Cosmological Models Flashcards
What does the solution of the Fluid equation for matter show?
The energy density of matter gets diluted as universe expands
What does the solution of the Fluid equation for radiation have and show?
It has an extra factor of a due to the energy density of photons (1/v for the number of photons = 1/a^3 and 1/a for redshifting of photons)
When does radiation density dominate over matter density?
When going back in time due to a^-4
a<a_eq
(when a is small)
When does matter density dominate over radiation density?
When going forward in time due to a^-3
What are the assumptions for the matter density solution of the Freidmann equation?
K = 0, p = 0
ρ ∝ a^-3
What is the matter density solution of the Freidmann equation?
a ∝ t ^2/3
What are the assumptions for the radiation density solution of the Freidmann equation?
K = 0, p = ρ c^2 /3
ρ ∝ a^-4
What is the radiation density solution of the Freidmann equation?
a ∝ t ^1/2
What can be ignored when look at the early universe when radiation dominates?
a is small enough and K ≠ 0 so can be ignored
When is the age of the universe H^-1?
When the universe is empty (no acceleration or deceleration)
What happens in an empty universe?
Expansion only stops when infinity is reached so universe is expanding forever (not true for spherical universe)
When does curvature start to dominate?
when a > Ω_matter,0 / 1 - Ω_matter,0
a ∝ t
(there is free expansion and universe expands forever)
What values of K give the max value of a?
K > 0
What happens when K > 0?
H = 0
Gravitational attraction dominates, universe recollapses
Which values of K are used to find ages and what does it show?
K < 0
Low density universes are older, high density younger which indicates that universe must have been accelerating before at higher density
