Dirac Field in FRW Spacetime: Current and Energy Momentum

TL;DR

This paper analyzes the behavior of Dirac fields in Friedmann-Robertson-Walker spacetime, solving relevant equations to understand particle distributions, energy densities, and their implications for galactic rotation curves and structure formation.

Contribution

It provides new solutions for Dirac fields in FRW spacetime, including approximate methods for general cases and insights into particle current and density evolution.

Findings

One solution decays over time, another grows with the universe expansion.

Particles form a distribution pattern producing a constant Newtonian potential.

Density contrast increases as the universe expands.

Abstract

The behaviour of the Dirac field in FRW space-time is investigated. The relevant equations are solved to determine the particle and energy distribution. The angular and radial parts are solved in terms of Jacobi polynomials. The time dependence of the massive field is solved in terms of known function only for the radiation filled flat space. WKB method is used for approximate solution in general FRW space. Of the two independent solutions, one is found to decay in time as the Universe expands, while the other solution grows. This could be the source of the local particle current. The behaviour of the particle number and energy density are also investigated. It is found that the particles arrange themselves in a number and density distribution pattern that produces a constant Newtonian potential as required for the flat rotation curves of galaxies. Further, density contrast is found to grow with the expansion.