Lecture 40: The Future of the Universe

Key Ideas:

The Fate of the Universe depends on the density of matter.

Closed Universe:

• Enough matter to stop the expansion
• Collapses in a "Big Crunch"

Open Universe:

• Expands forever
• Ends in a cold, disordered state.

Critical Density

All galaxies attract each other via gravity.

• Gravitational attraction slows the expansion.

How it behaves depends on the density:

• High Density: Expansion slows, stops, & reverses.
• Low Density: Keeps expanding forever.

Dividing Line = "Critical Density"

Density Parameter:

Cosmological Density Parameter:

>1: High Density "Closed" Universe

=1: Critical Density "Open" Universe

<1: Low Density "Open" Universe

What is ?

Observers:

Best Estimate is =0.1-0.3 (or higher)

• Hard to measure slowing of expansion rate.
• Galaxies evolve in an (as yet) unknown way.
• Problem of accounting for Dark Matter.

Theorists:

(Some) Would like =1.

Closed Universe: >1

Gravity of all matter is enough to eventually overcome the expansion of the Universe:

• Expansion slows to a maximum size & stops.

Universe re-collapses:

• Galaxies get closer together
• Get a Blueshift instead of a Redshift
• Universe grows hotter and denser
• Collapses in the Big Crunch

A Phoenix from the Ashes?

After the Big Crunch, what then?

• Nothing.
• Another Big Bang creates a new Universe.

Second Law of Thermodynamics:

• Entropy increases in a closed system.
• Next Big Bang starts with greater entropy.
• Will expand for longer than previous one.

Open Universes: <1 or =1

Universe keeps expanding forever.

Gravity slows the expansion a little:

• Lower the density, the less the expansion slows.
• A Critical Density Universe slows to a stop at infinite time.
• A Sub-critical Density Universe approaches a constant speed at infinite time.

Evolution of an Open Universe

As the Universe expands:

• Space between clusters widens.
• Universe steadily cools down.
• Expansion continues forever.

Details depend on:

• Stellar Evolution
• Quantum Mechanics

Star Formation

Present Time (t~10¹⁰ yrs):

• Most stars are metal rich, and make more metals ejected in supernova explosions.
• Next generation starts with a little less Hydrogen and more metals.
• Some fraction of the mass is locked into stellar remnants: white dwarfs, neutron stars & black holes.

End of Star Formation

t=10¹⁴ years:

• Successively more mass is locked up in stellar remnants, depleting the free gas reserves.
• Cycle of star birth, death, and birth is broken.
• Nuclear fuel is exhausted.
• Red dwarfs burn out as low-mass white dwarfs
• Remaining mass is locked into black dwarfs, cold neutron stars, and black holes.

Solar System "Evaporation"

t=10¹⁷ years:

• Gravitational encounters between stars are rare, but slowly disrupt orbiting systems:
• Planetary systems disrupted by stellar encounters and their planets scattered.
• Wide binary systems are broken apart.
• Close binary stars coalesce into single remnants.

Dissolution of Galaxies

t=10¹⁹ years:

• Stellar remnants within galaxies interact over many many orbits.
• Some stars gain energy from the interaction and ~90% get ejected from the galaxy.
• Others lose energy and sink towards the center.
• These coalesce into a Supermassive Black Hole.

Dissolution of Matter?

t=10³² years:

• Some GUTs theories predict that protons are unstable.
• Protons decay into electrons, positrons, to neutrinos.
• All matter not in Black Holes comes apart.
• Current experimental limits on the proton decay time may be much larger than 10³² years.

Evaporation of Black Holes

t=10¹⁰⁰ years:

• Black Holes slowly evaporate by emitting particles and photons via Hawking Radiation.
• Supermassive Black Holes evaporate completely one-by-one in a last final weak flash of gamma rays in ~10¹⁰⁰ years.

The Big Chill

After black holes all evaporate:

• Universe continues to cool off towards a Temperature of absolute zero.
• Only matter is a thin, formless gas of electrons, positrons, neutrinos.
• Increasingly redshifted photons.

Possible Fates of the Universe

"The opinion on which [fate of the Universe] is preferable cannot be classified as a debate in science, however, unless we can explain what point is served by the outcome of the debate."

P.J.E. Peebles, Principles of Physical Cosmology (1993)

"Some say the world will end in fire.
Some say in ice.
From what I've tasted of desire
I hold with those who favor fire.
But if it had to perish twice,
I think I know enough of hate
To say that for destruction ice
Is also great
And would suffice."

Robert Frost, Fire and Ice (1923)

"This is the way the world ends
This is the way the world ends
This is the way the world ends
Not with a bang but a whimper."

T.S. Eliot, The Hollow Men (1925)