11.3 Hubble's Law and the Expanding Universe

Hubble's Law and Cosmic Expansion

Hubble's Law and the Expansion of the Universe

In 1929, Edwin Hubble published observations that changed cosmology forever. By measuring the distances and velocities of dozens of galaxies, he found a striking pattern: the farther away a galaxy is, the faster it's moving away from us.

This relationship is Hubble's Law, and it's expressed as:

$v = H_0 \times d$

where $v$ is the recessional velocity of a galaxy, $d$ is its distance from Earth, and $H_0$ is the Hubble constant, the proportionality factor that links the two.

A few things to keep straight about what this means:

• Hubble's Law implies the universe is expanding uniformly in all directions. Every galaxy sees every other galaxy receding from it. There's no special center to the expansion.
• The expansion is not galaxies flying through space like shrapnel from an explosion. Instead, the fabric of space itself is stretching, carrying galaxies along with it. Think of dots on a balloon as it inflates: the dots don't move across the surface, but the growing surface increases the distance between them.

Implications of Hubble's Law

If you run the expansion backward in time, everything converges to a single point. That's the core logic behind the Big Bang theory: the universe had a definite beginning.

• The reciprocal of the Hubble constant, $1/H_0$, gives a rough estimate of the age of the universe. This is sometimes called the Hubble time. It assumes a constant expansion rate, which is a simplification, but it gets you in the right ballpark. Current measurements place the age of the universe at approximately 13.8 billion years.
• Hubble's Law also raises questions about the universe's ultimate fate. Depending on the total density of matter and energy, the universe could:
  • Expand forever (open universe)
  • Eventually collapse back on itself (closed universe)
  • Sit right at the boundary, expanding at an ever-decreasing rate (flat universe)

Evidence for an Expanding Universe

Redshift of Distant Galaxies

The primary evidence Hubble used was redshift. When light travels through expanding space, the stretching of space elongates the light's wavelength, shifting it toward the red end of the spectrum. The greater the distance the light has traveled, the more stretching it undergoes.

• The amount of redshift in a galaxy's spectrum is proportional to its distance from Earth. More distant galaxies show greater redshift, exactly as Hubble's Law predicts.
• This is technically different from the ordinary Doppler effect, where a source moves through space and its motion shifts the wavelength. Cosmological redshift is caused by the expansion of space itself stretching the light waves while they're in transit.
• Hubble measured redshift using the absorption lines in galaxy spectra. Each element absorbs light at specific known wavelengths. When those lines appear shifted toward longer (redder) wavelengths compared to a lab reference, you can calculate how much the light was stretched during its journey.

Cosmic Microwave Background Radiation

The cosmic microwave background (CMB) is a faint glow of microwave radiation that fills the entire sky, coming from every direction equally. It was discovered accidentally in 1965 by Arno Penzias and Robert Wilson, who initially thought the persistent signal in their radio antenna was caused by pigeon droppings. It wasn't.

The CMB is the afterglow of the early universe. About 380,000 years after the Big Bang, the universe cooled enough for atoms to form, and light could finally travel freely through space. That light has been traveling ever since, stretched by the expansion of space from its original high-energy state down to microwaves.

• The CMB has a nearly perfect blackbody spectrum with a temperature of about 2.7 Kelvin, exactly matching predictions from the Big Bang theory.
• Tiny temperature fluctuations in the CMB (on the order of one part in 100,000) reveal slight variations in the density of matter in the early universe. These small clumps eventually grew, under gravity, into the galaxies and galaxy clusters we see today.
• These fluctuations also support the idea of cosmic inflation, a brief period of exponential expansion in the universe's first fraction of a second.

The Big Bang Theory

Overview of the Big Bang Theory

The Big Bang theory is the prevailing cosmological model for the origin and evolution of the universe. It proposes that approximately 13.8 billion years ago, the universe began in a state of extraordinarily high density and temperature, and has been expanding and cooling ever since.

The theory's strength comes from explaining several independent observations at once:

• The expansion of the universe (Hubble's Law)
• The existence and properties of the cosmic microwave background
• The relative abundances of light elements in the universe: roughly 75% hydrogen, 25% helium, and trace amounts of lithium. These ratios match what nuclear physics predicts would form in the first few minutes after the Big Bang, a process called Big Bang nucleosynthesis.

When multiple unrelated lines of evidence all point to the same conclusion, that's a strong sign the model is on the right track.

Key Stages in the Evolution of the Universe

The history of the universe after the Big Bang unfolded in distinct stages:

1. Cosmic inflation (less than $10^{-32}$ seconds after the Big Bang): The universe expanded exponentially, growing by a factor of at least $10^{26}$ in linear size. This brief burst smoothed out the universe and explains why the CMB looks so uniform across the sky, even between regions that would otherwise be too far apart to have ever been in contact.
2. Particle formation (first few minutes): As the universe cooled, quarks combined into protons and neutrons. These then fused into the nuclei of light elements: hydrogen, helium, and lithium. This is Big Bang nucleosynthesis.
3. Recombination (about 380,000 years): The universe cooled enough for electrons to bind with nuclei, forming neutral atoms. Light decoupled from matter and began traveling freely. This is the light we now detect as the CMB.
4. Structure formation (millions to billions of years): Gravity pulled matter into denser regions, forming the first stars, galaxies, and eventually the large-scale cosmic web of galaxy clusters and filaments we observe today.

Possible Scenarios for the Ultimate Fate of the Universe

The universe's fate depends on a tug-of-war between the expansion rate and the gravitational pull of all the matter and energy within it. There's a critical density that determines which side wins:

• Open Universe (density below critical value): Expansion wins permanently. The universe keeps expanding forever, eventually experiencing a "Big Freeze" as stars burn out and galaxies drift apart into cold, dark isolation.
• Closed Universe (density above critical value): Gravity eventually overcomes expansion. The universe stops expanding, reverses, and collapses back on itself in a "Big Crunch."
• Flat Universe (density exactly at critical value): Expansion continues forever but gradually slows, approaching zero expansion rate in the infinite future.

Current Observations and the Role of Dark Energy

In 1998, two independent teams studying distant Type Ia supernovae made a surprising discovery: the expansion of the universe isn't just continuing, it's accelerating. This was the opposite of what most physicists expected, since gravity should be slowing the expansion down.

To explain this acceleration, cosmologists introduced the concept of dark energy, a hypothetical form of energy that permeates all of space and exerts a kind of repulsive pressure, pushing the expansion to speed up.

• Current observations, including CMB measurements and supernova data, indicate the universe is very close to spatially flat. Its energy budget breaks down to roughly 68% dark energy, 27% dark matter, and 5% ordinary matter.
• The nature of dark energy remains one of the biggest open questions in physics. Leading candidates include the cosmological constant (a fixed energy density of empty space, which Einstein originally introduced into his field equations for a different reason and later reportedly called his "greatest blunder") and quintessence (a dynamic field whose energy density changes over time).
• If dark energy continues to dominate and even strengthens, one speculative outcome is the "Big Rip," where the accelerating expansion eventually tears apart galaxies, stars, planets, and even atoms.

Understanding dark energy is one of the central goals of modern cosmology, and new observational programs are actively working to pin down its properties.