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Cosmology

Cosmology

Observation 1 universe is homogeneous and

isotropic at large scales

It cannot be stationary! It should expand or

contract

Observation 2 universe is expanding (Hubble)

It should have a beginning!

Hot or cold??

Observation 3 Cosmic microwave background

radiation

Hot Big Bang!

Observation 4 Abundance of light elements

Confirms Hot Big Bang

Fate of the universe depends on mass

distribution (or curvature)

Observation 5 density measurements

Observation 6 Fluctuations of background

radiation

Universe is nearly flat it contains dark matter

and dark energy

Problems with standard Big Bang model

Theory of inflation

Formation of structure Planck scale, Theory of

Everything

WHY our universe has the parameters that we

observe?

Anthropic Principle and beyond

Observation 1 universe is very inhomogeneous

and anisotropic at smaller scales

Groups

clusters

superclusters

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but homogeneous and isotropic at large

scale (The Cosmological Principle)

The universe is homogeneous. This means there is

no preferred observing position in the universe.

The universe is also isotropic. This means you

see no difference in the structure of the

universe as you look in different directions.

The Cosmological Principle

Considering the largest scales in the universe,

we make the following fundamental assumptions

1) Homogeneity On the largest scales, the local

universe has the same physical properties

throughout the universe.

Every region has the same physical properties

(mass density, expansion rate, visible vs. dark

matter, etc.)

2) Isotropy On the largest scales, the local

universe looks the same in any direction that one

observes.

You should see the same large-scale structure in

any direction.

3) Universality The laws of physics are the same

everywhere in the universe.

The universe cannot be stationary!

Conclusion the universe should either contract

or expand with decreasing speed, because the

gravity slows down the expansion

What is in reality?

Hubble and Humason 1931 Vrecession H0 R

The universe expands!

Hubbles Law

Distant galaxies are receding from us with a

speed proportional to distance

Necessity of the Big Bang

Velocity distance / time

The time of expansion is T 1/H0 14 billion

years

14 billion years ago all distances R were equal

to 0

Current value of the Hubble constant H0 ? 70

km/s/Mpc

Fig. 15-12, p.307

Olbers' Paradox and the Dark Night Sky IF the

universe is infinite, eternal, and static, then

the sky should be as bright as the surface of the

Sun all of the time! Heinrich Olbers (lived

1758--1840) popularized this paradox in 1826, but

he was not the first to come up with this

conclusion. Thomas Digges wrote about it in 1576,

Kepler stated it in 1610, and Edmund Halley and

Jean Philippe de Cheseaux talked about it in the

1720's. If the universe is uniformly filled with

stars, then no matter which direction you look,

your line of sight will eventually intersect a

star (or other bright thing).

Solved by finite size of the expanding universe

Olberss Paradox

Why is the sky dark at night?

If the universe is infinite, then every line of

sight should end on the surface of a star at some

point.

- The night sky should be as bright as the surface

of stars!

Solution to Olberss Paradox

If the universe had a beginning, then we can only

see light from galaxies that has had time to

travel to us since the beginning of the universe.

- The visible universe is finite!

Newtonian model of the universe

Mass within radius r(t)

Energy per unit mass

Hubble law

Hubble constant changes with time!

Main equation

Critical density

Indefinite expansion

Expansion will be replaced by contraction

Indefinite expansion but with speed approaching

zero

Solution for k 0

T 2/3H0 9.5 billion years

But the age of globular clusters is 13 billion

years!

Fig. 15-12, p.307

Cosmology and General Relativity

According to the theory of general relativity,

gravity is caused by

the curvature of space-time.

The effects of gravity on the largest

cosmological scales should be related to the

curvature of space-time!

The curvature of space-time, in turn, is

determined by the distribution of mass and energy

in the universe.

Space-time tells matter how to move

matter tells space-time how to curve.

General relativistic models

Matter (mass, energy, pressure)

Einsteins equations

Geometry of space-time

The Expanding Universe

On large scales, galaxies are moving apart, with

velocity proportional to distance.

Its not galaxies moving through space. Space is

expanding, carrying the galaxies along!

The galaxies themselves are not expanding!

