Advances in contemporary physics and astronomy --- our current understanding of the Universe

Lecture 5: Evolution of Early Universe

April 30th, 2003

Timetable of the Universe

Relativistic Doppler EffectWhen the speed between the object and the observer is close to the speed of the light, the Doppler effect need to be revised,

Redshift z

Redshift z: 1/1/1

cvcv

emλemλobsλ

Z

velocity 0.25c 0.5c 0.75c 0.9c 0.95c

redshift 0.29 0.73 1.65 3.36 5.24

World line and space-time diagram

Hubble’s law revisited•Current measurement of Hubble’s constant from WMAP: Ho= 71 km/sec/Mpc (up to 5%)

The distance in Hubble’s law is not measured in any specific frames, rather it considers the whole expansion of universe.

“Speed” of far away galaxies can exceed the speed of light, however, this “speed” is not the speed of these galaxies measured from our own:

The characteristic expansion time

• Hubble’s constant: Ho= 71 km/sec/Mpc (up to 5%)

• Consider two arbitrary “galaxies” with a distance D, and V~ Ho D. If assuming Ho is not time-dependent. Then

• characteristic expansion time t ~ 1/Ho

The critical density

The gravitational potential energy of a “galaxy” at an imaginative sphere is decided by the enclosed mass through:

The total energy of the “galaxy” is the sum of kinetic energy and the gravitational energy:

The critical energy corresponding to a “ZERO” energy.

Temperature history

At earlier time, the expansion time scale is given by:

When temperature is higher than 3,000K, radiation dominates universe:

When temperature is lower than 3,000 K, matter dominates the universe

Early Universe Chronology

                                                                

The Planck Epoch

Before t=10-43 sec:

•All 4 forces unified into a single Superforce

•1 force rules all of physics

•We cannot say much else about the time before this, as we do not yet have a quantum theory of gravity to guide us.

• Maybe String Theory?

Very likely our understanding will be dramatically changed from current available theory.

The Grand Unification Epoch

At t=10-43 sec, T=1032 K:

•Gravity separates from the Superforce

•Strong & Electroweak Forces unified into the GUTs force.

2 forces rule physics:

•Gravity & GUTs

The Universe at this phase is a hot, dense particle soup of quarks, antiquarks, & photons in equilibrium with each other.

The Inflationary EpochAt t=10-36 sec, T=1028 K:

•Strong Force separates from the GUTs force

•EM and Weak forces are still unified

3 forces rule physics:

•Gravity, Strong & Electroweak forces.

The rapid separation of the Strong Force from the GUTs Force triggers a rapid "inflation" of the Universe.

Universe grows exponentially by a factor of about 1043 in size between 10-36 to 10-34 seconds:

•The expansion greatly slows down (back to normal) after Inflation.

Inflation helps to explain why the Universe is so smooth and flat:

•Smooth: Cosmic Background Radiation is smooth to 1 part in 100,000

•Flat: current observations suggest 0=1.

Horizon and the Isotropy problem

Total separation of Fundamental Forces

At t=10-12 sec, T=1016 K:

•Electroweak force separates into the Electromagnetic & Weak forces.

•All forces are now separate.

4 forces rule physics:

•Gravity, Strong, Weak, & Electromagnetic

As the Universe continues to cool, conditions will soon become right for matter to begin to exist in free form, instead of in a soup of matter and photons in equilibrium.

Quark Freeze-outAt t=10-6 sec, T=1013 K:

•Free quarks combine into hadrons (primarily protons & neutrons)

•Equilibrium between particle-antiparticle pairs and photons:

No more free quarks in the Universe.

Nucleon Freeze-out

At t=0.01 sec, T=1011 K

•Protons & neutrons decouple from photons and exist as free particles.

•electrons & positrons in equilibrium with photons.

•neutrinos & nucleons in equilibrium.

Temperature is still high and free neutrons are stable during this epoch.

Neutrino Decoupling

At t=1 sec, T=1010 K

•neutrinos decouple from matter and radiation.

•stream out into space freely.

•These form a Cosmic Neutrino Background (not yet observed).

