Astronomy 1101

Astronomy 1101 --- Planets to Cosmos

Todd Thompson
Department of Astronomy
The Ohio State University

Einstein's Universe: Isotropy & Homogeneity

Key Ideas

Cosmological Principle:: The Universe is Homogeneous and Isotropic on Large Scales.; No special places or directions.
General Relativity predicts an expanding universe.
Einstein's Greatest Mistake (?)

Cosmology

Cosmology is the study of the entire Universe:

Physics of the Universe.
Distribution of objects on all scales.
Motions of objects in the Universe.
Evolution of the Universe.
Age, Origin, and Fate of the Universe.

The Universe in 1917

Einstein explored the cosmological implications of General Relativity.

Observational State in 1917:

Kapteyn model of the Milky Way was favored by some (but not all) astronomers.
No agreement on the "spiral nebulae."
First good calibrations of the P-L relation for Cepheids and RR Lyrae variables.

The Cosmological Principle

"The Universe is Homogeneous and Isotropic on the Largest Scales."

Critical assumption underlying Cosmology.

Homogeneous:

No special places in the Universe.

Isotropic:

No special directions

Largest Scales:

Large enough to average out the small-scale details of the matter distribution

Homogeneity

When viewed on the largest scales:

The average density of matter is about the same in all places in the Universe.
The Universe is fairly smooth on large scales.

Does not apply locally:

We see planets, stars, galaxies in regions nearby in space.
The Universe is locally rather "lumpy".

Isotropy

When viewed on the largest scales:

The Universe looks the same to all observers.
The Universe looks the same in all directions as viewed by a particular observer.

Does not apply locally:

We see different numbers of local objects in different directions.

The Dynamic Universe

Einstein applied the Cosmological Principle to General Relativity and got a surprise:

The spacetime of the Universe could not be static and unchanging.
The Universe must either expand or contract!

Astronomers assured him that no such general motion was observed.

The Cosmological Constant

To make the Universe static, he was required to add a new term in his equations:

The Cosmological Constant, L (Lambda):

"Repulsive" gravitational force term
Arises from empty space.
Balances the effects of gravity.
Halts the motion of spacetime.

At the time there was no physical reason to introduce a Cosmological Constant, it was motivated by a presumption that the Universe must be static.

Cosmic Expansion

1914-1922: Vesto Slipher, Lowell Observatory

Measured the radial velocities of the brightest "spiral nebulae".

Results: 21 out of 25 spirals showed a systematic redshift.

Apparent systematic motion away from us.
Some radial velocities are large: >2000 km/second.

Einstein's Greatest Blunder...

By introducing an ad hoc Cosmological Constant, Einstein missed being able to predict the expansion of the Universe.

1920s:

de Sitter showed that Einstein had made a mathematical error, and that his Cosmological Constant made the universe static but unstable (like a needle balanced on its point).
Friedmann & Lemaitre showed that without a cosmological constant, GR predicts that the Universe is expanding.

Edwin Hubble firmly established the facts of general cosmic expansion observationally in 1929.

State of the Art

Einstein's guess about the homogeneity and isotropy of the Universe was brilliant and far ahead of the scanty empirical data of his time.

Modern observations bear out large-scale homogeneity & isotropy on average:

Large-scale galaxy surveys show that the distribution of galaxies is essentially the same everywhere on scales larger than 100 Mpc. (homogeneity)
Maps of the cosmic background radiation show that it looks generally the same in all directions. (isotropy)

Modern Cosmological Constant

In current cosmological theory, Lambda reappears in a somewhat altered form as the "vacuum energy" of space.

Quantum ground-state of empty space.
Acts as an extra pressure on the Universe.

Distinction:

It actually accelerates the expansion of the universe rather than stopping it.
There is increasing observational evidence that a Cosmological Constant, or something very like it, may be real!

We'll discuss this surprising new result in a future lecture.