Minimum Length Universe in a Robertson Walker Geometry

TL;DR

This paper introduces a model where a minimum length universe, enforced by a diffusive field, modifies standard cosmological equations, leading to new insights into universe expansion, the cosmological constant, and the role of diffusion without requiring dark matter.

Contribution

It develops a novel framework incorporating diffusive fields into spacetime geometry, deriving modified cosmological equations and linking diffusion parameters to observable universe expansion properties.

Findings

Derived a relationship between diffusion, expansion acceleration, and expansion speed.

Expressed the cosmological constant as a function of minimum length and Higgs field.

Showed the universe can have higher deceleration parameters without dark matter.

Abstract

A minimum length universe is enforced via a diffusive Markovian field. Requiring the invariance of the proper time functional under spacetime transformations generated by such fields provides us with many new terms added to the Christoffel Connection, Equations of Motion, and Friedmann Equation. Under the Robertson-Walker (RW) metric, we obtain species-specific energy-density evolution, now a function of both the parameters defining the diffusive fields as well as the RW scale factor. The math leads us to a relationship between temporal diffusion, universe expansion acceleration, and the speed of universe expansion, along with a derivation of the cosmological constant as a function of both minimum length and the scalar field expectation value of the Higgs mechanism. The theory gives us a means of relating the Hubble parameter to its diffusive ML 'equivalent', and a means to express the effective equation of state in terms of the deceleration parameter, q. We find that q can take on a range of higher values without invoking the need for a dark matter species, and that the universe inhabits a vacuum or matter dominated regime as a function of q.