Free neutrons are no longer stable:

•Decay into protons, electrons, and neutrinos.

•Left with about 1 neutron for every 7 protons.

The Epoch of Nucleosynthesis

At t=3 minutes, T=109 K:

Fusion of protons and the remaining free neutrons:

•Formation of 2H (Deuterium) & 4He

•End up with ~75% 1H, 25% 4He

•Also end up with traces of 2H, 3He, Li, Be, B

We cannot observe this epoch directly, but we can look for the products of these events.

The Epoch of Recombination

At t=300,000 years, T=3000 K:

Electrons & nuclei combine into neutral atoms:

•Universe becomes transparent

•Photons stream out into space

•Origin of the Cosmic Background Radiation.

This represents the earliest epoch of the Universe we can observe directly using photons.

Previous to this, the Universe is opaque to photons.

The "Dark Ages" after the end of Recombination but before the first generation of stars formed.

•No visible or infrared light because there were no stars ("dark")

•The hydrogen and helium in the Universe are neutral

•Universe is mostly opaque to UV photons because of absorption by neutral H and He.

Time of rapid evolution:

•Matter density drops by factor of ~10 Million.

•Matter starts organizing into large-scale structures via gravitational collapse.

Galaxies Formation

At t= 500 Myr - 1 Gyr, T=30 K

•First generation of stars form, ending the "Dark Ages"

•Quasars first form

•First heavy metals made by the first supernovae

Present: t=13 Gyr, T=2.726 K

•Galaxies, stars, planets, us...

•Metals from supernovae of massive stars.

Big Bang Nucleosynthesis

•Two ways for creating elements observed in the Universe.

•Light elements (namely deuterium, helium, and lithium) were produced in the first few minutes of the Big Bang,

•Heavy elements (heavier than helium) originate from the interiors of stars.

•The Universe's light-element abundance is another important criterion by which the Big Bang hypothesis is verified.

Element Abundances•protons and neutrons collided to produce deuterium (one proton bound to one neutron).

•Most of the deuterium then collided with other protons and neutrons to produce helium and a small amount of tritium (one proton and two neutrons).

•Lithium 7 could also arise from the coalescence of one tritium and two deuterium nuclei.

The prediction of relative abundance only depends on the density of baryons (ie p and n) at the time of nucleosynthesis.

Formation of deuteron

                          

                        

                         

1. Weak Interaction freeze-out: Less than 1 second after the Big Bang,

neutron:proton ratio is in thermal equilibrium. About 1 second after the Big Bang, the temperature is slightly less than the neutron-proton mass difference, these weak reactions become slower than the expansion rate of the Universe, and the neutron:proton ratio freezes out at about 1:6.

2. Balance of neutron decay and neutron capture: Free neutrons decay to protons with a half-life of 615 seconds. This neutron depletion process is balanced by neutron capture on protons to form Deuteron. This reaction, being exothermic, only viable when the Universe falls to 100 billion K or kT = 0.1 MeV, ~100 seconds after BB. The neutron:proton ratio is about 1:7 at that time.

Formation of helium

                                

                                 

Once deuteron is made, reactions that make helium nuclei can happen. These reactions continue till eventually the temperature gets so low that the electrostatic repulsion between deuterons causes the reaction to stop. The deuteron:proton ratio when the reactions stop is quite small, and essentially inversely proportional to the total density in protons and neutrons. Almost all the neutrons in the Universe end up in normal helium nuclei. For a neutron:proton ratio of 1:7 at the time of deuteron formation, 25% of the mass ends up in helium.

or

BBN summary

                                                                           

References• Webpages1) ABOUT BIG BANG:

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html2) INFLATIONARY COSMOLOGY:

http://nedwww.ipac.caltech.edu/level5/Watson/Watson1.html3) Big Bang Nucleosynthesis: http://www-

thphys.physics.ox.ac.uk/users/SubirSarkar/bbn.html

• Books

1. Principles of Physical Cosmology by P.J.E. Peebles

2. The First Three Minutes by Steven Weinberg

3. The Fullness of Space by Bareth Wynn-Williams