standard power spectrum of primordial fluctuations of a scalar field in the early universe. The auxiliary fields are the negative norm solutions of the field equation and as is shown, with a fixed boundary condition, utilizing these states results in a finite power spectrum without any infinity. The power spectrum is determined by the de Sitter solutions up to some corrections and the space-time symmetry is not broken in this point of view. The modulation to the power spectrum is of order ( H ) 2 , where H is the Hubble parameter and is the energy scale, e.g., the Planck scale.

Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter spacetime as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods.

We present some features of early universe cosmology in terms of Hankel functions index ( ν ). 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 ν [1]. These constrains stimulate us to use general solution of inflaton field equation for ν = 3 2 . To obtain the general solution for the inflationary background, we use asymptotic expansion of Hankel functions up to non-linear order of 1 kη . 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 ν . These results are general and in the quasi-de Sitter and de Sitter limit confirm the conventional results.Pacs: 04.62.+v, 98.80.Cq

The power spectrum of scalar field and space-time metric perturbations produced in the process of inflation of universe, have been presented in this paper by an alternative approach to field quantization namely, Krein space quantization [1,2]. Auxiliary negative norm states, the modes of which do not interact with the physical world, have been utilized in this method. Presence of negative norm states play the role of an automatic renormalization device for the theory.Comment: 8 pages, appear in Int. J. Theor. Phy