- #1
LeoChan
- 5
- 1
- TL;DR Summary
- In ΛCDM, to find t and z when the matter density equal to the vacuum energy density.
In ΛCDM, H(t0) = 70km/s/Mpc,
Ωd(t0) = 0.3, Ωr(t0) = 0 and ΩΛ(t0) =0.7,
so that Ω(t0) = Ωd(t0) + Ωr(t0) + ΩΛ(t0) = 1and the universe is spatially flat.
I want to know the t and z when the matter density equal to the vacuum energy density. By total energy density equation, I think Ωd(t) + ΩΛ(t) = 1, so they are both equal to 0.5 .
Maybe 0.5 = Λ / ( 3 * H(t) ^ 2 ). As for the matter, I am not sure since I only know it is proportional to a^-3. Is it related to the redshift dependent Hubble parameter, H(z)?
Thank you for your attention.
Ωd(t0) = 0.3, Ωr(t0) = 0 and ΩΛ(t0) =0.7,
so that Ω(t0) = Ωd(t0) + Ωr(t0) + ΩΛ(t0) = 1and the universe is spatially flat.
I want to know the t and z when the matter density equal to the vacuum energy density. By total energy density equation, I think Ωd(t) + ΩΛ(t) = 1, so they are both equal to 0.5 .
Maybe 0.5 = Λ / ( 3 * H(t) ^ 2 ). As for the matter, I am not sure since I only know it is proportional to a^-3. Is it related to the redshift dependent Hubble parameter, H(z)?
Thank you for your attention.