Scalar field inflation driven by a modification of the Heisenberg algebra

TL;DR

This paper explores how modifying the Heisenberg algebra affects scalar field inflation, showing that such modifications can independently produce exponential expansion without additional sources.

Contribution

It introduces a general framework for modifying the Heisenberg algebra and demonstrates how these modifications can lead to inflationary behavior in cosmology.

Findings

Modified slow roll parameters depend differently on standard parameters.

Analytical solutions for exponential expansion with algebra modifications.

Exponential expansion can occur without a cosmological constant when modifications are significant.

Abstract

We study the modifications induced on scalar field inflation produced by considering a general modification of the Heisenberg algebra. We proceed by modifying the Poisson brackets on the classical theory whenever the corresponding quantum commutator is modified. We do not restrict ourselves to a specific form for such modification, instead we constrain the functions involved by the cosmological behaviour of interest. We present whenever possible the way in which inflation can be realized approximately via three slow roll Hubble parameters that depend on the standard slow roll parameters in a very different form than in the usual case and that can be less restrictive. Furthermore we find a general analytical solution describing an expanding universe with constant Hubble parameter that generalizes the standard cosmological constant case by restricting the form of the modification of the Heisenberg algebra. It is found that even if such modification can be neglected in some limit and the cosmological constant is set to zero in that limit, the exponential expansion is present when the modification is important. Thus an appropriate modification of the Heisenberg algebra is sufficient to produce an exponentially expanding universe without the need of any other source.