*Homogeneity and isotropy of the universe
*Based on cosmological principle – on a large enough scale the universe looks
very much the same no matter where the observer is located. The universe has no
unique center and therefore no unique boundary.
galaxies
are distributed evenly across the sky
stars – size ~ 1 light year
galaxies – size ~ 106 light years
clusters – size ~ 3 x 107 light years
1 light year = 9.461 x 1015 m
evidence: 1) distribution of galaxies in the sky and in the distribution of their apparent
magnitudes and red-shifts.
2) isotropy of the distribution of radio sources on the sky.
3) Isotropy of the cosmic microwave radiation (discovery in 1965)
Standard Hot Big Bang Model
Evolution governed by laws of thermodynamics, hydrodynamics, atomic physics, nuclear
physics, high-energy physics and gravitation dominates the over-all expansion.
Assumption of the model: The universe “began” in a state of rapid expansion from a
very nearly homogeneous, isotropic condition of infinite (or near infinite) density and
temperature ( a singularity – incomplete physical understanding).
Time after beginning
1s,
temperature of the universe was so high that there was complete thermodynamic
equilibrium between photons, neutrinos, electrons, positrons, neutrons, protons,
various hyperons, and mesons, and perhaps even gravitons (gravitational waves).
few s temperature dropped to about 1010 K and its density was down to ~105 g/cm3; so
all nucleon-antinucleon pairs had recombined, all hyperons and mesons had
decayed, and all neutrinos and gravitons had decoupled from matter. Universe
consisted of freely propagating neutrinos, perhaps gravitons, with black-body
spectra at temperature T ~ 1010 K, plus electron-positron pairs in the process of
recombining, plus electrons, neutrons, protons and photons all in thermal
equilibrium at T ~ 1010 K.
The gravitons (if present) and neutrinos have continued to propagate freely,
maintaining black-body spectra, but their temperature have been red-shifted by
the expansion of the universe in accordance with the law
T
1
,
a
a = radius of universe
Their temperatures today should be roughly 3K and should still fill the universe.
“Sea” of neutrinos and gravitons still undetected with today’s technology.
2s  t  103 s, temperature is ~1010 to ~109 K,  ~ 10+5 to 10-1g/cm3, during which
primordial element formation occurred. Calculations reveal that about 25% of the
baryons in the universe should have been converted into He4 during this period,
and about 75% should have been left as protons (H1). Traces of deuterium, He3,
and Li should have been also created, but essentially no heavy elements. Heavy
elements observed today must have been made later, in stars. Current
astronomical studies of the abundances of the elements give some support for
these predictions, but the observational data are not yet very conclusive.
103s  t  105 years
Matter and radiation continue to interact thermally through frequent ionization
and recombination of atoms keeping each other at same temperature, if not,
radiation will cool more slowly than matter.
1
, but Tm  1 2 . Tn is the radiation
a
a
temperature. Thus thermal equilibrium was maintained only by a constant
transfer of energy from radiation to matter. Energy transfer held up the
temperature of matter (Tm = Tn) without significantly lowering the temperature of
the radiation. The total mass-energy of matter was and is dominated by rest mass.
So energy transfer had negligible influence on m (density of matter).
For adiabatic expansion, Tn 
t ~ 105 years. The falling temperature reached a few thousand degrees (a/a0 ~ 10-3; a =
radius at time of emission; a0 – initial radius;  ~ 10-20 g/cm3), two things of
interest happened: universe ceased to be radiation – dominated and became
matter dominated;  n   no (ao / a) 2 exceeds    ro (ao / a) 2 and photons
ceased to be energetic enough to keep hydrogen atoms ionized; so electrons and
protons quickly recombined. That these two events were roughly coincident is a
result of the specific, nearly conserved value that the entropy per baryon has in
our universe.
(# of photons in universe)
~ 108
(# of baryons in universe)
Recombination of the plasma at t ~ 105 years was crucial, because it brought an
end to the interaction and thermal equilibrium between radiation and matter.
With very few electrons off which to scatter, and with Rayleigh scattering of
S  entropy per baryons ~
atoms and molecules unimportant, the photons propagated almost freely through
space.
The expansion of the universe has red-shifted the temperature of the freely
1
propagating photons in accordance with T  . As a consequence, today they
a
have a blackbody spectrum with a temperature of 2.7 K. They are identified with
the cosmic microwave radiation discovered in 1965 and they give one direct
information about the nature of the universe at the time they last interacted with
matter
(a / ao ~ 10 3 ,
t ~ 105 years
if
reionization
did
not
occur;
a / ao ~ 0.1, t ~ 5  108 years if reionization did occur).
108y  t  109 y
Before plasma recombination, the photon pressure prevented the uniform matter
(25% He4, 75% H1) from condensing into stars, galaxies, or clusters of galaxies.
After recombination, the photon pressure was gone, and condensation could
begin. Small perturbations in the matter density, perhaps dating back to the
beginning of expansion, then began to grow larger and larger.


