Lecture 39: The Fate of the Universe

Key Ideas

Matter-dominated Universe:

High-W: expansion stops & collapses (Big Crunch)

Low-W or Flat: expands forever (Big Chill)

Cosmological Constant

Evidence from Supernova distances

Flat, accelerating, Infinite Universe

Fate of an Accelerating Universe:

Expands forever at an ever-increasing rate

Ends in a cold, dark, disordered state

Matter-Dominated Universes

Future depends on the density of matter

High Density (W₀ > 1):

Enough matter to slow and stop expansion

Universe collapses in a “Big Crunch”

Low Density or Flat (W₀ < or = 1):

Keeps expanding forever

Cools off, ending in a “Big Chill”

DENSITY IS DESTINY!

What is the matter density W_m?

Baryonic Matter (stars & gas)

Best estimate W_b~0.04 +/- 0.01

Contribution from stars W_* ~0.004

Radiation (photons):

Cosmic Background W_rad ~0.00005

Dark Matter:

Galaxy Cluster dynamics gives W_dm ~ 0.26

TOTAL: W_m =0.2-0.4

Expansion Forever?

If the Universe is matter dominated,

Total Density: W₀ = W_m = 0.2-0.4

This means W₀ < 1

Too little matter to stop the expansion

The universe has a hyperbolic geometry

Future:

Universe will expand forever at a steadily decreasing rate

What About L?

If there is a Cosmological Constant (L), the Density Parameter becomes

W_m =Density of Matter and Energy (photons)

W_L= Density of the Vacuum Energy

DENSITY IS NO LONGER DESTINY!

What does W_L do?

If W_L=0, matter slows the expansion:

Expansion rate is faster in the past

Distant galaxies (distant past) will have larger recession velocities than “steady” expansion

If W_L is large, the expansion accelerates

Expansion rate is slower in the past

Distant galaxies have smaller recession speeds

Test:

Make a Hubble diagram for deep space

See Figure 28-17b

Distant Type Ia Supernova

Type Ia SNe are excellent standard candles

Exploding white dwarfs in binary stars

Very Luminous (can see them very far away)

Have a characteristic spectrum

Distant Supernovae show that the Universe is accelerating

See Figure 28-18

The Accelerating Universe

The SNIa results combined with constraints from the cosmic background radiation and galaxy clusters give:

Taken together: W₀ ~ 1

We live in a spatially flat, accelerating, infinite Universe

The Once & Future Universe

As the Universe expands:

Expansion continues forever at a faster rate

Space between galaxy clusters widens

Universe cools down at a faster rate

Details of the future Universe depend upon:

Stellar Evolution

Gravity

Quantum Mechanics

Epoch of Star Formation

The Present Day (t=14 Gyr):

Most stars are metal-rich, and make more metals ejected in supernova explosions.

Next generation starts with a little less H and a few more metals.

Some fraction of the star’s matter gets locked away in stellar remnants:

White dwarfs, neutron stars & black holes

End of Star Formation

After t~10¹² years

Successively more matter is locked up in stellar remnants, depleting the free gas reserves

Cycle of star birth and death is broken:

Nuclear fuel is exhausted, not enough gas to make more stars

Red dwarfs burn out as low-mass white dwarfs

Remaining matter is locked up in black dwarfs, cold neutron stars, and black holes

The last stars fade into a long night….

Solar System “Evaporation”

After t=10¹⁷ years:

Gravitational encounters between stars are rare, but disrupt orbiting systems:

Planetary systems get disrupted by stellar encounters and their planets scattered

Wide binary systems are broken apart

Close binary stars coalesce into single remnants

Dissolution of Galaxies

After t=10²⁷ 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

The last 10% coalesce into Supermassive Black Holes

Dissolution of Matter?

After 10³² years:

Some particle models predict that protons are unstable

Protons decay into electrons, positrons and neutrinos

All matter not in Black Holes comes apart

Current experimental limits suggest that the proton decay time may > 10³² years

Evaporation of Black Holes

After t=10⁶⁷ years:

Remaining stellar-mass black holes evaporate by emitting particles and photons via Hawking radiation

After t=10¹⁰⁰ years

Supermassive Black Holes evaporate one-by-one in a last final weak flash of gamma rays

End of the epoch of organized matter

The Big Chill

After black holes have all evaporated

Universe continues to cool off towards a Radiation Temperature of absolute zero

Only matter is a thin, formless gas of electrons, positrons and neutrinos

Only radiation is a few increasingly redshifted photons

The end is cold, dark, and disordered…