29.2 A Model of the Universe

The Universe's Expansion and Evolution

The fate of the entire universe comes down to a tug-of-war between expansion and gravity. How fast the universe expands, and whether that expansion speeds up, slows down, or reverses, depends on what the universe is made of and how dense it is. This section covers the models cosmologists use to describe that fate.

Rate of Universe Expansion

The universe's expansion rate determines its ultimate fate, and that rate depends on the universe's density. Higher density means stronger gravitational attraction pulling everything back together, which slows expansion. Lower density means gravity has less pull, so expansion proceeds more freely.

There are three possible outcomes based on how the actual density compares to a critical threshold:

• Open universe (density below critical): The universe expands forever, with expansion never slowing to zero.
• Flat universe (density exactly at critical): The universe expands forever, but the rate gradually approaches zero without ever reaching it.
• Closed universe (density above critical): Gravity eventually wins. Expansion stops and reverses, leading to collapse.

As the universe expands, the densities of its components change at different rates:

• Matter density decreases because the same amount of matter spreads across a larger volume.
• Radiation density decreases even faster than matter density, because expanding space also stretches (redshifts) the wavelength of radiation, reducing its energy.
• Dark energy density stays constant. No matter how much space expands, dark energy maintains the same energy per unit volume. This means dark energy becomes the dominant component over time.

Possibilities for the Universe's Future

• Open universe (eternal expansion): The universe keeps expanding. Galaxies become increasingly isolated as the space between them grows. Stars eventually exhaust their fuel and die, leaving a cold, dark cosmos. Even gravitationally bound groups like the Milky Way and Andromeda will eventually be alone in an empty sky.
• Flat universe (critical expansion): Very similar to the open case. Expansion continues forever but at an ever-decreasing rate that approaches zero. The long-term result is the same: isolation and cooling.
• Closed universe (eventual collapse): Expansion halts and reverses. Galaxies draw closer together, temperatures rise, and the universe compresses back into an extremely hot, dense state, sometimes called the "Big Crunch."
• Oscillating universe (hypothetical): In this scenario, a closed universe collapses in a Big Crunch but then "bounces" into a new expansion phase, cycling between Big Bangs and Big Crunches. Whether this is physically possible depends on poorly understood physics at extreme densities. Most current evidence does not support this model.

Understanding the Expansion of the Universe

What "Expansion" Actually Means

A common misconception is that galaxies are flying outward from some central explosion point. That's not what's happening. Space itself is expanding, carrying galaxies along with it. Galaxies aren't moving through space; the space between them is stretching.

There's no center of the expansion. Every point in the universe sees other galaxies moving away from it. On large scales, this expansion is uniform: galaxies recede from each other at a rate proportional to their distance. This relationship is Hubble's law:

$v = H_0 \times d$

where $v$ is the recession velocity of a galaxy, $H_0$ is the Hubble constant (the current expansion rate), and $d$ is the galaxy's distance from the observer.

This expansion is a fundamental property of spacetime, described by solutions to Einstein's field equations of general relativity. The rate of expansion is influenced by the matter, radiation, and dark energy present in the universe. Current observations show the expansion is accelerating, which is attributed to dark energy.

Critical Density in Cosmology

Critical density is the precise density the universe would need to have a perfectly flat geometry. It acts as the dividing line between the three fates described above. The formula for critical density is:

$\rho_c = \frac{3H_0^2}{8\pi G}$

where $H_0$ is the Hubble constant and $G$ is the gravitational constant.

Cosmologists express the actual density of the universe as a fraction of critical density, using the parameter $\Omega$:

• $\Omega = 1$: flat universe
• $\Omega < 1$: open universe
• $\Omega > 1$: closed universe

The total density $\Omega$ includes contributions from multiple components:

• Matter ($\Omega_m$), including both ordinary and dark matter
• Radiation ($\Omega_r$), which is negligible in the current universe
• Dark energy ($\Omega_\Lambda$), which is now the dominant component

The relative contributions shift over time as the universe expands. Pinning down the actual value of $\Omega$ is a central goal of observational cosmology, using tools like the cosmic microwave background, large-scale galaxy surveys, and Type Ia supernovae.

