10. Inflation Flashcards
What is the flatness problem?
Where a non flat universe will grow further away from flatness over time
What is the scale factor proportional to when we are in a radiation universe?
a is prop. to t^1/2
What is the scale factor proportional to when we are in a matter universe?
a is prop. to t^2/3
How do different curvatures look like on a log(density parameter) time graph?
Skewed parabolas to the positive axis with different steepnesses
- Steeper the increase = more curvature
What is the horizon problem?
Opposite sides of the sky haven’t had time to come into thermal equilibrium
- Yet CMB temp is nearly the same in all directions
What is the non-inflation solution to the horizon problem?
Size of d_horizon at t_last scattering is only ~1 degree on the sky
- Regions not causally connected are at separations of more than 1 degree
What is the monopole problem?
Magnetic monopoles are not observed in the Universe
When did inflation occur?
at 10^-36 seconds when the scale factor increase was accelerating
In order for the scale factor to have been accelerating for the early universe, what must the energy density be equal to?
P < - energy density / 3
Which parameter do we use to model inflation?
Cosmological constant Λ_i
What is the initial Hubble parameter equal to?
H_i = (a dot / a )^2 = Λ_i / 3
What is the proposed solution for the scale factor?
a(t) is prop. to e^(H_i t)
How does inflation solve the flatness problem?
| - Sufficiently long inflation will make this -> 0, solving the flatness problem
1 - Ω(t) | is prop. to e^(-2 H_i t)
What is the sufficiently long period of inflation equal to in order for inflation to have solved the flatness problem?
We assume a period of inflation from t_i -> t_f during which the scale factor increased by e^N where N is the number of Hubble times (H_i) ^-1
- Inflation lasted for ~ 60 Hubble times/ 10^-34s
How does inflation solve the horizon problem?
A small patch of the universe is in thermal equilibrium and expanded to be larger than the horizon distance
- After inflation, visible U was 60cm, total U was 5m