Somewhere between a / ao ~ 1 / 30 and a / ao ~ 1 / 10 108 y  t  10 9 y . These
perturbations began developing into stars, galaxies and clusters of galaxies.
Slightly later, at a / ao ~ 1 / 4 , quasars probably “turned on”, emitting light which
astronomers now receive on Earth.
Summary:
1.
2.
3.
4.
5.
6.
7.
8.
initial state
thermal equilibrium, decay of particles, recombination of pairs (0 < t  10 sec)
decoupling and free propagation of gravitons and neutrinos (t  1 sec)
primordial element formation (2 sec  t  103 sec)
thermal interaction of matter and radiation (103 sec  t  105 years)
plasma recombination and transition to matter dominance (t ~ 105 years)
subsequent propagation of photons (t  105 years)
condensation of stars, galaxies and clusters (108 years  t  109 yrs)
Need quantum gravitational effects to see what preceded the big-bang
Other cosmological theories
1. Steady-state theory (Hoyle, Bondi and Gold, 1948) – has not succeeded in
accounting for the cosmic microwave radiation or in explaining observed
evolutionary effects in radio sources and quasars.
2. Hierarchic cosmology of matter in an asymptotically flat space time (Alfven-Klein,
Moritz, de Vaucauleurs) – disagrees with cosmic ray and gamma-ray observation.
The standard big-bang model of the universe predicted by general relativity accords
remarkably well with observation.
Fate of the Universe: Parameters
Central problem of cosmology – will the universe continue to expand forever; or will it
slow to a halt, reverse into contraction, and implode back to a state of infinite (or near
infinite) density, pressure, temperature and curvature?
*universe after big bang expands to maximum dimension, then recontracts and collapses
Reprocessing the universe reprocesses also the physical constants.
c
e
2
 137.0360 
1

~ 1080 particles in the universe
~ 10 40 ~
10 28 cm
10
~ 10 40 ~
~ 10 20 ~
12
~
cm
(radius of universe at max . exp ansion )
(" size" of an elementary particle )
2
e
(electricforces )
~
GmM ( gravitationalforces )
e 2 / mc 2
(G / c 3 )1 / 2
~
(" size" of an elementary Particle )
( Planck length)
Planck length = 1.616x10-33cm
~ 1010 ~
# of
# of
photons in universe 
baryons in universe 
These are part of the initial value data. Such #s are freshly given for each fresh cycle of
expansion of the universe.
A % change one way in say c / e 2 will cause all stars to be red stars; and a comparable
change the other way will make all stars blue stars. In neither case will any star like the
Sun be possible. So life as we know it may not exist.
Could life have developed if the determinants of the physical constants had differed
substantially from those that characterize this cycle of the universe?
1.
2.
3.
4.
5.
What good is that universe without awareness of that universe?
But awareness demands life.
Life demands the presence of elements, heavier than hydrogen.
The production of heavy elements demands thermonuclear combustion.
Thermonuclear combustion normally requires several 109 years of cooking time in a
star.
6. Several 109 years of time will not and cannot be available in a closed universe,
according to general relativity, unless the radius-at-maximum expansion of that
universe is several 109 light years or more.
Hubble’s Work
1. isotropic universe
2. all galaxies except our nearest neighbors show a red shift in their spectral features (an
expanding universe)
Hubble’s law v = Hr, H = 17 x 10-3 m/(s ly) velocity of recession indicated by the red
shift is  distance of galaxy from us.
Arno Pensias and Robert Wilson
- Discovered the cosmic microwave background – the echo of the Big Bang itself
 = 7 cm
- equivalent to the radiation from a blackbody with a temperature between 2.5 K
(actually 2.7 K) and 4.5 K, left-over radiation from the hot phase still permeating
today.
The basic parameter that governs the physical processes is the temperature of the gas of
interacting quantum particles that fills the whole space of the universe. Temperature
because it is proportional to the average energy of the colliding particles, establishes
which new quantum particles can be created from the energy of the collisions.
Birth, Life & Death of Stars
What is the source of stellar energy? 1926
- subatomic nuclear processes according to Arthur Eddington were responsible for the
star’s energy.
- center is about 40 million Kelvlin (today ~ 14 million K)
1928 Quantum Theory of Gammow, Gurney and Condon (tunnel effect)
- particles did not have to surmount the repulsive energy barrier but could tunnel under
it
1929 Robert d’Atkinson and Fritz Houtermans
- energy production of stars by nuclear fusion explained through the “tunneling effect”
Hans Bethe and Carl Friedrich von Weizsacker suggested the “carbon cycle” –
where hydrogen nuclei and carbon nucleus as a catalytic agent, burned hydrogen
into helium, liberating a huge amount of energy.
Subsequently Bethe and Charles Crithchfield – suggested the “proton-proton” chain –
where hydrogen burns into helium without the carbon nucleus.
1938
-
Some scientific advances.
A. Observational facilities in understanding features of stars
1.
2.
3.
4.
5.
B.
C.
sensitive electronic detector
artificial satellites
X-ray astronomy
new optical, infrared and radio telescopes
sophisticated electronic system.
Emergence of quantum theory of atoms, the theoretical and experimental
understanding of nuclear physics and plasma physics (charged particles) .
Advent of powerful computers.

