From these equations, simplified by the cosmological principle for the homogeneous and isotropic universe
, Einstein first derived the stationary model universe by introducing a hypothetical cosmological constant for incorporating Mach's principle.
 revealed that, irrespective of the level of anisotropy in geometry of the universe and dark energy EoS, the SNIa data are always more consistent with standard isotropic universe
It appears that the dynamics of the 3-space, in the presence of primordial black holes, essentially defects in the space emerging from the quantum foam, renders a homogeneous and isotropic universe
dynamically unstable, even without the presence of matter, resulting in a spatial bubble network.
A symmetric and isotropic universe
would have begun with a spherically symmetric explosion shaped like a basketball.
Together, these numbers describe the past, present, and future of any possible homogeneous, isotropic universe
where general relativity is the right theory of gravitation.
The expansion of a homogeneous and isotropic universe
is characterized by the expansion factor S (= S(t)) in the Robertson-Walker line element [3, p.
Let us consider a homogeneous and isotropic Universe
represented by FRW space-time metric as
On the other hand, most cosmologists use the concept of a homogeneous isotropic Universe wherein all points and directions are equivalent.
Relativistic models of a homogeneous isotropic universe (which include the Friedmann solutions) are only a few partial solutions to Einstein's equations.
By combining the basic principles of the thermodynamics of open systems with the cosmological Einstein equations for a flat, homogeneous, and isotropic Universe we obtain a set of first-order ordinary differential equations describing matter creation due to the decay of the scalar field.
Then, by starting from this formulation, we particularize it to the case of a homogeneous and isotropic Universe, by also deriving the entropy of the system .