Early Universe and Cosmic Evolution

Big Bang Theory and Cosmic Inflation

The Big Bang theory describes a universe that began roughly 13.8 billion years ago in an extremely hot, dense state and has been expanding and cooling ever since. This is the foundation of modern cosmology.

Cosmic inflation is a proposed addition to the Big Bang model. It suggests that in the first tiny fraction of a second (around $10^{-36}$ to $10^{-32}$ seconds after the Big Bang), the universe underwent an extraordinarily rapid expansion, increasing in size by a factor of at least $10^{26}$. Inflation solves two major puzzles:

• The horizon problem: Why the cosmic microwave background has nearly the same temperature in all directions, even in regions that seemingly could never have been in contact with each other. Inflation explains this by proposing that these regions were in contact before inflation stretched them apart.
• The flatness problem: Why the universe's geometry is so close to flat. Inflation drives $\Omega$ extremely close to 1, regardless of its initial value.

Inflation also provides a mechanism for generating the tiny density fluctuations in the early universe that eventually grew into galaxies and galaxy clusters.

Dark Matter and the Observable Universe

Dark matter doesn't emit, absorb, or reflect light, so it's invisible to telescopes. Its existence is inferred from gravitational effects: galaxies rotate faster than their visible matter alone can explain, and galaxy clusters contain far more mass than what we can see. Dark matter makes up about 27% of the universe's total energy content and plays a crucial role in the formation of large-scale cosmic structure, acting as gravitational scaffolding around which ordinary matter collects.

The observable universe is the portion of the universe from which light has had time to reach us since the Big Bang. Its radius is about 46.5 billion light-years, which is larger than you might expect from a 13.8-billion-year-old universe. The extra distance comes from the expansion of space itself: light that was emitted billions of years ago has been carried farther away by the ongoing expansion while it was in transit.

Cosmological Constant

The cosmological constant ($\Lambda$) is a term in Einstein's field equations of general relativity. Einstein originally introduced it to balance gravity and produce a static, non-expanding universe. After Hubble discovered that the universe is expanding, Einstein reportedly called the cosmological constant his "biggest blunder."

The term was revived in the late 1990s when observations of Type Ia supernovae revealed that the universe's expansion is accelerating. Today, the cosmological constant is associated with dark energy and represents the energy density of empty space. Unlike matter and radiation densities, which decrease as the universe expands, the cosmological constant remains the same everywhere and at all times.

Observational Evidence and the Universe's Fate

Three major lines of evidence, taken together, point strongly toward a flat, accelerating universe dominated by dark energy.

Cosmic Microwave Background (CMB)

The CMB is the afterglow of the Big Bang, a faint glow of microwave radiation filling all of space. It's remarkably uniform in temperature (about 2.725 K), but contains tiny fluctuations on the order of 1 part in 100,000. The pattern of these fluctuations is sensitive to the universe's geometry. Measurements from the WMAP and Planck satellites show fluctuation patterns consistent with a flat universe ($\Omega \approx 1$).

Type Ia Supernovae as Standard Candles

Type Ia supernovae occur when white dwarf stars reach a consistent critical mass and explode. Because they reach roughly the same peak luminosity every time, they serve as standard candles: by comparing their known brightness to their observed brightness, astronomers can calculate their distance. In 1998, two independent teams found that distant Type Ia supernovae were dimmer than expected, meaning they were farther away than a decelerating universe would predict. This was the first direct evidence that the universe's expansion is accelerating, driven by dark energy.

Large-Scale Structure

The distribution of galaxies and galaxy clusters across the universe also encodes information about cosmic density and geometry. Surveys like the Sloan Digital Sky Survey (SDSS) and the Dark Energy Survey (DES) have mapped millions of galaxies, revealing a cosmic web of filaments and voids. The observed structure is consistent with a universe dominated by dark matter and dark energy.

Putting It All Together

When CMB, supernova, and large-scale structure data are combined, they converge on a consistent picture:

• ~5% ordinary (baryonic) matter
• ~27% dark matter
• ~68% dark energy

This composition, with dark energy as the dominant component, means the universe's expansion will almost certainly continue to accelerate. The most likely long-term fate is an ever-expanding, ever-cooling cosmos where galaxies drift apart and stars gradually burn out.