Cosmology &The Big Bang Theory

Dr Alex Calverley

222 dydxdl

222 dydxdl 22

2222

ddr

drdrdl

2,1,

2

ji

jiij dxdxgdl

1001

ijg

Cartesian coordinates

20

01r

gij

Polar coordinates

3

0,

2

dxdxgds

11

11

g

Special relativity

22222 dzdydxdtds

tata

tag

2

2

2

1

General relativity

22222222 dztadytadxtadtds

TcGRgR 42

1 8

In 1915...

TcGgRgR 42

1 8

In 1917...

Using the GR metric from the last slide Friedmann solved the equation in 1922 to get...

338 2

2

22c

akcG

adtda

33

34 2

2

2

2

ccpG

adtad

k > 0

k < 0

k = 0

Demonstrating the relationship between comoving (i.e. coordinate) distances and physical distances

a = 1 today (a0), and a(t) < 1 at earlier times

In 1929...

dHv 0

However, in 1927...

If D(t) is the proper distance between two objects at time t and D0 is the proper distance now, then:

taDtD 0 tatDD 0

and

dtdaD

dttDd

0

Then combining these

tDHtDtadt

tDd dtda

taH dtda

dHv 0So Lemaître had predicted

EVIDENCE FOR THE BIG BANG THEORY (1)

An expanding universe where the recessional speed is proportional to the distance away

In 1948...

George Gamow predicts the ratio of light elements due to Big Bang Nucleosynthesis

Ralph Alpher and Robert Herman predict the glow from the Big Bang will still be visible in the microwave spectrum with a temperature of about 5 K

Colours represent fluctuations of size ΔT/T ~ 10-5

EVIDENCE FOR THE BIG BANG THEORY (2)

A near perfect blackbody spectrum at T ≈ 2.7 K, suggesting the Universe was once much hotter and denser

xn

xnpn eXexHdx

dX 11

15.0xX n

EVIDENCE FOR THE BIG BANG THEORY (3)

BB Nucleosynthesis can explain the observed ratios of light elements in pristine primordial gas

In 1999...

The Universe’s expansion is accelerating!Need an extra component to the Friedmann equations called Dark Energy – which acts just like Einstein’s Λ term!

Colours represent fluctuations of size ΔT/T ~ 10-5