Astronomy 1144: Lecture 38

Astronomy 1144: Introduction to Stars, Galaxies, and Cosmology

Todd Thompson
Department of Astronomy
The Ohio State University

Lecture 38: The Fate of the Universe

Key Ideas

Matter-Dominated Universes:: High-density: expansion stops and collapses ("Big Crunch"); Low-density or Flat: expands forever ("Big Chill")
Cosmological Constant: Evidence from Supernova distances; Suggests we live in a spatially flat, accelerating, infinite Universe
The Fate of an Accelerating Universe: Expands forever at an ever-increasing rate; Ends in a cold, dark, distordered state

Matter-Dominated Universes

Theses are the simplest class of Universe models to consider.

Their futures depend on the density of the matter within them:

High-Density:

Enough matter to slow and eventually stop the expansion
Universe turns around and collapses in a "Big Crunch"

Low-Density or Flat:

Not enough matter to stop the expansion
Keeps expanding forever
Keeps getting cooler, ending in a "Big Chill"

The idea is simple: "Density is Destiny" in such a Universe. All we have to do is measure the matter density, and we know the fate of the Universe (in outline, if not in detail).

What is the matter density?

There are three sources of matter and energy density:

Baryonic Matter: (gas and stars)

Best estimate: W_b = 0.04 +/- 0.01
Contribution from stars: W_stars = 0.004
Most of the baryons are still in the form of gas today.

Radiation: (photons)

Cosmic Background Radiation: W_rad = 0.00005
Insignificant today (much more important in the hot, dense past)

Dark Matter:

Galaxy Cluster dynamics gives: W_dm = 0.26
Dark matter dominates the matter content of the Universe today

Adding these all up gives: W_m = 0.2 - 0.4

Expansion Forever?

If this really were a matter-dominated Universe, then

Total Density: W₀ = W_m = 0.2 - 0.4

This means W₀ < 1:

Too little matter to stop the expansion.
The Universe would have a hyperbolic geometry.

Future: The Universe would expand forever and a steadily decreasing rate.

What about L?

If, however, there is a cosmological contant, the density parameter W₀ becomes:

Density Parameter with matter and Lambda

(Graphic by R. Pogge) where:

W_m = Density of Matter & Energy

W_L = Density of the Vacuum Energy

Now the fate is tied to knowing both the density and the cosmological constant (the vacuum energy of the Universe).

Density is no longer Destiny...

What does W_L do?

If W_L = 0, matter slows the expansion rate:

Expansion rate would have been faster in the past.
Very distant galaxies (distant past) will have larger recession velocities than with a steady expansion.

If W_L is large enough the expansion will accelerate:

Expansion rate would have been slower in the past.
Very distant galaxies will have a smaller recession speed than with a steady expansion.

To measure this, you need to make a Hubble Diagram (plot of recession velocity versus distance) for very distant galaxies in deep space, where we look back to when the Universe was younger.

(Graphic by R. Pogge)

Distant Type Ia Supernovae

Type Ia Supernovae are excellent standard candles:

Exploding white dwarfs in binary systems.
Very luminous (can see them very far away)
Have a characteristic spectrum (different from Type II SN, which are exploding massive stars)

A number of projects are underway to search for and characterize distant Type Ia SNs.

Hubble diagrams created from the SNIa results show compelling evidence of accelerated expansion of the Universe:

Distant galaxies are receding a little slower than expected from nearby galaxies.
The amount of acceleration suggests W_L = 0.6 - 0.8

The Accelerating Universe

The SNIa results combined with constraints from complementary observations of details of the cosmic microwave background and galaxy clusters give the following numbers:

W_m = 0.3 ± 0.1

W_L = 0.7 ± 0.1

Taken together, they give W₀ = 1, with a range of about 10-15%.

We live in a spatially flat, accelerating, infinite Universe.

The Once & Future Universe

As the Universe expands:

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

The details of the future Universe depend upon:

Stellar Evolution
Gravity
Quantum Mechanics

Epoch of Star Formation

The Present Time (t = 14 Gyr):

Most stars are metal rich, and make more metals ejected in supernova explosions.
The next generation of stars starts with a little less Hydrogen and a few more metals.

Some fraction of the mass cycled into stars, however, gets locked away in stellar remnants:

White Dwarfs, Neutron Stars & Black Holes

End of Star Formation

After t=10¹² years:

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

The 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.

The last stars fade into a long night...

Solar System "Evaporation"

After t=10¹⁷ years:

Gravitational encounters between stars are rare, but when they do happen, they can 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.

While rare, the thing to remember is that an eternally expanding Universe has plenty of time to wait for rare occurances ("rare" doesn't mean "never").

Dissolution of Galaxies

After t=10²⁷ years:

Stellar remnants within galaxies interact over many many orbits.
Some stars gain energy from the interactions and ~90% get ejected from the galaxy.
Others lose energy and sink towards the center.

These coalesce into a Supermassive Black Holes at the center of what was once a galaxy.

The bigger the galaxy, the bigger the black hole.

Dissolution of Matter?

After t=10³² years:

Some particle models 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, but the Universe has plenty of time...

Evaporation of Black Holes

After t=10⁶⁷ years:

The 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.

Marks the end of the epoch of organized matter.

The Big Chill

After the black holes have all evaporated:

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

The end is cold and dark.