Abstract
The well known (3+1) decomposition of Thorne and Macdonald is invoked to write down the Einstein–Maxwell equations generalizedto (d+1) dimensions and also to formulate the plasma equations in a flat Friedmann–Robertson–Walker-likespacetime in higher dimensions. Assuming an equation of state for the background metricwe find solutions also as dispersion relations in different regimes of the universe in a unifiedmanner, both for magnetized and for unmagnetized cold plasma. We find that for a freephoton in an expanding background we get maximum redshift in 4D spacetime, while for aparticular dimension this occurs in the pre-recombination era. Further wave propagation inmagnetized plasma is possible for a restricted frequency range only, dependingon the number of dimensions. It is worth pointing out that, unlike the case forthe special relativistic result, this allowed range evolves with time. Interestinglythe dielectric constant of the plasma media remains constant, not sharing theexpansion of the background, which generalizes a similar 4D result of Holcomb andTajima for a radiation background to the case of higher dimensions with cosmicmatter obeying an equation of state. Further, like for the flat space static case,we observe the phenomenon of Faraday rotation in the higher dimensional casealso.
Highlights
While great strides have been made by general relativists to address the issues coming out of the recent observations in the field of astrophysics and cosmology and despite the fact that more than 90 percent of the cosmic stuff in stellar interior and intergalactic spaces is made up of matter in plasma state the much sought after union between the plasma dynamics and general relativity still remains elusive
We occasionally come across stray works like ‘plasma suppression of large scale structure formation in the universe’ [1] as even the simulation techniques [2] where it is argued that the geometry of the spacetime can be purported to be structured by observing sound waves in primordial plasmas the fact remains that as the field equations both in general relativity and plasma dynamics are highly nonlinear it is very difficult to obtain closed form solutions in physics
The Milky Way possesses a magnetic field whose strength is of the order of the microgauss corresponding to an energy density roughly comparable with the energy density today stored in the Cosmic Microwave Background Radiation (CMBR) energy spectrum peaked around a frequency of 30 GHz
Summary
On the other hand there has been, of late, a resurgence of interests in physics in higher dimensional spacetime [9] in its attempts to unify all the forces in nature, to give a physical explanation of the current accelerating era of the universe without bringing in any hypothetical quintessencial type of scalar field [10] by hand, in the newly fashionable area of brane cosmology [11] where the gravity is supposed to act in the bulk while other forces in the physical 3D space It has received serious attention in the recently proposed induced matter theory pioneered by Wesson and others [12].
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