Cosmology and the Early Universe
Review for Astronomy 123 Midterm Exam 3

February 21, 2011 jeb

Cosmology
The Early Universe

Cosmology

Cosmology
The study of the structure and evolution of the entire universe
Largest structures of universe
200 - 300 Mpc

Cosmological Principle
On a large scale, universe is homogeneous and isotropic
Universe has no edge
Universe has no "center"

Universality of physical laws
The same physical laws apply everywhere in the universe

The Expanding Universe and the Big Bang
Olbers's Paradox - why is the sky dark at night?
red-shift of starlight
finite age of universe

Big-Bang established by observation
Hubble's Law (1st evidence)
v = H × d
H &asymp 20 km/s/Mly
for d = 100 Mly, v = 2,000 km/s
for d = 15,000 Mly, v = 300,000 km/s
(Note - in these examples, H is set to 20 for simplicity. It is actually slightly larger, so d never exceeds 13,700 Mly)

existence of quasars (early universe was different)
cosmic microwave background (CMB)
abundances
Helium, deuterium, lithium, beryllium
Helium is about 25% of the mass of normal matter in the universe

Early on the whole universe was compressed to very high density
Since then the entire universe has been expanding
Since the universe is expanding everywhere, distant galaxies appear to be moving away from us in every direction

Discovery of Cosmic Microwave Background
Predicted by Big Bang
Universe's distant past was very dense and hot

First detected by Penzias and Wilson with radio telescope
Very sensitive measurement achieved after eliminating sources of extraneous noise
Fixed loose joints
Repaired faulty connections
Removed pigeon droppings that created noise in detector

Found 2.7 K background
Uniformly coming from all directions
Uniform throughout the day
Uniform through the seasons

Peak wavelength about 1 mm
Matches blackbody spectrum
Emerged from big bang fireball when the universe was 400,000 years old and had a temperature of 3000 K
Following big bang, as universe expands, background radiation gets cooler
from background radiation we can determine motion of earth through universe

COBE
small asymmetry due to the Earth's motion through space

Steady State Theory
Alternative to Big Bang
Consistent with Hubble expansion
Could not explain CMB - therefore rejected

Prediction of Big Bang
Expansion of the universe shifted the initially high energy radiation in the universe to longer and longer wavelengths
Cosmological redshift

The Big Bang predicted that the universe should be "hissing" EM radiation (static)
Coming from all directions
Follows "black body" curve
Temperature about 3 K (we now know it is 2.7 K)

Age since Big Bang
13.7 billion years measured from CMB fluctuations
Time of expansion depends on the density of matter
and the cosmological constant (or "dark energy")

Space-Time Geometry
3 possibilities in Einstein's General Theory of Relativity
open
flat
closed

Open, flat, or closed depends on density of matter (and "dark energy")
Astronomers define a ratio of densities, &Omega₀("Omega nought") = actual density / critical density
the amount of mass needed to close the universe is call the critical density
critical density = 9 × 10 ^-27 kg/m ³
Earth's atmosphere contains about 1.2 kg/m ³

We know &Omega₀ is close to 1
Luminous matter explains &Omega₀ = 0.02-0.05 ("a few percent" of critical density)
Dark matter is much more, bringing &Omega₀ to about 0.3
Dark energy completes closure of the universe, bringing &Omega₀ close to 1.00

Einstein found the General Theory of Relativity required the universe to be expanding of contracting, not static
Einstein invented "cosmological constant", a kind of "fudge factor" to add to his theory
Allowed the universe to be static, neither expanding nor contracting
Or it could still be expanding or contracting, depending on the densities of matter, and the cosmological constant
When Hubble discovered the universe was expanding, and it didn't need to be static, Einstein considered the "cosmological constant" his "greatest blunder"
Cosmological constant is similar to "dark energy" or the energy of the vacuum

density of matter nature of universe geometry of universe future

less matter than critical OPEN infinite and unbounded expand forever

critical density FLAT infinite and unbounded expand forever

more matter than critical CLOSED finite and unbounded collapses in BIG CRUNCH

Dark Energy and the Future of the universe
Future of expansion also depends on the matter density and the dark energy density ("the cosmological constant")
The expansion of the universe is accelerating
Supernovae at large redshift are fainter than they would be if the universe were expanding at a constant speed

This acceleration must be caused by an unknown cosmic force field
Called "dark energy"
Appears like "cosmological constant"
Perhaps Einstein did not "blunder"

Could come from "vacuum energy"

WMAP
Wilkinson Microwave Anisotropy Probe
NASA satellite which measured the tiny fluctuations in the CMB in different directions
CMB fluctuations tell us many things
Age of the universe
Total energy-mass density (&Omega₀)
Fractions of ordinary matter, dark matter, and dark energy

WMAP results as of 2010
Age of the universe = 13.7 billion years (with about 1% uncertainty)
&Omega₀ = 1.00 (about 1% uncertainty)
in other words, the universe is flat

Ordinary matter makes up about 4.6% of the universe
Dark matter makes up about 23%
Dark energy makes up about 72%

Note- dark matter represents more than 80% of the matter
23%/(23%+4.6%) = 83%

The Early Universe

Major Events of the Early Universe

10^-43 seconds	GUT epoch begins, leading to inflation
10^-32 seconds	Inflation ends
10^-4 seconds to about 1 minute	Matter emerges as dominant over anti-matter
few minutes	Nucleosynthesis - fusion of neutrons and protons into light elements
50,000 years	Radiation Era ends Matter Era begins
400,000 years	Light de-couples from matter
Today	Dark energy era is underway Expansion of the universe is accelerating

