Astronomy 162: Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30

# Lecture 39:"This is the way the world ends..." The Fate of the Universe

Readings: Ch 28, Section 28-7

## 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: Wb = 0.04 +/- 0.01
• Contribution from stars: Wstars = 0.004
• Most of the baryons are still in the form of gas today.

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

Dark Matter:

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

Adding these all up gives: Wm = 0.2 - 0.4

## Expansion Forever?

If this really were a matter-dominated Universe, then
• Total Density: W0 = Wm = 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:
where:
Wm = Density of Matter & Energy
WL = 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 WL do?

If WL = 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 WL 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.

## 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 WL = 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:
Wm = 0.3 ± 0.1
WL = 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 readiation is a few, increasingly redshifted photons.

The end is cold, dark, and disordered...

## Possible Fates of the Universe

On that note, I'll give the last word to the obligatory poets...
"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 (Harper's Magazine, Dec 1920)

"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 (1924)

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Updated: 2006 February 25