1207.5514 (Stefano Bolognesi)

Cosmology of a Trans-Planckian Theory and the Dark Energy    [PDF]

Stefano Bolognesi

We here continue the investigation of the trans-Planckian theory introduced in arXiv:0908.3034. This model is based on a generalized version of the Fourier transform for curved space-time manifolds. This construction is made possible if the metric has an asymptotic flat region which allows to implement a duality between coordinates and momenta, hence the name trans-Planckian. The theory and the action are based on the postulate of absolute egalitarian relation between coordinate x and momenta p. Extension to the curved interior of the manifolds is constrained by requirement of diffeomorfism and gauge invariances. We show how to implement this in an explicit cosmological setting with a Friedman-Robertson-Walker metric where the asymptotic time infinity plays the role of the required asymptotic flat region. We discuss the effect of gravity, and in particular of the Hubble expansion of the universe scale factor, on the Fourier map and of the inflationary stage in making the dual sector of the action not accessible at ordinary low energies. We propose a scenario in which the dark energy is due to the reappearance at late-time of the dual sector which affects the equation of state for a dark matter particle in a way to account for a fake cosmological constant term. The magnitude of the dark energy term is directly related to the number of e-folds of the inflationary stage and fits the measured value for exactly the minimal number of e-folds required to solve the horizon problem.

View original: http://arxiv.org/abs/1207.5514