The Friedmann equations of cosmology divide the model universes by space geometry into three classes, specified by different values of the scaled curvature parameter k, namely:
Thereafter several cosmologists, among them also I, when extrapolating Friedmann equations back to the past reached the Planck epoch of the Big Bang, characterized by fundamental constants of physics.
Equations (19-20) are known as Friedmann equations
In this section we will try to investigate the solutions to the Friedmann equations
that corresponds to a quintessence scalar field [theta] assuming an equation of state with perfect fluid form .
Some Exact Solutions of the Friedmann Equations
with the Cosmological Term.
In the Friedmann equations
the expansion of the universe is determined solely by the presence of matter or energy, as would be expected since it derives from (1), and it then requires, at the present epoch, some 73% dark energy, 23% dark matter and 4% baryonic matter.
The standard bigbang cosmology then assumes various energy-momentum tensors for the right side of (2) to derive the Friedmann equations
for S in the various phases of the expanding universe [2, pp.