13.1 Long-term evolution of the universe

The universe's long-term evolution is shaped by dark energy, matter density, and space curvature. These three factors together determine whether the universe will expand forever or eventually collapse. Understanding their interplay is the key to predicting the cosmos's ultimate fate.

As the universe evolves, its expansion rate changes. It initially slowed due to the gravitational pull of matter and radiation, but it's now accelerating because of dark energy. This shift has profound implications for the future, potentially leading to a "heat death" where no usable energy remains anywhere.

Long-term Evolution of the Universe

Factors in universe evolution

Three ingredients control how the universe evolves over time:

• Dark energy
  • Permeates all of space and causes the expansion of the universe to accelerate
  • Its density remains constant as the universe expands (this is the cosmological constant model, where dark energy doesn't dilute even as space stretches)
• Matter density
  • Includes both ordinary (baryonic) matter (protons, neutrons, electrons) and dark matter
  • Density decreases as the universe expands because the same amount of matter occupies an ever-growing volume
  • The gravitational attraction of matter works against expansion, slowing it down
• Curvature of space
  • Determined by the total energy density compared to a threshold called the critical density
  • Flat universe ($\Omega = 1$): total energy density equals the critical density. Without dark energy, expansion would asymptotically approach zero. With dark energy, expansion accelerates indefinitely.
  • Open universe ($\Omega < 1$): total energy density is less than the critical density. The universe expands forever.
  • Closed universe ($\Omega > 1$): total energy density exceeds the critical density. Without dark energy, the universe would eventually stop expanding and collapse in a "Big Crunch."

Current observations strongly favor a flat (or very nearly flat) universe with a dominant dark energy component, meaning accelerating expansion is the most likely long-term trajectory.

Changes in universe expansion rate

The expansion rate is quantified by Hubble's law, which relates a galaxy's recessional velocity to its distance:

$v = H_0 \times d$

• $v$: recessional velocity of the galaxy (km/s)
• $H_0$: the Hubble constant, measuring the current expansion rate (~70 km/s/Mpc)
• $d$: distance to the galaxy (Mpc)

The expansion rate hasn't been constant throughout cosmic history. It depends on which energy component dominates at a given epoch:

1. Radiation-dominated era (first ~47,000 years): Radiation energy density was highest. Expansion slowed rapidly because radiation density drops as $a^{-4}$ (dilution from volume increase plus the redshifting of photon wavelengths).
2. Matter-dominated era (~47,000 years to ~9.8 billion years): Matter density dominated. Expansion still decelerated, but more slowly, since matter density drops as $a^{-3}$ (volume increase only).
3. Dark energy-dominated era (~9.8 billion years to present and beyond): Dark energy density stays constant while matter and radiation thin out. Expansion accelerates.

Current observations of distant Type Ia supernovae and the cosmic microwave background confirm that we're in the accelerating phase. In the far future, as matter and radiation densities become negligible, dark energy will dominate completely. The universe will then expand exponentially, approaching what's called de Sitter space.

Heat death concept and implications

Heat death is the projected end state of a universe that expands forever: it eventually reaches thermodynamic equilibrium, meaning no temperature differences or energy gradients exist anywhere. Without gradients, no work can be done and no processes can occur.

This scenario applies to an open or flat universe. Here's the timeline of how it unfolds:

1. Stars exhaust their fuel (hydrogen, helium) and die, leaving behind white dwarfs, neutron stars, or black holes. Star formation ceases as gas is used up or dispersed.
2. Galaxies become isolated. Accelerating expansion pushes galaxy clusters beyond each other's observable horizons.
3. Black holes slowly evaporate through Hawking radiation over staggering timescales (on the order of $10^{67}$ years for a stellar-mass black hole, and up to $10^{100}$ years for supermassive ones).
4. Entropy reaches its maximum. All energy is spread uniformly across space with no concentrations or structures left.
5. Nothing remains to drive any process: no nuclear fusion, no chemistry, no structure formation.

There are alternative scenarios to heat death, depending on the nature of dark energy:

• Big Rip: If dark energy strengthens over time (phantom energy, where $w < -1$), expansion eventually accelerates so violently that it tears apart galaxies, stars, planets, and ultimately atoms themselves.
• Big Crunch: If dark energy weakens or reverses, gravity could win out, causing the universe to contract and collapse.
• Oscillating universe: Repeated cycles of expansion and contraction, avoiding a permanent end state. This idea lacks strong observational support but remains a theoretical possibility.