Cosmological Constant

Question 1

When is the cosmological constant used?

Answer 1

When H = 0 (unstable)

Question 2

What is the Ω_matter and Ω_Λ?

Answer 2

Ω_matter = 0.3
Ω_Λ = 0.7

1+z = 1.3

Question 3

What is p total?

Answer 3

0 + 3(-ρ_Λc^2)/c^2 ∝ -3Ω_Λ,0

Question 4

What is ρ total?

Answer 4

Ω_matter + Ω_Λ = 1

Question 5

What is Ω_total?

Answer 5

Ω_Λ + Ω_matter + Ω_radiation = 1

(up to 1 is in Hubble time and there is not age problem of cosmological constant)

Question 6

At what redshift does ρ of Λ start to dominate?

Answer 6

z = 0.5
(1 + z = 1.5)

Question 7

What can the cosmological constant cause?

Answer 7

Acceleration which makes universe older

Question 8

What is the w value for the cosmological constant?

Answer 8

w = -1 (causes acceleration on its own)

Question 9

Why was the cosmological constant introduced?

Answer 9

To fix the stable static universe theory

Question 10

What is the pressure of the cosmological constant?

Answer 10

no time derivative so Δρ_Λ = 0

p_Λ = - ρ_Λ c^2

Question 11

What does the negative pressure caused by the cosmological constant imply?

Answer 11

(negative pressure = anti-gravity)

anti gravity implies a continuous driving force pushing on going expansion

Question 12

How do K and ρ change in the Steady State model?

Answer 12

ρ_matter = constant (even though universe is expanding)

K = 0

Question 13

Why was Steady State model discounted?

Answer 13

Due to the need of Λ and real matter term (matter term needed as Λ on its own doesn’t match low redshift of universe

Question 14

If w = -1/3, is universe accelerating?

Answer 14

no acceleration or deceleration

Question 15

If w > -1/3, is universe accelerating?

Answer 15

it is decelerating

Question 16

If w < -1/3, is universe accelerating?

Answer 16

it is accelerating

Question 17

What is Ω_Λ + Ω_matter for flat universe?

Answer 17

Ω_Λ + Ω_matter = 1

Question 18

What is Ω_Λ + Ω_matter for closed universe?

Answer 18

Ω_Λ + Ω_matter > 1

Question 19

What is Ω_Λ + Ω_matter for open universe?

Answer 19

Ω_Λ + Ω_matter < 1

Question 20

What can a small positive Ω_Λ stop?

Answer 20

Can stop high density matter dominated universe from collapsing

Question 21

For H_o t_o vs Ω_matter,0 graph, what does H_o t_o > 1 indicate?

Answer 21

Universe is older than Hubble time

Question 22

What is H_o t_o for observations made of Supernovae Ia?

Answer 22

1

Question 23

What does the data from Supernovae Ia which are observed out to significant distances suggest?

Answer 23

Λ ≠ 0 as matter-only model don’t fit

Question 24

What is the effect of introducing Λ?

Answer 24

Makes things further away K =0 as the universe is now expanding rapidly

Question 25

What dominates the late universe?

Answer 25

cosmological constant (as scale factor increases, constant wins)

Question 26

How is a scale factor for every choice of Ω_matter and K derived?

Answer 26

Using the 1+z vs Ω_vac graph