Lecture 11: Inflation

Question 1

major successes of the hot big bang theory

Answer 1

concordance model

observed thermal history

Question 2

big bang success - the concordance model

Answer 2

generally consistent and tight constraints on cosmological model parameters over a wide range of redshifts

Question 3

big bang success - thermal history

Answer 3

• the observed thermal history of the universe matching theory over a wide range of temperatures with the physical properties of the CMBR and the light element abundances being accurately predicted.

Question 4

problems with the hot big bang

Answer 4

flatness problem
horizon problem

Question 5

equation to demonstrate the flatness problem

Answer 5

Ωm + Ωr + ΩΛ - kc^2/a^2H^2 =1

Question 6

flatness problem, set Ωtotal=

Answer 6

Ωm +Ωr +Ω Λ

|Ωtotal(t) -1| = |k|c^2/a^2H^2

Question 7

ΩΛ is dominant when?

Answer 7

now

Question 8

Ωm was dominant from

Answer 8

zeq = approx 3500

Question 9

Ωr was dominant

Answer 9

beofre zeq=3500

Question 10

what determines how a^2H^2 and |Ωtotal(t)-1| evolve with time

Answer 10

which of the Ωs is dominant

Question 11

radiation domination

Answer 11

a^H^2 prop to t^-1
|Ωtotal-1| prop to t

Question 12

matter domination

Answer 12

a^2H^2 prop to t^-2/3

|Ωtotal-1| prop to t^2/3

Question 13

|Ωtotal-1| is an increasing function of

Answer 13

time

Question 14

If we require, for example, 0.9 ≤ Ωtotal ≤ 1.1 at the present day then at the epoch of nucleosynthesis we require

Answer 14

0.9999999999 </= Ωtotal <= 1.0000000001

Question 15

The flatness problem is about explaining how

Answer 15

the initial value of |Ωtotal-1| could have been so finely tuned to a value of zero

Question 16

The CMBR (as a description of a thermal distribution) is almost, but not quite

Answer 16

perfectly isotropic

Question 17

isotropy implies

Answer 17

thermal equilibrium

Question 18

thermal equilibrium implies that

Answer 18

sufficient interactions have happened

Question 19

interactions implies

Answer 19

causal connectedness

Question 20

causal connectedness

Answer 20

The circular lines (solid and dashed) are horizons for the observers at the centres. So if A and B represent the points on the CMBR surface of last scattering there’s enough time for their photons to reach us but not each other.

Question 21

issue with causal connectedness

Answer 21

if there’s not enough time for A and B to interact how are they the same
temperature.

Question 22

The CMBR formed at

Answer 22

the epoch of decoupling, at 370 000 years after the Big Bang.

Question 23

CMBR formed at the epoch of decoupling so the particle horizon of the universe was

Answer 23

much smaller

theta_cmbr =2 degrees for Z+cmbr=1000

Question 24

the CMBR sky consists of thousands of

Answer 24

causually disconnected regions that are, nonetheless, at almost exactly the same temperature

Question 25

In fact, because the CMBR is not exactly isotropic you need to explain not just the similarities in temperature but

Answer 25

a mechanism for providing temperature variations

Question 26

solution for all of the problem's we've noticed with the hot big bang

Answer 26

cosmological inflation

Question 27

inflation

Answer 27

a proposed period of accelerated expansion in the very early universe

Question 28

Recall that in the de Sitter universe the scale factor

Answer 28

grows exponentially, driven by the cosmological constant

Question 29

We write the solution to the de Sitter universe construction as

Answer 29

a(t)=a(tbegin) exp [H(t-tbegin)]

Question 30

important term in the solving the flatness inflation equation

Answer 30

the exponential term on the RHS whatever value |Ωtotal-1| has when inflation begins, it is very quickly driven to zero

Question 31

how much inflation is needed - require to=

Answer 31

4 x 10 ^17 s

Question 32

how much inflation is needed, matter -radiation equality at

Answer 32

2x10^12 s

Question 33

how much inflation is needed- |Ωtotal(teq)-1|=

Answer 33

3 x10^-5 quite small but not awful

Question 34

we want to keep |Ωtotal(teq)-1| < or =

Answer 34

3x10^-5 while also remembering that prior to t=teq, the universe was radiation-dominated (ie |Ωtotal(teq)-1| prop to t)

Question 35

assume inflation was between

Answer 35

tbegin=10^-36s tend = 10^-34s

Question 36

|Ωtotal(teq)-1| using tbegin and tend values gives

Answer 36

1.5x10^-51 crazy small

Question 37

aend/abegin=

Answer 37

2.5x10^25 ie require this much expansion in such a tiny time

Question 38

aend/abegin can be written as

Answer 38

exp[H(tend-tbegin)] gives 10^43 so the scale factor easiy grows by enough to solve the flatness problem

Question 39

Exponential expansion means that a causally connected patch of the universe in existence before inflation can

Answer 39

be magnified beyond our observable horizon.

Question 40

solving the horizon problem - So long as you already have fluctuations these will be

Answer 40

both smoothed out and yet still exist, allowing for causally disconnected regions to have the same statistical properties.

Question 41

what might have triggered inflation

Answer 41

some kind of phase transition

Question 42

phase transition

Answer 42

some kind of sudden and dramatic change in the properties of the system

Question 43

we’d expect phase transitions at points where

Answer 43

the four fundamental forces 'broke off' from each other

Question 44

What we really need is a phase transition that generates the sort of

Answer 44

negative pressure discussed earlier in the context of Λ. this is compatible with theories of supersymmetry

Question 45

The CMBR offers us some ways to search for inflationary signatures such as:

Answer 45

super horizon b modes

Question 46

super horizon

Answer 46

fluctuations due to primordial density fluctuations produced during inflation causing the gravitationally redshift of CMBR photons – direct evidence of Sachs-Wolfe plateaus at large angular scales.

Question 47

b-modes

Answer 47

in the polarisation of the CMBR (that would be consistent by primordial gravitational waves generated during inflation) – no direct evidence as yet.

Question 48

What can we say about the the physics of the pre-inflationary era?

Answer 48

We believe that the CMBR fluctuations were the result of quantum fluctuations at the Planck time. So we’re going to need a theory of quantum gravity. We don’t have such a theory yet so we remain in a speculative arena.