1. Introduction :
Cosmological models play a vital role
in the understanding of the universe around us.
The present day universe appears, an astronomical consideration, to be
of the friedmann-Robertson- Walker (FRW) type.
That is the standard FRW Cosmological model which prescribes a homogeneous
and Isotropic distribution for its matter content, has been quite successful in
describing the present state of the universe. Recently higher dimensional space
time is an active field of research in the attempts to unify gravity with other
gauge interaction 30. The concept of extra dimensions is relevant in
cosmology particularly at the early universe-theoretically the present 4D stage
of the universe might have been preceded by a multidimensional phase. In fact
there exist solutions of Einstein’s equations such that, as time evolves, the
standard dimensions expand while extra space shrinks to planckian dimension
beyond our ability to detect with the currently available experimental
facilities (Chatterjee 31, 32 and Chatterjee et al 9. It is encouraging to
note that both the concept of higher dimensional space time and string theory
assumed added importance in the domain of the early universe.
The concept of string theory was
developed to describe events of the early stage of the evolution of the
universe. The general relativistic treatment of strings was initiated by
Stachel 33 and Letelier 34. The gravitational effects of cosmic strings
have been extensively discussed by vilenkin 35. Gott 36 in general relativity. Relativistic string models in the context of
Bianchi space time have been obtained by Krori et. al. 37. Banerjee and Bhuj 38, Tikekar and Patel 39.
In this study, I will attach strange
quark matter to string cloud. It is
plausible to attach strange quark matter to the string cloud. Because, one of such transitions during the
phase transitions of the universe could be Quark Glucon Plasma (OGP) – hardon
gas (called quark-hardon phase transition) when cosmic temperature was T » 200
Mev. The possibility of the existence of quark matter dates back to early
seventies. Bodmer 12 and Witten 13
proposed two ways of formation of strange matter. The quark-hadrom phase
transition in the early universe and conversion of neutron stars into strange
ones at ultrahigh densities. In the
theories of strong interaction quark bag models suppose that breaking of
physical vacuum takes place inside hadrons.
As a result vacuum energy densities inside and outside a hadron become
essentially different and the vacuum pressure on the bag wall equilibrates the
pressure of quarks matter is true, then some of neutrons stars could actually
be strange stars, built entirely of strange matter 14, 15.
Typically, strange quark matter is
modeled with an equation of state based on the phenomenological bag model of
quark matter, in which quark confinement is described by an energy term
proportional to the volume. In this model, quarks are though as degenerate
Fermi gales, which exist only in a region of space endowed with a vacuum energy
density BC (called as the bag constant). Also, in the framework of this model the
quark matter is composed of mass less u, d quarks, massive s quarks and
In the simplified version of the bag
model, it is assumed that quarks are mass less and non interacting. So, we have quark pressure.
Pq = . (1)
me quark energy density
The total energy density is
r = rq + Bc
the total pressure is
P = Pq
– Bc (3)
this paper, I have solved Einstein’s field equations for Five dimensional
Bianchi type-III, Space- time with strange quark matter attached to the string