چکیده
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The Einstein static (ES) state is a good candidate for describing
the very early universe in terms of a regular cosmological model
in which the Big Bang singularity is avoided. In the present
study we propose an ES solution in the framework of generalized
Rastall gravity (GRG), a modified version of original Rastall theory
in which the coupling parameter is allowed to vary with respect
to the spacetime coordinates. Introducing an ansatz for the
Rastall parameter, existence and the corresponding stability of
the solutions are investigated. We show that the GRG is capable
of describing a stable singularity-free state for the universe. The
problem of transition from an ES to an inflationary state is also
addressed. We find that a time variation of the equation of state
parameter from values lying in the range |w| < 1/3 to the value
w = −1/3 can give rise to such a phase transition. The vector
and tensor perturbations around the ES solution are studied, as
well. In the case of GRG, the vector perturbations remain frozen,
nevertheless, the tenor perturbations can grow in such a way
that the ES solution remains stable provided the ratio of Rastall
gravitational constant to the Einsteinian one always exceeds a
minimum value for each tensor mode.
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