Chaotic Inflation with Time-Variable Space Dimensions

TL;DR

This paper explores a model of chaotic inflation where the number of spatial dimensions decreases over time, affecting inflation dynamics and providing bounds on space dimensions at the Planck scale.

Contribution

It introduces a novel inflation model with decreasing space dimensions and derives the impact on inflationary parameters and bounds on dimensions at the Planck scale.

Findings

Space dimension decreases during inflation affecting inflaton field values.

An upper limit for space dimensions at the Planck length is established.

Results align with previous models of variable gravitational constant.

Abstract

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2\phi^2/2$. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.