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arXiv · 2307.04196

Trans-Planckian Effect in $f(R)$ Cosmology

S. Cheraghchi·F. Shojai·M. H. Abbassi
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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 $Λ$ \cite{Danielsson:2002kx}. 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 \cite{Lim}, and furthermore, the results are in sufficient agreement with the $Λ$CDM model.

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S. Cheraghchi, F. Shojai, M. H. Abbassi. 2023-07-09. Trans-Planckian Effect in $f(R)$ Cosmology. https://doi.org/10.1088/1402-4896%2Face706

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