Astronomy 162: Professor Barbara Ryden

Tuesday, March 11

THE FUTURE OF THE UNIVERSE

``Some say the world will end in fire,
Some say in ice.''
- Robert Frost

Key Concepts

In the future, dark energy will cause an ever-increasing expansion rate.
In the future, stars will die out and galaxies will become unbound.
Eventually, black holes will evaporate into particles and antiparticles.

(1) In the future, dark energy will cause an ever-increasing expansion rate.

The available evidence indicates that repulsive dark energy provides about 70 percent of the universe's density. (In the jargon of cosmologists, dark energy is the ``dominant'' component.) However, dark energy was not always dominant. During the first 2500 years after the Big Bang, light dominated the density of the universe. For the next 10 billion years, matter dominated the density. From an age of 10 billion years onward, dark energy dominated.

To see why different components of the universe dominate at different eras, consider what happens during a time span when distances in the universe double:

Volume increases by a factor of 2³ = 8.
Number density of photons (photons per cubic meter) decreases by a factor of 8.
Energy per photon decreases by a factor of 2.
Consequently, the energy density of photons decreases by a factor of 8 x 2 = 16.
Mass density of matter decreases by a factor of 8.
Energy density of dark energy remains constant.

Thus, as the density of light (photons) decreases by a factor of 16, the density of matter decreases only by a factor of 8, and the density of dark energy doesn't decrease at all.

Today, the energy density of light (divided by c²) is far smaller than the mass density of matter. However, extrapolate backward in time to 2500 years after the Big Bang, and you find that the density of light was equal to the density of matter.

Today, the mass density of matter is somewhat smaller than the energy density of dark energy (divided by c²). However, extrapolate backward in time to 10 billion years after tha Big Bang, and you find that the density of matter was equal to the density of dark energy.

In the far future, as the density of light and matter continue to dwindle, dark energy will strongly dominate!!

(2) In the future, stars will die out and galaxies will become unbound.

In the future, dark energy will drive expansion at an accelerating rate; distances will double every 20 billion years or so, into the indefinitely far future. It looks like the end will be in ``ice'', not ``fire''; the universe will expand forever in an increasingly cool ``Big Chill'' rather than recollapsing in a fiery ``Big Crunch''. On a smaller scale, what will happen to our galaxy and other galaxies as the universe chills out?

In the near future, stars will continue to form as they do now. However, with each generation of stars that form, more and more of the matter in the universe is locked away into stellar remnants (white dwarfs, neutron stars, and black holes). Eventually, all the gas will be used up, and no more stars will form.

10¹² (1 trillion) years after the Big Bang:
Stars die. No more fusion-powered stars, as the lowest-mass stars from the last generation of star formation dwindle away into white dwarfs. Galaxies will be filled with white dwarfs, neutron stars, and black holes, with no more brightly-shining stars.

10²⁷ (1000 trillion trillion) years after the Big Bang:
Galaxies ``dissolve''. Close encounters between stellar remnants within galaxies fling half of them out of the galaxy into intergalactic space. The remaining stars are swallowed by the galaxy's central supermassive black hole, swelling it to a gargantuan size (about 100 billion solar masses for a fair-sized galaxy like our own). Galaxies no longer exist - stellar remnants have been strewn throughout space.

10³¹ (10 million trillion trillion) years after the Big Bang:
Supermassive black holes merge. After galaxies become unbound, flinging their stellar remnants into space, clusters of gargantuan black holes exist where clusters of galaxies used to be. The black holes, as they orbit through space, radiate ``gravitational waves''. These gravitational waves are ripples in space-time itself; just as ripples in water carry energy, so ripples in space-time carry energy away from the moving black holes, allowing them to spiral in toward the center of the cluster in which they live. Eventually, all the gargantuan black holes in the cluster will merge together to form a hyper-gargantuan black hole (about 1000 trillion solar masses for a fair-sized cluster like the Virgo Cluster).

10⁴⁵ (1 billion trillion trillion trillion) years after the Big Bang:
Protons and neutrons decay. Although we think of protons as being stable particles (unless they happen to meet up with an antiproton), they are actually subject to decay on extremely long time scales. The half-life of the proton is uncertain (because it is so long), but it's in the neighborhood of 10⁴⁵ years. After this time, protons (and their close relations, neutrons) decay into positrons, electrons, and photons. As a consequence, white dwarfs and neutron stars (and any planets, asteroids, and comets that are still around) will disintegrate into expanding clouds of electrons, positrons, and photons. For a long time after protons and neutrons decay, the universe will be fairly stable -- electrons, positrons, black holes, neutrinos, and photons will be spread throughout an ever-expanding universe.

(3) Eventually, black holes will evaporate into particles and antiparticles.

As Steven Hawking writes in his popular cosmology book, A Brief History of Time, ``Black holes ain't so black.'' According to classical physics, black holes can only absorb particles; they can't emit them. However, the laws of quantum mechanics state that black holes can emit particles and antiparticles. One of the fundamental laws of quantum mechanics is the Uncertainty Principle, which states that can't know precisely both the position and the velocity of a subatomic particle. In other words, there is a fundamental uncertainty built into the universe. On subatomic scales it is impossible to have complete knowledge of the universe. One of the attributes of the universe which is uncertain is the energy density of space. What we think of as ``empty'' space is actually filled with very tiny, very rapid fluctuations in energy, seething and bubbling on a subatomic length scale. If the energy is large enough, it is possible for a particle-antiparticle pair to form spontaneously at the location of the fluctuation. Under ordinary circumstances, the particle and antiparticle annihilate each other very shortly afterwards. However, consider what can happen if a particle-antiparticle pair spontaneously pops out of empty space very close to a black hole. In this case, it is possible for one member of the particle-antiparticle pair to fall into the event horizon, while the surviving ``widowed'' particle escapes in the opposite direction, carrying energy with it.
Bottom line: Thanks to the Uncertainty Principle, a black hole appears to be spitting out particles and antiparticles from its event horizon. Since these particles and antiparticles carry energy away from the black hole, the energy of the black hole decreases. Since energy is equivalent to mass, the mass of the black hole decreases. The time it takes for a black hole's mass to reach zero is very long. For a black hole initially equal in mass to the Sun, it takes about 10⁶⁵ years.

10¹⁰⁶ (10 billion trillion trillion trillion trillion trillion trillion trillion trillion) years after the Big Bang:
Supermassive black holes evaporate. After this mind-bogglingly long period of time, the hyper-gargantuan extra-massive black holes finally evaporate. The universe now contains electrons, positrons, photons, and neutrinos (none of which are subject to decay, as far as we know). The density of the universe is so staggeringly low that the electrons and positrons never have an opportunity to collide and annihilate.

Prof. Barbara Ryden (ryden@astronomy.ohio-state.edu)

Updated: 2003 Mar 10