A star is a sphere of a hot gas, (H2 & He) held together by gravity. Gravitational
force increases with mass, so the larger the star, the greater the force tending to
collapse the star. But there is an opposing pressure to prevent this collapse. The
rapidly moving gas particles collide with each other. The frequent collisions means
greater pressure, thus, making the gas expands more thereby preventing the collapse.
At the core of the star, the nuclei are squeezed closely together. The enormous
weight due to the entire mass - equivalent to about 2 million tons resting on a peso
coin. The extreme pressure and high burning temperature at the core ignites the
thermonuclear burning process of hydrogen fusing into helium, generating heat
energy. If temperature is small in the core, nucleus fusion will not last and the star
lives for about 20 million years. When a star contracts, ½ of gravitational energy
released becomes heat energy, which in turn supports the star.

The stability of a star is due to the dynamic balance of gravity and the heat that this
collapse generates.

Stars continue to shrink as fuel is burned and due to relentless crush of gravity – so
they are not really that stable. Some sources of energy to prevent utter collapse are:
1. chemical sources to last 20 million years.
2. nuclear burning of Hydrogen to keep a solar-mass star going for billions of years.
3. Burning of He extends this period.
The Interior of Stars.
Core inner connective layer
– connective currents of hot matter
- cooking pot for heavy elements essential for building planets and life
layer of gas – transfers radiant energy from core to stars outer connective layer
[ See e.g. Sun and Solar Radiation]
Jupiter has 0.1% of sun’s mass – about 1/20 the mass of the lowest-mass star.
Planets form out of flattened disk of gas and cosmic debris surrounding a newly born star.
Stars are opaque – light cannot get out right away from the core. This radiation heats up
the gas in the star’s outer layers stirring them up the way the sun heats the air on a hot
day. This interior movement creates sound waves, which bounce around inside the star.
This acoustic energy is dumped in the solar corona - upper very hot atmosphere of the
sun. These groans, screams, drum-rolls can be detected. The sun also vibrates like a
shaking bowl of gelatin, which gives clues on the internal motion of the core relative to
its outer layer.
A picture of the universe can be gleaned from distant sources of electromagnetic
radiation: visible, radiowave, infrared and microwave, X-rays and -rays.
A star has color and luminosity – its total energy output.

red to blue  cold to hot surface

related to
These are plotted as luminosity vs. temperature
surface temperature called Hetzspring – Russell diagram
Spectra stars from modern spectroscopy developed by Fraunhoffer, Kirchoff and Bunsen
– stars differ in chemical composition.
A. Population I – 1 to 2% of chemical elements heavier than H or He.
B. Population II – those relatively lacking in heavy elements.
Baade discovered these in 1942.
[See p. 12-13] of readings on singularity.
How is a star made?
- formation of stars in giant molecular – cloud complexes – clouds consisting mostly of
hydrogen and whose mass >> individual star.
-
cloud fragments into smaller clump and results in mutual gravitational attraction of
gas particles and dust.
Sun was probably formed by a disk of leftover matter swishing around it like the
white (scalar nebula) of a fried egg surrounding the yolk and from it the solar system
of planets subsequently formed.
Stars lead uneventful, middle-class lives, lasting for billions of years.
A. T - Tauri stars – about 100 K to 106 years; they exhibit unconventional behavior –
rich, complex, often anomalous emission spectra. Surrounded by hot gas and
luminous sets of matter.
B. Cepheid variables – brightness oscillates with period ranging from 3 days to weeks.
Blinking beacons in the sky, e.g. polaris, the Ninth star. They release energy by
pulsating their intrinsic brightness. Discovered by Henrietta Leavitt in 1912, period –
luminosity relation.
Death of Stars

when burning stops, star resumes collapsing.
Three possible fates
1. white dwarfs – tiny stars made of solid carbon matter thousands of times denser than
ordinary matter. Stars with mass < 1.4 times the sun’s mass.
2. Neutron – star – recurrent of a supernova explosion when more cursive stars
collapse. The recurrence is a gigantic atomic nucleus the size of a city. (discovered in
1967) pulsars – spring neutron star.
3. Black hole – stars with masses > 2 solar masses collapse to objects in which space
itself gets turned “inside out”