Abstract
Abstract Apart from the assumption that the inflation started at an infinite time in the past, the more realistic initial state of the quantum fluctuations is described by a mixed quantum state imposed at a finite value of the initial time. One of the most important non-trivial vacua is the α-vacuum, which is specified by a momentum cutoff Λ U H Danielsson (2002 Phys. Rev. D 66, 023511). As a consequence, the initial condition is imposed at different initial times for the different k-modes. This modifies the amplitude of the quantum fluctuations, and thus the corresponding power spectra. In this paper, we consider the imprint of the α-vacuum state on the power spectrum of scalar perturbations in a generic f(R) gravity by assuming an ultraviolet cutoff Λ. As a specific model, we consider the Starobinsky model and find the trans-Planckian power spectrum. We find that the leading order corrections to the scalar power spectra in f(R) gravity have an oscillatory behavior as in general relativity C Armendáriz-Picón, Eugene A Lim, (2003 JCAP 12 006), and furthermore, the results are in sufficient agreement with the ΛCDM model.
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