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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 34: The Expanding Universe

Readings: Ch 26, section 26-5 & Ch 28, section 28-2

Key Ideas

Hubble's Law
Galaxies are receding from us.
Recession velocity gets larger with distance.

The Hubble Parameter (H0)
Measures the present-day rate of expansion of the Universe.

Cosmological Redshifts
Due to the expansion of space
Redshift distances
Redshift maps of the Universe

Discovery of Expansion

1917: work by Vesto Slipher at Lowell Observatory


Most galaxies are rapidly receding from us.

Hubble's Discovery

1929: Edwin Hubble measured distances to 25 galaxies:


Systematic expansion of the Universe.

Hubble's Data in 1929
Edwin Hubble's 1929 expansion data

Hubble and Humason's Data in 1931
Refined version by Hubble & Humason in 1931
[Modern plots using the original data.]

Hubble's Law

Hubble's Law
v = recession velocity in km/sec
d = distance in Mpc
H0 = expansion rate today (Hubble Parameter)

In words:

The more distant a galaxy, the faster its recession velocity.


Hubble's Law demonstrates that the Universe is expanding in a systematic way:


Nature of the Expansion

General Expansion of Spacetime:

What is the recession velocity?

Expanding Universe Schematic

As the Universe get 2x larger, the distances between galaxies get 2x larger.


While the distances between galaxies increase over time, the sizes of the galaxies remain the same. This is because galaxies are bound together by gravitation locally, and so do not share in the global expansion of spacetime around them.

Hubble Parameter: H0

Measures the rate of expansion of the Universe today.

H0 is very hard to measure

Cosmological Redshifts

All galaxies (with very few exceptions) are receding from us.

The recession is quantified in terms of the "cosmological redshift" of the galaxy, z:

Cosmological Redshift Formula
The above is not a Doppler Shift! It measures the expansion of spacetime, not motions through space.

As the universe expands, light waves get stretched out:

Animated GIF of Cosmological Redshift, courtesy of Wayne Hu, at the University of Chicago.

Redshift Distances

For relatively nearby galaxies, the redshift is directly proportional to the distance, through the Hubble Law:
Hubble Distance Formula for nearby galaxies
z = cosmological redshift
c = speed of light
This formula is only valid for relatively nearby galaxies.


Nonetheless, because cosmological redshift is a direct observable related to distance, it used as a surrogate for distance, especially for distant galaxies.

Mapping the Universe

We can map the large-scale distribution of galaxies using their cosmological redshifts.

The largest map to date is from the 2dF Galaxy Redshift Survey, which includes about 220,000 galaxies:

Sloan Digital Sky Survey

Dedicated 2.5-meter telescope in New Mexico

Making images of 1/4 of the sky in 5 colors:

Redshift Survey:

One of the results will be a 3D map of a large segment of the local universe. A preliminary version of this map.

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Updated: 2019 October 25
Copyright © Richard W. Pogge, All Rights Reserved.