2D analogy with houses on the balloon

No center and no edge

Now add another dimension and you have our

situation. Just like there is not new balloon

material being created in the 2D analogy, new

three-dimensional space is not being created in

the expansion. Like any analogy, though, the

balloon analogy has its limits. In the analogy,

the balloon expands into the region around

it---there is space beyond the balloon. However,

with the expanding universe, space itself is

expanding in three dimensions---the whole

coordinate system is expanding. Our universe is

NOT expanding into'' anything beyond''.

The Expanding Universe (2)

Hubble law does not mean that we are at the

center of the universe!

You have the same impression from any other

galaxy as well.

Expanding Space

Analogy A loaf of raisin bread where the dough

is rising and expanding, taking the raisins with

it.

Raisin Bread

(SLIDESHOW MODE ONLY)

Cosmological redshift

General relativity picture

Galaxies are at rest in the comoving (expanding)

frame

Due to the presence of matter, the universe is

non-stationary all distances change scale

factor R(t) is a function of time

Curvature

Metric of the homogeneous and isotropic Universe

Robertson, Walker, Friedman, Lemaitre

Compare with metric for empty flat space

Scale factor R(t) describes expansion or

contraction

Finite, But Without Edge?

2-dimensional analogy Surface of a sphere

Surface is finite, but has no edge.

For a creature living on the sphere, having no

sense of the third dimension, theres no center

(on the sphere!) All points are equal.

Alternative Any point on the surface can be

defined as the center of a coordinate system.

k 1 positive curvature (sphere)

finite volume

k -1 negative curvature (saddle)

k 0 zero curvature (flat)

Shape and Geometry of the Universe

Back to our 2-dimensional analogy

How can a 2-D creature investigate the geometry

of the sphere?

Measure curvature of its space!

Flat surface

(zero curvature)

Closed surface

Open surface

(positive curvature)

(negative curvature)

p.309

p.309

p.309

The Necessity of a Big Bang

If galaxies are moving away from each other with

a speed proportional to distance, there must have

been a beginning, when everything was

concentrated in one single point

The Big Bang!

?

The Age of the Universe

Knowing the current rate of expansion of the

universe, we can estimate the time it took for

galaxies to move as far apart as they are today

Time distance / velocity

velocity (Hubble constant) distance

T d/v 1/H 14 billion years

Einsteins equations

Equation of state relation between pressure P

and energy density ?c2

? 0 for dust (no pressure)

? 1/3 for radiation (very hard pressure)

Critical parameter

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Hot or cold universe??

Any signatures of the past around us?

Microwave background radiation!

George Gamow (lived 1904--1968) predicted in 1948

that there should be a faint glow left over from

when the universe was much hotter and denser. The

entire universe would have glowed first in the

gamma ray band, then the X-ray band, then to less

energetic bands as the universe expanded. By now,

about 14 billion years after the start of the

expansion, the cold universe should glow in the

radio band.

George Gamow

Born 1904 in Russia Studied and worked at

St.-Petersburg University Fled Russia in

1934 Worked at GW University and University of

Colorado

Proposed the concept of the Hot Big

Bang Explained the origin of chemical elements

in the universe Built the theory of

radioactivity and explained the nucleosynthesis

in stars Proposed a concept of genetic code and

explained how the code is implemented in DNA by

the order of nucleotides

The cosmogenesis paper with Alpher (The origin

of chemical elements) was published as the

Alpher-Bethe-Gamow theory, Gamow had added the

name of Hans Bethe to make a pun on the first

three letters of the Greek alphabet, alpha beta

gamma.

Looking Back Towards the Early Universe

The more distant the objects we observe, the

further back into the past of the universe we are

looking.

Fig. 15-9, p.304

The Cosmic Background Radiation

The radiation from the very early phase of the

universe should still be detectable today

R. Wilson A. Penzias

Was, in fact, discovered in mid-1960s as the

Cosmic Microwave Background

Blackbody radiation with a temperature of T

2.73 K

Arno Penzias and Robert Wilson observed in 1965 a

radio background source that was spread all over

the universe---the cosmic microwave background

radiation. The radiation has the same intensity

and spectral character as a thermal continuous

source at 3 K (more precisely, 2.728 0.004 K)

as measured by the COBE satellite in every

direction observed. To a high degree of precision

the sky is uniformly bright in radio. The

uniformity of the background radiation is

evidence for the cosmological principle.

From 3000 K to 2.7 K The redshift of 1000!

Fig. 15-6c, p.301