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

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

Obler’s 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

The Expanding Universe

Edwin Hubble discovered in the 1920's that the universe is not static---it is expanding (Hubble’s Law).

The wavelength of light “stretches” as a consequence of the expansion, decreasing the energy—a cosmological redshift

Because the luminosity = the energy/time, the apparent brightness will be reduced enough by the expansion to make the sky dark.

The Hubble Expansion LawThe 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.

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),

Hubble’s Law

Hot Big Bang TheoryThe 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.

Cosmic Microwave Background (CMB) Radiation

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

Image courtesy COBE homepage.

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.

(A Brief) History of the CMB• 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

Tim

e

EarlyUniverse

Present

13 Gyr

0.5 Myr

<1 yr • Radiation Dominated

–universe even hotter and denser

–CMB photons coupled to matter through collisions

•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

Cosmic GeometriesIf 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.

Geometries for the Universe

Consequences of Curvature

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 Matter—matter that does not radiate

• Evidence for Dark Matter includes:

• Galaxy clusters

• Rotation of galaxies

• Gravitational lensing

• Confined Gas Nebulas

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

Inflationary Universe