Lecture 14: Hubble's Law and the Big Bang: Observational Cosmology

ASTR 230 Stars, Galaxies, and the Universe

Context and Why This Matters

Edwin Hubble’s 1929 discovery that galaxies’ recession velocities are proportional to their distance was the first direct observational evidence that the universe is expanding, transforming cosmology from philosophical speculation into a quantitative, testable science and eventually leading to the Big Bang model this lecture summarizes.

Learning Goals

  1. State Hubble’s law and use redshift-distance data to estimate the Hubble constant.
  2. Explain how the Hubble constant sets an approximate age for the universe (the Hubble time).
  3. Summarize the observational pillars of the Big Bang model.

Opening Phenomenon

A sample of five well-studied galaxy clusters, spanning distances from about 16.5 Mpc (Virgo) to about 520 Mpc (Bootes), shows recession velocities that increase in direct proportion to distance — exactly the linear relationship Hubble first identified with a far smaller and less precise data set in 1929.

Terms Developed in Context

These terms form the reasoning chain from observation to model, calculation, and interpretation. Each entry expands the corresponding term-explorer panel and should be read alongside the worked example.

Hubble's law

Hubble's law states that a galaxy's recession velocity v is proportional to its distance d: v = H0 d, where H0 (the Hubble constant) sets the current expansion rate of the universe.

Use and relationship: Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance. The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

Hubble constant

Hubble's law states that a galaxy's recession velocity v is proportional to its distance d: v = H0 d, where H0 (the Hubble constant) sets the current expansion rate of the universe.

Use and relationship: Because H0 has units of inverse time, its reciprocal (the Hubble time, 1/H0) gives an order-of-magnitude estimate for the age of the universe, exact only for a universe that has expanded at a perfectly constant rate (which ours has not, given the accelerating expansion of Lecture 13). The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

Hubble time

Because H0 has units of inverse time, its reciprocal (the Hubble time, 1/H0) gives an order-of-magnitude estimate for the age of the universe, exact only for a universe that has expanded at a perfectly constant rate (which ours has not, given the accelerating expansion of Lecture 13).

Use and relationship: Hubble time: 1/H0 = 1 / (71.5 km/s/Mpc), converting units (1 Mpc = 3.086e+19 km) gives t_Hubble ≈ 13.7 billion years — remarkably close to the independently measured age of the universe from the cosmic microwave background (about 13.8 billion years), especially given this estimate assumes a constant expansion rate rather than the universe’s actual expansion history. The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

redshift

The cosmic microwave background (a near-perfect 2.7 K blackbody radiation field filling the entire sky, discovered accidentally by Penzias and Wilson in 1965) is the cooled, redshifted afterglow of the hot, dense early universe, predicted by the Big Bang model decades before its detection.

Use and relationship: State Hubble’s law and use redshift-distance data to estimate the Hubble constant. The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

cosmic microwave background

The cosmic microwave background (a near-perfect 2.7 K blackbody radiation field filling the entire sky, discovered accidentally by Penzias and Wilson in 1965) is the cooled, redshifted afterglow of the hot, dense early universe, predicted by the Big Bang model decades before its detection.

Use and relationship: Hubble time: 1/H0 = 1 / (71.5 km/s/Mpc), converting units (1 Mpc = 3.086e+19 km) gives t_Hubble ≈ 13.7 billion years — remarkably close to the independently measured age of the universe from the cosmic microwave background (about 13.8 billion years), especially given this estimate assumes a constant expansion rate rather than the universe’s actual expansion history. The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

Big Bang nucleosynthesis

Independent observational pillars — the expansion itself (Hubble’s law), the cosmic microwave background, and the observed primordial abundances of hydrogen, helium, and lithium (Big Bang nucleosynthesis) — together support the Big Bang model of a universe that began in a hot, dense state roughly 13.8 billion years ago.

Use and relationship: The cosmic microwave background (a near-perfect 2.7 K blackbody radiation field filling the entire sky, discovered accidentally by Penzias and Wilson in 1965) is the cooled, redshifted afterglow of the hot, dense early universe, predicted by the Big Bang model decades before its detection. The lecture's quantitative connection is \( v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

Evidence

Model

Working Equation

\[ v = H_0\,d, \qquad t_{\rm Hubble} = \dfrac{1}{H_0} \]

Worked Example

  1. Fitting v = H0 d to the five-cluster sample (Virgo, Hydra, Ursa Major, Corona Borealis, Bootes) gives a best-fit Hubble constant H0 ≈ 71.5 km/s/Mpc.
  2. This is close to modern precision measurements (roughly 67-73 km/s/Mpc, depending on method — the ongoing "Hubble tension"), confirming that even a small five-cluster classroom sample recovers the right order of magnitude and rough value.
  3. Hubble time: 1/H0 = 1 / (71.5 km/s/Mpc), converting units (1 Mpc = 3.086e+19 km) gives t_Hubble ≈ 13.7 billion years — remarkably close to the independently measured age of the universe from the cosmic microwave background (about 13.8 billion years), especially given this estimate assumes a constant expansion rate rather than the universe’s actual expansion history.

Common Misconception

Interpreting galaxies’ recession as galaxies "moving through" space away from us, the way an explosion scatters debris from a central point. Hubble’s law describes the expansion of space itself between galaxies; there is no center of the expansion, and every observer in the universe sees the same pattern of galaxies receding in proportion to distance.

Active-Learning Guidance

Using the five-cluster data, discuss why fitting a straight line through the origin (rather than allowing a nonzero intercept) is the physically motivated choice for testing Hubble’s law, and what a large intercept would imply if it were required.

Lab Connection

Lab 07 has students fit the Hubble constant from the same five-cluster data set used in this lecture’s worked example, then use it to estimate the age of the universe and compare to the CMB-based value.

Synthesis Questions

References