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Observations suggest that the expansion of the universe will continue forever. If so, the universe will cool as it expands, eventually becoming too cold to sustain life. For this reason, this future scenario is popularly called the Big Freeze.
If dark energy—represented by the cosmological constant, a constant energy density filling space homogeneously, or scalar fields, such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space—accelerates the expansion of the universe, the space between clusters of galaxies will grow at an increasing rate. Redshift will stretch ancient, incoming photons (even gamma rays) to undetectably long wavelengths and low energies. Stars are expected to form normally for 1012 to 1014 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. And as existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker, one star at a time. §IID,  According to theories that predict proton decay, the stellar remnants left behind will disappear, leaving behind only black holes, which themselves eventually disappear as they emit Hawking radiation. Ultimately, if the universe reaches a state in which the temperature approaches a uniform value, no further work will be possible, resulting in a final heat death of the universe.
Infinite expansion does not determine the spatial curvature of the universe. It can be open (with negative spatial curvature), flat, or closed (positive spatial curvature), although if it is closed, sufficient dark energy must be present to counteract the gravitational attraction of matter and other forces tending to contract the universe. Open and flat universes will expand forever even in the absence of dark energy.
Observations of the cosmic background radiation by the Wilkinson Microwave Anisotropy Probe suggest that the universe is spatially flat and has a significant amount of dark energy. In this case, the universe should continue to expand at an accelerating rate. The acceleration of the universe's expansion has also been confirmed by observations of distant supernovae. If, as in the concordance model of physical cosmology (Lambda-cold dark matter or ΛCDM), the dark energy is in the form of a cosmological constant, the expansion will eventually become exponential, with the size of the universe doubling at a constant rate.
If the theory of inflation is true, the universe went through an episode dominated by a different form of dark energy in the first moments of the big bang; but inflation ended, indicating an equation of state much more complicated than those assumed so far for present-day dark energy. It is possible that the dark energy equation of state could change again resulting in an event that would have consequences which are extremely difficult to parametrize or predict.
In the 1970s, the future of an expanding universe was studied by the astrophysicist Jamal Islam and the physicist Freeman Dyson. More recently, the astrophysicists Fred Adams and Gregory Laughlin have divided the past and future history of an expanding universe into five eras. The first, the Primordial Era, is the time in the past just after the Big Bang when stars had not yet formed. The second, the Stelliferous Era, includes the present day and all of the stars and galaxies we see. It is the time during which stars form from collapsing clouds of gas. In the subsequent Degenerate Era, the stars will have burnt out, leaving all stellar-mass objects as stellar remnants—white dwarfs, neutron stars, and black holes. In the Black Hole Era, white dwarfs, neutron stars, and other smaller astronomical objects have been destroyed by proton decay, leaving only black holes. Finally, in the Dark Era, even black holes have disappeared, leaving only a dilute gas of photons and leptons., pp. xxiv–xxviii.
This future history and the timeline below assume the continued expansion of the universe. If the universe begins to recontract, subsequent events in the timeline may not occur because the Big Crunch, the recontraction of the universe into a hot, dense state similar to that after the Big Bang, will supervene., pp. 190–192;
The observable universe is currently 1.38×1010 (13.8 billion) years old. This time is in the Stelliferous Era. About 155 million years after the Big Bang, the first star formed. Since then, stars have formed by the collapse of small, dense core regions in large, cold molecular clouds of hydrogen gas. At first, this produces a protostar, which is hot and bright because of energy generated by gravitational contraction. After the protostar contracts for a while, its center will become hot enough to fuse hydrogen and its lifetime as a star will properly begin., pp. 35–39.
Stars whose mass is very low will eventually exhaust all their fusible hydrogen and then become helium white dwarfs. Stars of low to medium mass will expel some of their mass as a planetary nebula and eventually become white dwarfs; more massive stars will explode in a core-collapse supernova, leaving behind neutron stars or black holes. In any case, although some of the star's matter may be returned to the interstellar medium, a degenerate remnant will be left behind whose mass is not returned to the interstellar medium. Therefore, the supply of gas available for star formation is steadily being exhausted.
