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

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.