The Cosmological Principle

1
The Cosmological Principle
Viewed on sufficiently large distance scales,
there are no preferred directions or preferred
places in the Universe.
2
Consequences of the Cosmological Principle

• The twin pillars of Cosmology
• Cosmic homogeneity
• On a large enough scale, any region of the
  universe appears the same as any other
• Isotropy
• The universe looks the same in all directions,
  regardless of the way we view it

Implies that the universe has no center or edge
3
Oblers Paradox
The fact that the Universe is not static but
expanding solves a paradox that has been known at
least since the 1500s but that was popularized by
Heinrich Olbers in 1826 and has come to be known
as Olber's Paradox. It states that if the
Universe is static and uniformly filled with
stars and galaxies, the night sky should be as
bright as the surface of a star. That this is not
so constitutes the paradox. The expansion of the
Universe solves this problem
4
The Expanding Universe
Edwin Hubble discovered in the 1920's that the
universe is not static---it is expanding
(Hubbles Law). The wavelength of light
stretches as a consequence of the expansion,
decreasing the energya cosmological
redshift Because the luminosity the
energy/time, the apparent brightness will be
reduced enough by the expansion to make the sky
dark.
5
The Hubble Expansion Law
The redshift of galaxies is larger for more
distant galaxies. Hence, the farther a galaxy,
the faster it is receding from Earth. The Hubble
constant is given by H v/d where v is the
galaxy's radial outward velocity, d is the
galaxy's distance from earth, and H is the
current value of the Hubble constant. The units
of the Hubble constant are "kilometers per second
per megaparsec." The value of the Hubble
constant initially obtained by Hubble was around
500 km/s/Mpc, and currently is somewhere between
50 km/s/Mpc and 100 km/s/Mpc.
6
Hubble Time
Hubble time T is just the inverse of the Hubble
Constant T 1 / H Taking a value of H
20 km/s/Mly (where Mly means mega-light years),


7
Hubbles Law
8
Hot Big Bang Theory
The Hot Big Bang The big bang starts off with a
state of extremely high density and pressure for
the Universe. Under those conditions, the
Universe is dominated by radiation. This means
that the majority of the energy is in the form of
photons and other massless or nearly massless
particles (like neutrinos) that move at near the
speed of light. As the big bang evolves in time,
the temperature drops rapidly as the Universe
expands and the average velocity of particles
decreases. Finally, one reaches a state where
the energy of the Universe is primarily contained
in non-relativistic matter (matter sufficiently
massive that its average velocity is very much
less than the speed of light). This is called a
matter dominated universe. The early Universe was
radiation dominated, but the present Universe is
matter dominated.
9
Cosmic Microwave Background (CMB) Radiation
10
COBE CMB Image

• The sky temperature with range from 0-4 Kelvin
• Microwave background is very uniform at 3 Kelvin

Image courtesy COBE homepage.
11
The Cosmic Background Radiation (CMB)
Cosmic background radiation is the afterglow of
the big bang, cooled to a faint whisper in the
microwave spectrum by the expansion of the
Universe for 15 billion years. Red
denotes hotter fluctuations and blue and black
denote cooler fluctuations around the average.
These fluctuations are extremely small,
representing deviations from the average of only
about 1/100,000 of the average temperature of the
observed background radiation.
12
(A Brief) History of the CMB
Present

• Matter dominated
• Universe cold (3K) with low matter density
• one hydrogen atom per 10 cubic meters
• 400 million CMB photons per cubic meter
• CMB photons and matter rarely interact -
  transparent
• typical matter in form of atoms and molecules

13 Gyr

• Matter/Radiation
• universe hot (3,000K) and a billion times denser
• atoms and molecules broken up
• matter in form of electrons and nuclei
• CMB photons coupled to matter through collisions

0.5 Myr
Time

• Radiation Dominated
• universe even hotter and denser
• CMB photons coupled to matter through collisions

lt1 yr
Early Universe
13
Cosmic Geometries
If space has negative curvature, there is
insufficient mass to cause the expansion of the
Universe to stop. The Universe in that case has
no bounds, and will expand forever. If space has
no curvature (it is flat), there is exactly
enough mass to cause the expansion to stop, but
only after an infinite amount of time. Thus, the
Universe has no bounds in that case and will also
expand forever, If space has positive curvature,
there is more than enough mass to stop the
present expansion of the Universe. The Universe
in this case is not infinite, but it has no end
(just as the area on the surface of a sphere is
not infinite but there is no point on the sphere
that could be called the "end"). The expansion
will eventually stop and turn into a contraction.
14
Geometries for the Universe
15
Consequences of Curvature
16
Dark Matter

• Most astronomers believe that as much as 90
  percent the mass in the universe may be objects
  or particles that cannot be seen.
• This missing mass is referred to as Dark
  Mattermatter that does not radiate
• Evidence for Dark Matter includes
• Galaxy clusters
• Rotation of galaxies
• Gravitational lensing
• Confined Gas Nebulas

17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
Inflationary Universe
22
Dark Energy

• Dark Energy is a form of energy that opposes the
  self-attraction of matter and causes the
  expansion of the universe to accelerate.
• The universe is made mostly of dark matter and
  dark energy
• Necessary to invoke in order to explain current
  observations of the expansion of the universe

23
Inflationary Universe