Otterbein College Department of Physics and Astronomy

COSMOLOGY

Cosmology is the study of the Universe as a whole.

on the largest scale, the Universe appears to be relatively homogeneous (same at every point), and isotropic (same in all directions). The assumption that the Universe is homogeneous and isotropic is the cosmological principle.

This is quite a strong assumption, because it implies that the Universe has no edge and no center
This is the ultimate statement of the Copernican principle, or the principle of mediocrity: no one can be at the center of the Universe, because it has no center

HUBBLE'S LAW AND THE BIG BANG

If all the objects in the Universe started from a single point at a single time, but with different velocities, they would have travelled a distance proportional to their velocity, distance=velocity x time

Compare Hubble's law, distance = velocity x 1/Hubble's constant

so Hubble's law says that the Universe looks as though everything exploded from a single point at a time 1/H₀, 11-16 billion years ago: this is the Big Bang. (Model to be refined, see below).

Note: this does not imply that there is a center of the Universe.

OLBER'S PARADOX

Why is the sky dark? If space has no end, and is uniformly filled with stars, if we look far enough in any direction, we should see a star. (More distant stars will appear dimmer, but there are more of them.)

Resolution: the Universe has a finite age, and light from the most distant stars hasn't had time to reach Earth.

COSMOLOGICAL ORIGIN OF THE HUBBLE REDSHIFT

Another way to think of the Hubble redshift: it's not that the galaxies are receding from Earth, it's that the space between Earth and the distant galaxies is increasing in size. As a photon travels from a distant galaxy towards Earth, it is stretched by the expansion of space, so when it arrives at Earth it has a longer wavelength than it had when it started.

THE 3-DEGREE BACKGROUND RADIATION (also called cosmic background radiation or microwave background radiation)

Heat of the explosion should still be detectable in the form of black-body radiation but redshifted by the expansion of the Universe to longer wavelengths (cooled) to a temperature of 3 K (microwave radio wavelengths). Predicted by G. Gamow, 1948; observed by Arno Penzias and Robert Wilson, 1964.

There are also slight variations in temperature of the background radiation. The largest part is due to the motion of the Earth with respect to the radiation--redshifted behind (to lower T) and blue shifted before (to higher T).

The Earth's velocity is 360 km/s with respect to the background radiation (a fairly small velocity on cosmic scales--the Earth is nearly at rest with respect to the Universe)

THE EARLY UNIVERSE

TIME
TEMPERATURE
DESCRIPTION
<10^-43 s	>10^{32 K}	?????? (Planck era)
10^-43 s	10³² K	gravity splits from other forces
10^-43 to 10^-35 s		Grand Unification era
10^-35 s	10²⁸ K	Strong force splits from others. Epoch of inflation?
10^-35 s to 10^-10 s		Electroweak era
10^-10 s	10¹⁵ K	electromagnetic force separates from others
10^-10 s to 10^-4 s		Quark era
10^-4 s	10¹³ K	Quarks combine to form protons and neutrons.
10^-4 to 500,000 years		Radiation era
180 s	10⁹ K	protons and neutrons combine to form nuclei; primordial helium formed
500,000 years	3000 K	nuclei and electrons combine to form atoms
500,000 years to present		Matter era

EVIDENCE FOR THE BIG BANG THEORY

The Hubble expansion.
The 3 K background radiation.
The observed cosmic abundance of helium and other elements

ALTERNATIVES TO THE BIG BANG THEORY

Steady State hypothesis (Hoyle and others, 1940's): as the Universe is now, it always has been and always will be. Problems:

Since the galaxies are spreading out, new matter must be continually created to replace them
distant galaxies (and quasars) appear different than nearby galaxies, implying that the Universe has not always been as it is now

Big Bang theory is very successful, so Steady State hypothesis is not popular any more

THE FATE OF THE UNIVERSE

The Hubble expansion is opposed by the gravitational attraction of the mass in the Universe. Is the Hubble velocity of the galaxies enough to exceed the "escape velocity" of the gravity of the Universe?

If yes, then the galaxies will fly apart and the Universe will expand forever
If no, then eventually expansion will end, universe will contract, heat up, and end in a "Big Crunch".

WELL, WHICH ONE IS IT?

To answer the question, we need to know:

the Hubble constant H₀ (expansion velocity)
the density of mass in the Universe (gravity)

cosmic density parameter is defined to be the fraction of the amount of mass required to halt expansion that is actually present,

₀= actual density/critical density

much of the mass in the Universe is dark, so we don't know the density of the Universe.

Visible matter gives ₀=0.01.
Including all known dark matter, ₀=0.2-0.3
some theories favor ₀=1. Not yet ruled out by observation.

H₀ is not known very accurately either.

THE GEOMETRY OF SPACE

In cosmology, Newton's theory of gravity must be replaced with Einstein's theory of gravity, general relativity. In general relativity, the bending of the path of objects by gravitational forces is described as being due to the curvature of space. Classical tests of general relativity:

bending of starlight by the Sun's gravitational field (and other gravitational lensing effects)
precession of the perihelion of Mercury
redshift due to gravity

In the simplest model, discussed in the text, there is simple relationship between the fate of the universe, its curvature, and its size:

fate	curvature	2-D illustration	type	size
ends in Big Crunch	positive	sphere	closed	finite
expands forever	zero (flat)	plane	critical	infinite
expands forever	negative	saddle	open	infinite

To summarize, if the Universe is infinite in time, it is also infinite in space; if finite in time, it is finite in space.

Graph New results. General relativity also includes a possible new effect called the cosmological constant, ₀, which can be either attractive like gravity or repulsive like a pressure opposing gravity. Our text discusses what happens if ₀=0. If ₀ 0, then we need to know three things to know the fate of the Universe:

the Hubble constant H₀ (expansion velocity)
the density parameter ₀ (gravity),
the cosmological constant ₀

The results are summarized in the graph to the right. Recent results appear to favor values near the border between the purple and yellow areas.

Key to graph:

area of graph	beginning	fate	curvature	size
red	no beginning	expands forever	positive	finite
yellow	Big Bang	expands forever	positive	finite
green	Big Bang	Big Crunch	positive	finite
blue	Big Bang	Big Crunch	negative	infinite^*
purple	Big Bang	expands forever	negative	infinite^*

^*If space has zero or negative curvature, the simplest model again implies it is infinite in size; but it may also be finite. You can read more about this possibility in an article in the 4/99 issue of Scientific American.

THE AGE OF THE UNIVERSE (revisited)

Our simple model that the age of the Universe = 1/H₀ is not quite correct, because it assumed constant velocity -- neglecting effects of gravity and ₀. For example, in one popular model, ₀=0 and ₀=1, then instead the age of the Universe is 2/3H₀.

The latest results indicate that H₀=70 km/s/Mpc ± 10% and ₀=0.3, which would make the age of the Universe 12 to 13 billion years old (even older, if the cosmological constant is not zero).

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