26.5 The Expanding Universe

Discovery and Implications of the Expanding Universe

Before Edwin Hubble's work in the 1920s, most astronomers thought the Milky Way was the entire universe. Hubble's observations changed everything by showing that galaxies are moving away from us, and the farther away they are, the faster they're receding. This discovery provided the first strong evidence that the universe itself is expanding.

Hubble's Universe Expansion Discovery

Hubble used the 100-inch Hooker telescope at Mount Wilson Observatory to study distant galaxies. His approach combined two key measurements:

• Distance measurements using Cepheid variable stars as "standard candles." These stars pulsate at a rate directly tied to their true brightness, so by comparing how bright they appear to how bright they actually are, you can figure out how far away they are.
• Redshift measurements from galaxy spectra. When a galaxy moves away from us, its light gets stretched to longer (redder) wavelengths. This is the Doppler effect, the same principle that makes an ambulance siren sound lower-pitched as it drives away from you.

Hubble found a clear pattern: more distant galaxies had greater redshifts, meaning they were receding faster. This relationship became known as Hubble's law. It's now called the Hubble-Lemaître law, recognizing that Belgian astronomer Georges Lemaître independently derived the same relationship a couple of years before Hubble published his data.

Application of Hubble's Law

Hubble's law states that a galaxy's recession velocity is proportional to its distance:

$v = H_0 \times d$

where $v$ is the recession velocity, $d$ is the distance to the galaxy, and $H_0$ is the Hubble constant.

The Hubble constant represents the current expansion rate of the universe. Its value is approximately 70 km/s/Mpc (kilometers per second per megaparsec, where 1 Mpc equals 3.26 million light-years). That means a galaxy 1 Mpc away recedes at about 70 km/s, a galaxy 2 Mpc away recedes at about 140 km/s, and so on.

To calculate a galaxy's distance using Hubble's law:

1. Measure the galaxy's redshift from its spectrum.
2. Convert that redshift to a recession velocity using the Doppler shift formula.
3. Divide the recession velocity by the Hubble constant to get the distance: $d = v / H_0$.

The redshift caused by the expansion of space itself is called cosmological redshift, which is distinct from redshift caused by a galaxy's individual motion through space.

Models of the Expanding Universe

The fate of the universe depends on how much matter and energy it contains. Astronomers have proposed several models:

• Critical density model: The universe contains exactly enough matter to slow expansion to zero over infinite time, but never quite reverse it. Space is flat (no curvature). Think of a ball rolled uphill with just barely enough speed to reach the top.
• Open model: The universe has less than the critical density of matter. Expansion continues forever and never slows to zero. Space has negative curvature, sometimes described as saddle-shaped.
• Closed model: The universe has more than the critical density. Gravity eventually halts and reverses expansion, leading to a collapse called the "Big Crunch." Space has positive curvature, like the surface of a sphere.
• Accelerating expansion model: This is the model best supported by current evidence. In the late 1990s, observations of distant Type Ia supernovae showed that the expansion of the universe is actually speeding up, not slowing down. This acceleration is attributed to dark energy, a mysterious form of energy that permeates all of space. If this continues, the universe will expand at an ever-increasing rate, eventually leading to a "Big Freeze" where galaxies drift apart and stars burn out.

Variations in the Hubble Constant

You might expect the Hubble constant to be a single agreed-upon number, but different measurement methods actually give slightly different values. This discrepancy is one of the biggest open questions in cosmology right now.

Different measurement techniques include:

• Cepheid variable stars and Type Ia supernovae, which serve as standard candles at different distance scales
• Gravitational lensing, where light bending around massive objects provides distance information
• The cosmic microwave background (CMB), leftover radiation from the early universe that encodes information about expansion history

Systematic errors compound across the "cosmic distance ladder." Each rung of the ladder (parallax, then Cepheids, then supernovae) relies on calibrating against the previous rung, so small errors at one step get amplified at larger distances.

Local variations also play a role. Large-scale structures like galaxy clusters exert gravitational pull that can speed up or slow down nearby expansion, making local measurements differ from the global average.

Model assumptions matter too. The value you derive for $H_0$ depends on what you assume about matter density, dark energy, and other cosmological parameters built into your calculations.

Fundamental Concepts in Cosmology

These terms come up frequently when discussing the expanding universe:

• Cosmological principle: On the largest scales, the universe looks the same everywhere (homogeneous) and in every direction (isotropic). This is a foundational assumption of modern cosmology.
• Friedmann equations: A set of equations derived from general relativity that describe how the expansion of space changes over time in a homogeneous, isotropic universe.
• Scale factor: A value that tracks how the size of the universe changes relative to some reference time. As the universe expands, the scale factor increases.
• Cosmic inflation: A theory proposing that the very early universe underwent an extremely rapid burst of expansion in a tiny fraction of a second, which helps explain why the universe appears so uniform on large scales.