$$\require{cancel}$$

# 17.18 Fate of the Universe

What does the future hold for our universe? Even though the brief flicker of human existence seems inconsequential in the eons of the universe, it is irresistible to ask the question. Today, astronomy paints a rather bleak future. While the spatial geometry is flat, dark energy will cause the universe to continually expand at faster and faster rates. Eventually, this expansion will pull galaxies so far apart that light won't be able to travel from one cluster of galaxies to another. Over time even these structures will disintegrate, leaving behind nothing but a diffuse smear of energy. This fate is referred to as heat death. In broad brush strokes, over time the stars will all run out of fuel, and the dust and gas needed to form new stars will all get used up. When this happens, all that will remain will be the dead cores of stars: white dwarfs, neutron stars, and black holes. These objects will slowly radiate all their energy into space. The galaxies that they live in will also slowly merger. Clusters will come to consist of super galaxies — giant elliptical that have consumed all the smaller galaxies. These clusters will be carried apart by cosmic expansion such that each exists as an island unto itself, with no potential to receive light from more distant objects. But in some ways this is only the beginning of the end. It is thought that given enough time even protons will decay into energy. This means that in most distant future even the stars will decay back into energy. The black holes will evaporate. The neutron stars will decay. The white dwarfs will decay. One evaporating or decaying dead star at a time our universe will become nothing more than a smooth, cold, distribution of energy. That's the overview; now let's look at these stages of the future in more detail.

Examples of curved spaces in everyday life. Click here for original source URL.

All of the 1022 stars in all of the 1011 galaxies in the observable universe amount to just one part in two hundred of the cosmic "pie chart." Well-tested theories of stellar evolution allow astronomers to confidently predict the fate of the luminous component of the universe. When stars form, their first nuclear reaction fuses hydrogen into helium. The lifetime of a star is a sensitive function of its mass. The highest mass stars last millions of tens of millions of years and die violently, leaving behind neutron stars or black holes. Intermediate mass stars like the Sun live for billions of years; the Sun is currently halfway through its lifetime and it will end life as a fading ember called a white dwarf. The lowest mass stars eke out their existence for roughly 1013 years before fading away.

The universe is still in its boisterous youth. As stars age and die they return a fraction of their mass to the interstellar medium, where it can become part of a new cycle of star birth and death. But over time star formation will be quenched as more mass is trapped in stellar remnants and the universe continues to expand, reducing the probability that galaxies will merge or gather new gas from the intergalactic medium. The most massive stars will leave dark remnants — neutron stars and black holes. But 90% of the mass will be in the form of white dwarfs, gradually cooling stellar embers supported by electron degeneracy pressure. The tail of new stars forming will stretch out for trillions of years, but after 1014 years the era of stellar fusion will be over. By 1015 years from now, even the white dwarfs will have cooled to a temperature of a few Kelvin. This scenario applies to the Milky and Way and all the other 200 billion galaxies in the universe. Fade to black.

The second phase of the far future involves the dynamics of gravitational systems. Solar systems will not survive intact because close encounters between stars will eject some planets and resonant instabilities between planets will eject others. Those that survive will eventually spiral into their stars by the release of gravitational radiation. Meanwhile, galaxies will dissipate due to the process of dynamical relaxation. Although stellar collisions are very rare, long range encounters between stars tend to add kinetic energy to the lower mass star and remove kinetic energy from the higher mass star. A net result is that some stars reach escape velocity and leave the system, while others move inwards, making the galaxy smaller and denser. After about 1019 years, over 90% of the stars have escaped, and the remaining small fraction feed the massive black hole found at the center of every galaxy. It is noted that the fate of galaxies is tied in part to the nature of dark matter, so until the particle candidate is identified, the story remains somewhat uncertain. Essentially, galaxies "evaporate."

Timescales are now prodigious, dwarfing the age of the universe to this point. If grand unified theories of particle physics are correct, protons are not stable, but will decay on a timescale that must be longer than the observed limit of 1034 years. These theories are motivated by the unification of the weak force that governs low mass particles like electrons and the strong force that governs massive particles like protons. Protons can then decay into lighter particles like positrons and pions. We know proton number cannot be absolutely conserved since the universe contains much more matter than antimatter. If grand unified theories are correct, the proton lifetime should be less than about 1037 years. Proton decay causes a whole new phase in the dissolution of objects in the universe. It adds a feeble amount of heat to both white dwarfs and neutron stars, after which they shrink and dissipate. Any remaining planets or sub-stellar object will also disintegrate as their protons decay. Space will become filled with electrons, positrons, neutrinos, and dark matter particles assuming they are stable.

The last redoubt of matter is the black hole. Even if protons decay, that process will be hidden by a black hole’s event horizon. Yet black holes are not eternal. In the 1970s, Stephen Hawking proposed that black holes had the property of temperature as well more obvious properties of mass and spin, and so were not completely black. Vacuum fluctuations spontaneously create particle-antiparticle pairs which come in and out of existence in tiny fractions of a second. If this occurs near the event horizon of a black hole, there’s a finite probability that one member of the pair will be trapped within the event horizon while the other escapes. The net effect is that the black hole loses mass or evaporates. Black holes the mass of the Sun evaporate in 1066 years, while the most massive black holes at the centers of galaxies will last for an almost unimaginable 1098 years. As William Butler Yeats said in his poem The Second Coming: "Things fall apart; the center cannot hold, mere anarchy is loosed upon the world." This anarchy is the chaos and disorder implied by the second law of thermodynamics.

Finally, we discuss the container. Cosmology is the study of the universe as a single, space-time entity; the dominant contents of dark matter and dark energy prescribe its expansion from the big bang into the far future. The universe has had three phases of expansion. There was a dramatic, exponential phase of expansion in the first fraction of a second that inflated a quantum fluctuation to macroscopic proportions; there is some experimental support for this phase, called inflation. For the next eight billion years the universe expanded at a decelerating rate due to the retarding influence of dark matter. About five billion years ago, the mysterious entity called dark energy — the strength of which appears to be independent of space and time—began to dominate and cause the expansion rate to accelerate.

We are subject to a cosmological horizon, a distance beyond which we cannot see. The horizon in an expanding big bang universe is not an edge in space, it’s an edge in time. At the limit of vision of the Hubble Space Telescope we see 95% of the time back to the big bang, when the first small galaxies had just formed. The big bang model says that the distance between any two point in space was expanding faster than light for most of the early history. Therefore, the physical universe, or the totality of space-time, is larger than the observable universe. While the universe was decelerating, successively more distant galaxies came into view. But now, with dark energy dominant, galaxies are being accelerated to become unobservable.

The end result will be a dramatically shrunken universe. In about three billion years, the Milky Way will merge with its nearest large neighbor, the Andromeda galaxy. Sometime after that the dwarf galaxies in the Local Group will spiral in to create one large stellar system. Dark energy will increasingly dominate the dynamics of the universe. By 12 billion years from now, its contribution to the universe will have grown from 68% to 95%, and by 25 million years from now, it will have grown to over 99%. By 100 billion years from now — long before the lowest mass stars in our own galaxy have faded from view — the observable universe will have receded from view. All other galaxies become exponentially red shifted as they approach the horizon. We can imagine a civilization of the far distant future, when the Cheshire cat has faded, leaving just a smile. All the stars have died, all galaxies have been wrenched from view, and the denizens of the civilization huddle near Hawking radiation from the last massive black hole. They look at each other and say: it was good while it lasted.