Inflation and fractional quantum cosmology

TL;DR

This paper explores how fractional quantum cosmology modifies inflationary dynamics, showing that non-local fractional derivatives lead to power-law inflation instead of de Sitter expansion, with results depending on the fractal structure of space-time.

Contribution

It introduces a fractional quantum cosmology framework and demonstrates how non-local fractional derivatives alter inflationary behavior compared to standard models.

Findings

Fractional quantum cosmology predicts power-law inflation instead of de Sitter expansion.

Non-local fractional derivatives influence inflation based on the fractal dimension of space.

Results are independent of the inflaton's energy scale.

Abstract

The Wheeler--DeWitt equation for a flat and compact Friedmann--Lema\^{i}tre--Robertson--Walker cosmology at the pre-inflation epoch is studied in the contexts of the standard and fractional quantum cosmology. Working within the semiclassical regime and applying the WKB approximation, we show that some fascinating consequences are obtained for our simple fractional scenario that are completely different from their corresponding standard counterparts: (i) The conventional de Sitter behavior of the inflationary universe for constant potential is replaced by a power-law inflation. (ii) The non-locality of the Riesz's fractional derivative produces a power-law inflation that depends on the fractal dimension of the compact spatial section of space-time, independent of the energy scale of the inflaton.