if the density parameter is bigger than 1 and that the curvature is positive , so the universe is spherical and the dark energy permits a spherical expansion simply .......the real vaccuum so is this dark energy and is probably a fifth force antigravitational and informational.
The relationship between the density parameter, curvature, and dark energy in the context of cosmology is described by the Friedmann equations, which are a set of equations derived from Einstein's general relativity. The density parameter, often denoted as Ω (omega), it is mainly about the desnity and matter and energy , if the DE is dominant, that implies a natural spherical expension , the equation of state so implies a repulsive effect counteracting the atrractive force of matters and implies natura;lly this spherical expansion
. It is the meaning of my theory of spherisation where the evolution optimisation of the universe is considered ......
. If the total density parameter Ω total is greater than 1, indicating that the universe has more mass (including both matter and dark energy) than the critical density, it suggests a positively curved space. The equation for the curvature density parameter (
Ω curvature is given by:
Ωcurvature=Ωtotal−Ωmatter−Ωradiation−Ωdark energy
If Ωcurvature is positive, it implies a positively curved universe. For a universe dominated by dark energy with a cosmological constantΛ the density parameter for dark energy Ω dark energy is given by:
Ωdark energy= ρ c/ρ Λ
where ρ Λ is the energy density associated with the cosmological constant, and ρ c is the critical density. The critical density is determined by the Hubble constant H 0
) and the gravitational constant (G) as p c=3 H0 squar 2/8piG
If Ω curvature is positive, it contributes to the overall density and leads to a positively curved universe. The Friedmann equation that describes the evolution of the scale factor (a) for a universe with curvature (k) is given by:
H squar 2=8pi G/(p−k/a squar)
where H is the Hubble parameter,
ρ is the total energy density, and
a is the scale factor.
In summary, if
Ωtotal>1
and the positive curvature is dominated by dark
