Model of Universe + Equations

Question 1

What should a proper model of how the universe evolved contain?

Answer 1

Give an age (13Gyr)

Explain the observed redshift-distance relation to z ~2 where standard candles can

Explain changes in H with z

Show how these factors change with density

(full solution requires general relativity)

(modelling only works on bigger scale objects)

Question 2

What type of coordinate system do we live in?

Answer 2

One where the universe is expanding and its properties change with both position and time
(CP: position doesn’t matter)

Question 3

When is r fixed (equal to zero)?

Answer 3

For any object moving solely with expansion unlike x

Question 4

What is the scale factor a(t)?

Answer 4

Rate at which particles move apart/at which universe expands

Question 5

What is a(now) equal to?

Answer 5

1

Question 6

How does density behave when comoving coordinates are used?

Answer 6

The coordinates of density are independent of position by the CP and depend only on time through the scale factor

Question 7

What does the 1st law of thermodynamics indicate about the universe?

Answer 7

It is isolated (no energy in or out) so it is adiabatic

Question 8

What does the Fluid equation define?

Answer 8

How the density of any substance changes with time (scale factor)

Question 9

What links density and pressure in the Fluid equation?

Answer 9

An equation of state

Question 10

What can be assumed for ordinary rarely interacting matter?

Answer 10

p = 0

Question 11

What determines pressure effects?

Answer 11

Rest mass energy

Question 12

What is the general equation of state?

Answer 12

p = wρc^2

Question 13

What does the CP imply that supports the Friedmann equation?

Answer 13

Nowhere is special
No centre
Density is the same everywhere
Doesn’t matter where the radius is

Question 14

What does the Friedmann equation define?

Answer 14

The change in size of the universe with time

Question 15

What is K?

Answer 15

The curvature which is constant (comoving coordinates) in time and it is the same everywhere (CP)

units = 1/(length)^2

Question 16

How is the acceleration equation found from Friedmann equation?

Answer 16

Substituting the total density (matter,radiation etc) into the Friedmann eq

Question 17

Why does radiation density have more effects that matter density in the acceleration equation?

Answer 17

As radiation density contributes 3 times the amount of pressure that matter density does

Question 18

In the acceleration equation, if density is positive what is pressure?

Answer 18

negative

Question 19

What is p total equal to in the acceleration equation?

Answer 19

p_matter + p_radiation + p_Λ
= 0 + 1/3 ρc^2 - ρc^2

Question 20

Which part of the acceleration equation is used to find if the universe is accelerating?

Answer 20

The brackets

Question 21

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

Answer 21

yes

Question 22

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

Answer 22

no , decelerating

Question 23

If w = 0 is the universe accelerating?

Answer 23

no as empty universe

Question 24

What causes more deceleration, radiation or matter?

Answer 24

radiation