Generally covariant model of a scalar field with high frequency dispersion and the cosmological horizon problem
Abstract
Short distance structure of spacetime may show up in the form of high frequency dispersion. Although such dispersion is not locally Lorentz invariant, we show in a scalar field model how it can nevertheless be incorporated into a generally covariant metric theory of gravity provided the locally preferred frame is dynamical. We evaluate the resulting energymomentum tensor and compute its expectation value for a quantum field in a thermal state. The equation of state differs at high temperatures from the usual one, but not by enough to impact the problems of a hot big bang cosmology. We show that a superluminal dispersion relation can solve the horizon problem via superluminal equilibration; however it cannot do so while remaining outside the Planck regime unless the dispersion relation is artificially chosen to have a rather steep dependence on the wave vector.
 Publication:

Physical Review D
 Pub Date:
 February 2001
 DOI:
 10.1103/PhysRevD.63.041502
 arXiv:
 arXiv:hepth/0009052
 Bibcode:
 2001PhRvD..63d1502J
 Keywords:

 04.20.Cv;
 98.80.Cq;
 Fundamental problems and general formalism;
 Particletheory and fieldtheory models of the early Universe;
 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 4 pages, 1 figure