The Andromeda Galaxy is currently approximately 2.5 million light years away from our galaxy, the Milky Way Galaxy, and they are moving towards each other at approximately 120 kilometers per second. Approximately three billion years from now, or 17 billion years after the Big Bang, the Milky Way and the Andromeda Galaxy will collide with one another and merge into one large galaxy based on current evidence. Up until 2012, there was no way to know whether the possible collision was definitely going to happen or not. In 2012, researchers came to the conclusion that the collision is definite after using the Hubble Space Telescope between 2002 and 2010 to track the motion of Andromeda.
The galaxies in the Local Group, the cluster of galaxies which includes the Milky Way and the Andromeda Galaxy, are gravitationally bound to each other. It is expected that between 1011 (100 billion) and 1012 (1 trillion) years from now, their orbits will decay and the entire Local Group will merge into one large galaxy., §IIIA.
Assuming that dark energy continues to make the universe expand at an accelerating rate, 2×1012 (2 trillion) years from now, all galaxies outside the Local Supercluster will be red-shifted to such an extent that even gamma rays they emit will have wavelengths longer than the size of the observable universe of the time. Therefore, these galaxies will no longer be detectable in any way.
By 1014 (100 trillion) years from now, star formation will end, leaving all stellar objects in the form of degenerate remnants. This period, known as the Degenerate Era, will last until the degenerate remnants finally decay.
It is estimated that in 1014 (100 trillion) years or less, star formation will end., §IID. The least massive stars take the longest to exhaust their hydrogen fuel (see stellar evolution). Thus, the longest living stars in the universe are low-mass red dwarfs, with a mass of about 0.08 solar masses, which have a lifetime of order 1013 (10 trillion) years. Coincidentally, this is comparable to the length of time over which star formation takes place. §IID. Once star formation ends and the least massive red dwarfs exhaust their fuel, nuclear fusion will cease. The low-mass red dwarfs will cool and become white dwarfs. The only objects remaining with more than planetary mass will be brown dwarfs, with mass less than 0.08 solar masses, and degenerate remnants; white dwarfs, produced by stars with initial masses between about 0.08 and 8 solar masses; and neutron stars and black holes, produced by stars with initial masses over 8 solar masses. Most of the mass of this collection, approximately 90%, will be in the form of white dwarfs. In the absence of any energy source, all of these formerly luminous bodies will cool and become faint.
The universe will become extremely dark after the last star burns out. Even so, there can still be occasional light in the universe. One of the ways the universe can be illuminated is if two carbon-oxygen white dwarfs with a combined mass of more than the Chandrasekhar limit of about 1.4 solar masses happen to merge. The resulting object will then undergo runaway thermonuclear fusion, producing a Type Ia supernova and dispelling the darkness of the Degenerate Era for a few weeks. If the combined mass is not above the Chandrasekhar limit but is larger than the minimum mass to fuse carbon (about 0.9 solar masses), a carbon star could be produced, with a lifetime of around 106 (1 million) years., p. 91 Also, if two helium white dwarfs with a combined mass of at least 0.3 solar masses collide, a helium star may be produced, with a lifetime of a few hundred million years., p. 91 Finally, if brown dwarfs collide with each other, a red dwarf star may be produced which can survive for 1013 (10 trillion) years.
Over time, the orbits of planets will decay due to gravitational radiation, or planets will be ejected from their local systems by gravitational perturbations caused by encounters with another stellar remnant.
Over time, objects in a galaxy exchange kinetic energy in a process called dynamical relaxation, making their velocity distribution approach the Maxwell-Boltzmann distribution. Dynamical relaxation can proceed either by close encounters of two stars or by less violent but more frequent distant encounters. In the case of a close encounter, two brown dwarfs or stellar remnants will pass close to each other. When this happens, the trajectories of the objects involved in the close encounter change slightly. After a large number of encounters, lighter objects tend to gain kinetic energy while the heavier objects lose it., pp. 85–87
Because of dynamical relaxation, some objects will gain enough energy to reach galactic escape velocity and depart the galaxy, leaving behind a smaller, denser galaxy. Since encounters are more frequent in the denser galaxy, the process then accelerates. The end result is that most objects are ejected from the galaxy, leaving a small fraction (perhaps 1% to 10%) which fall into the central supermassive black hole., §IIIAD;, pp. 85–87
The subsequent evolution of the universe depends on the existence and rate of proton decay. Experimental evidence shows that if the proton is unstable, it has a half-life of at least 1034 years. If any of the Grand Unified theories are correct, then there are theoretical reasons to believe that the half-life of the proton is under 1041 years. Neutrons bound into nuclei are also expected to decay with a half-life comparable to the proton's.
