Alfven wave in higher dimensional space time

TL;DR

This paper investigates Alfven waves in higher-dimensional cosmological models, analyzing their behavior, velocity, and decay in an expanding universe with magnetic fields, revealing dimension-dependent effects and implications for cosmic magnetic field evolution.

Contribution

It extends magnetohydrodynamics equations to higher-dimensional spacetimes and explores how Alfven wave properties vary with dimensions and cosmic expansion.

Findings

Alfven wave velocity decreases with increasing dimensions.

High-frequency propagation is possible only in certain conditions.

Cosmic magnetic fields decay more rapidly in higher dimensions.

Abstract

Following the wellknown spacetime decomposition technique as applied to (d+1) dimensions we write down the equations of magnetohydrodynamics (MHD) in a spatially at generalised FRW universe. Assuming an equation of state for the background cosmic fluid we find solutions in turn for acous- tic waves and also for Alfven waves in a warm (cold) magnetised plasma. Interestingly the different plasma modes closely resemble the at space coun- terparts except that here the field variables all redshift with their time due to the expansion of the background. It is observed that in the ultrarelativistic limit the field parameters all scale as the free photon. The situation changes in the prerelativistic limit where the frequencies change in a bizarre fashion depending on initial conditions. It is observed that for a fixed magnetic field in a particular medium the Alfven wave velocity decreases with the number of dimensions, being the maximum in the usual 4D. Further for a fixed dimension the velocity attenuation is more significant in dust compared to the radiation era. We also find that in an expanding background the Alfven wave propaga- tion is possible only in the high frequency range, determined by the strength of the external magnetic field, the mass density of the medium and also the dimensions of the spacetime. Further it is found that with expansion the cosmic magnetic field decays more sharply in higher dimensional cosmology, which is in line with observational demand.