The Big Bang

The early universe was radiation dominated

In the early universe, matter and anti-matter were being created equally out of the radiation

pair production

Anti-Matter
anti-matter consists of anti-particles
Each type of particles is "matched" by an anti-particle of opposite charge
for example, the anti-electron(positron) carries a positive charge

Matter and anti-matter can be created in pairs from energy (or electromagnetic radiation)
E = m c²
E = energy
m = mass
c² = speed of light squared (here just a constant of proportionality)

Anti-matter and matter can also annihilate into energy

The Early Universe

Due to very high temperature matter and anti-matter were continuously created initially

As temperature decreased, eventually even the lightest particles could not be created

Eventually, through interactions, matter came to dominate anti-matter

this occurred about a minute after the Big Bang

Evolution of the Universe

Evolution of Matter

Radiation Era (The radiation era lasted for about 50,000 years)

Planck Epoch

First 10^-43 seconds after the Big Bang

No current theory of physics (quantum gravity) exists

GUT (Grand Unified Theory) Epoch

After 10^-43 seconds, temperature fell to 10³² K

Quark Epoch

Creation of protons and neutrons continued for about 10^-4 seconds

Temperature drops below 10¹³ K, and protons and neutrons are no longer produced in pairs

Lepton Epoch

Ends when the universe is about 100 seconds old

During this epoch, the leptons (electrons, neutrinos, and other light particles) are still produced in pairs, because they are light

Ends when temperature drops below 1 billion K

Nuclear Epoch

Protons and neutrons fuse into light nuclei
nucleosynthesis

Last until the Universe is about 15 minutes old

Matter Era

Atomic Epoch

Galactic Epoch

Stellar Epoch

Vacuum-energy Era (Dark Energy Era)
Last few billion years
Universe's expansion is accelerating
Our recognition of this era is too new to be in the textbook

Formation of Atoms and Nuclei

Light nuclei were formed during the Early Universe
Notably helium and deuterium
helium = 2 protons + 2 neutrons (+2 electrons)
deuterium = 1 proton + 1 neutron (+1 electron)

Why is there so much Helium?
About one quarter of the normal mass of the universe is helium
This is only exceeded by hydrogen, which comprises about three quarters of the normal mass
Heavier elements are a much smaller fraction of the normal mass of the universe

Helium (and other light elements) was produced just after the Big Bang due to extreme temperature in the Primordial Fireball

Present abundances (like deuterium) tell us what was going on very early in the evolution of the universe
Deuterium Cosmology

The amount of deuterium reveals the density of the early universe

Implys that the density of "normal" matter in the universe is at most a few percent of the critical value

deuterium is not formed in stars in much quantity

Heavier nuclei were formed later in burning stars and supernovae explosions.

Inflation

Puzzles of the Early Universe

Why does the universe appear so flat?

not clearly open or closed

If the early universe differed slightly from critical density (flat), it would differ greatly today

Flatness Problem

How did the universe become so homogeneous and isotropic?

Horizon problem

Background radiation nearly the same in all directions

Therefore - entire universe must have been at uniform temperature near beginning

But - different regions are not in contact and never have been

Answers from Grand Unified Theory (GUTS).

Inflationary Universe

Universe expanded 10⁵⁰-fold during first 10^-32 seconds
That's 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 - fold

Grand Unified Theory (GUTS) predicts period of inflation
Inflation Solves Mysteries

Why is universe so flat? (flatness problem)

Expansion flattens it

Like balloon suddenly expanding becomes very flat locally

Why so homogeneous and isotropic? (horizon problem)

Universe was in contact before inflation

but not now

Fundametal Basis for Inflation

Matter interacts through four forces (see note below)

gravity

weak nuclear force

electromagnetism

strong nuclear force

Note - these four forces can be thought of as just three, since the weak nuclear and electromagnetic force have been unified into the electroweak force

Forces of Nature Relative
Strength Role .

Strong Nuclear 1 Binds Nucleus (short range)

Electromagnetic 10^-2 Binds Atoms (long range)

Weak Nuclear 10^-13 Causes Radioactivity (short range)

Gravitational 10^-40 Binds earth to Sun
Binds galaxies (long range)

GUTS - Grand Unified Theories
States that strong, electromagnetic, and weak forces are manifestations of the same force
In other words, unifies the forces

Mathematical Theory of GUTS ------> predicts Inflation

When universe cooled to point that strong force separated from electroweak force

From about 10^-43 sec. to 10^-32 sec, universe expanded in size by 10⁵⁰

Inflation Solves:

Horizon problem

Flatness problem

Structure

Dark Matter

Recall, most of the universe is dark matter (80% or more)

So fluctuations in dark matter should be more important than baryonic.

What is dark matter?
Hot Dark Matter

lightweight particles

such as neutrinos, which have very small mass

Cold Dark Matter

heavy particles

such as exotic supersymmetric particles

Model which best explains observed universe:

Cold Dark Matter

How does Dark Matter relate to microwave background?

Density fluctuations appear first in the dark matter
then create some "ripples" in visible matter- but small "ripples"

1992 - "ripples" finally observed by COBE

at a few parts in 100,000.

21st Century - WMAP has measured "ripples" more precisely

Showing hot spots on cosmic fireball

WMAP angular structure measurement tells us the features of the universe

Flat universe (&Omega₀ = 1)
73% dark energy
27% matter
23% dark matter
4% normal matter
therefore, more than 80% of the matter is dark matter