Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

The FRW Universes with Barotropic Fluids in Jordan–Brans–Dicke Theory
and
The line element for the FRW metric in coordinates is
where is the scale factor, and or stands for positive,
vanishing or negative space curvature, respectively.
For a perfect fluid in a FRW cosmology its ordinary, but nonlinear field
equations comprise the two unknown variables and
is the field equation, together with
where overdots stand for time derivatives.
2. BAROTROPIC FLUIDS
The equation with distinguish barotropic
fluids. The conservation equation
yields
However instead of I use in this section the “time parameter
defined by with With it, the field equation is
once formally integrated
where is an integration constant, and
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