A Cosmology of a Trans-Planckian Theory and Dark Energy

TL;DR

This paper explores a trans-Planckian cosmological model using a generalized Fourier transform on curved spacetime, proposing a novel mechanism where dual sectors influence dark energy and the universe's accelerated expansion.

Contribution

It introduces a trans-Planckian framework with a duality between coordinates and momenta in cosmology, linking the dual sector to dark energy and cosmic acceleration.

Findings

Dual inflationary stage suppresses dual sector at low energies

Dual sector influences matter's equation of state

Model suggests a geometric origin for dark energy

Abstract

We investigate a model based on a generalised version of the Fourier transform for curved space-time manifolds. This model is possible if the metric has an asymptotic flat region which allows a duality to be implement between coordinates and momenta, hence, the models's name, trans-Planckian. The theory and the action are based on the postulate of the absolute egalitarian relation between coordinates $x$ and momenta $p$. We show how to implement this construction in a cosmological setting, on a Friedman-Robertson-Walker metric background, 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. The dual inflationary stage is responsible for making the dual sector of the action inaccessible at ordinary low energies. We propose a scenario in which an effective positive cosmological constant is caused by how the dual sector of the theory affects the equation of state for matter particles.