Shadows of trans-planckian physics on cosmology and the role of the zero-point energy density

TL;DR

This paper explores how trans-Planckian physics and zero-point energy influence cosmological evolution, predicting a link between primordial scalar perturbations and dark energy properties through a modified Einstein framework.

Contribution

It introduces a generalized Einstein equation incorporating zero-point energy regularized by a cutoff, linking trans-Planckian effects to cosmological parameters and perturbation spectra.

Findings

Logarithmic behavior of the Hubble parameter during inflation.

Predicted scalar spectral index ns depends on cutoff Lambda.

Dark energy equation of state w related to ns by w=-(2+ns)/3.

Abstract

We consider the role of the zero-point energy of a quantum field in cosmology and show that the flow of trans-planckian momenta due to redshift acts as a source for this energy, regularized with a cut-off Lambda in physical momenta. In order to fulfill Bianchi identity, we generalize Einstein equations, and discuss the corresponding Friedmann homogeneous and isotropic models. In case of a de Sitter phase, such as during inflation, the solution shows a logarithmic behaviour of the Hubble parameter, and a primordial spectrum of scalar perturbations characterized by the spectral index ns= 1- Lambda2/(3 pi mP2) with mP the Planck mass. We also discuss possible implications of the scenario on late accelerating stage of the Universe at small redshifts, and the emergence of a fluid characterized by an equation of state w=P/rho= -1+ Lambda2/(9 pi mP2). Primordial perturbation spectrum and dark energy parameter w are thus, predicted to be connected by the simple relation w=-(2+ns)/3.