Density Curvature Parameter: Can We Predict?

[Higgsy]

If I know the density curvature parameter for today $$ \Omega_{k,0} = \frac{-c^{2}k}{R_{0}H_{0}} $$ then is it possible to surmise what it would be, say, during the matter dominated era $$ \Omega_{k,t} = \frac{-c^{2}k}{R(t)H(t)}$$ ?

 

[Ambitwistor]

Yes, it is possible to estimate the density curvature parameter during the matter dominated era using the equation provided. The matter dominated era is characterized by the dominance of matter over other components (such as radiation or dark energy) in the universe. During this era, the scale factor (R) and the Hubble parameter (H) evolve differently compared to the present time. However, the curvature of the universe remains constant over time.

Assuming a flat universe, where the curvature parameter (k) is equal to 0, the equation can be simplified to:

$$ \Omega_{k,t} = 0 $$

This means that during the matter dominated era, the density curvature parameter would also be 0, indicating a flat universe. However, if the universe is not flat, the value of k would be different and the density curvature parameter would also vary accordingly.

In general, the density curvature parameter during the matter dominated era can be estimated by knowing the value of k and the evolution of the scale factor and Hubble parameter during that time. This information can be obtained from observations and theoretical models.