In the event that the proton does not decay at all, stellar-mass objects would still disappear, but more slowly. See Future without proton decay below.
The rest of this timeline assumes that the proton half-life is approximately 1037 years. Shorter or longer proton half-lives will accelerate or decelerate the process. This means that after 1037 years, one-half of all baryonic matter will have been converted into gamma ray photons and leptons through proton decay.
Given our assumed half-life of the proton, nucleons (protons and bound neutrons) will have undergone roughly 1,000 half-lives by the time the universe is 1040 years old. To put this into perspective, there are an estimated 1080 protons currently in the universe. This means that the number of nucleons will be slashed in half 1,000 times by the time the universe is 1040 years old. Hence, there will be roughly ½1,000 (approximately 10−301) as many nucleons remaining as there are today; that is, zero nucleons remaining in the universe at the end of the Degenerate Age. Effectively, all baryonic matter will have been changed into photons and leptons. Some models predict the formation of stable positronium atoms with a greater diameter than the observable universe’s current diameter in 1085 years, and that these will in turn decay to gamma radiation in 10141 years. §IID, 
After 1040 years, black holes will dominate the universe. They will slowly evaporate via Hawking radiation., §IVG. A black hole with a mass of around 1 solar mass will vanish in around 2×1066 years. As the lifetime of a black hole is proportional to the cube of its mass, more massive black holes take longer to decay. A supermassive black hole with a mass of 1011 (100 billion) solar masses will evaporate in around 2×1099 years.
Hawking radiation has a thermal spectrum. During most of a black hole's lifetime, the radiation has a low temperature and is mainly in the form of massless particles such as photons and hypothetical gravitons. As the black hole's mass decreases, its temperature increases, becoming comparable to the Sun's by the time the black hole mass has decreased to 1019 kilograms. The hole then provides a temporary source of light during the general darkness of the Black Hole Era. During the last stages of its evaporation, a black hole will emit not only massless particles but also heavier particles such as electrons, positrons, protons and antiprotons., pp. 148–150.
In the event the proton does not decay as described above, the Degenerate Era will last longer, and will overlap the Black Hole Era. In a timescale of approximately 1065 years, apparently rigid objects such as rocks will be able to rearrange their atoms and molecules via quantum tunnelling, behaving as a liquid does, but more slowly. However, the proton is still expected to decay, for example via processes involving virtual black holes, or other higher-order processes, with a half-life of under 10200 years., §IVF For example, under the Standard Model, groups of 2 or more nucleons are theoretically unstable because chiral anomaly allows processes that change baryon number by a multiple of 3.
After all the black holes have evaporated (and after all the ordinary matter made of protons has disintegrated, if protons are unstable), the universe will be nearly empty. Photons, neutrinos, electrons, and positrons will fly from place to place, hardly ever encountering each other. Gravitationally, the universe will be dominated by dark matter, electrons, and positrons (not protons).
By this era, with only very diffuse matter remaining, activity in the universe will have tailed off dramatically (compared with previous eras), with very low energy levels and very large time scales. Electrons and positrons drifting through space will encounter one another and occasionally form positronium atoms. These structures are unstable, however, and their constituent particles must eventually annihilate. Other low-level annihilation events will also take place, albeit very slowly. The universe now reaches an extremely low-energy state.
What happens after this is speculative. It is possible that a Big Rip event may occur far off into the future. Also, the universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state.
Finally, the universe may settle into this state forever, achieving true heat death.
Presumably, extreme low-energy states imply that localized quantum events become major macroscopic phenomena rather than negligible microscopic events because the smallest perturbations make the biggest difference in this era, so there is no telling what may happen to space or time. It is perceived that the laws of "macro-physics" will break down, and the laws of "quantum-physics" will prevail.
The universe might avoid eternal heat death, by spontaneous entropy decrease, either through quantum tunnelling or a Poincaré recurrence. Quantum tunnelling could produce a new Big Bang in roughly years. A Poincaré recurrence could generate a new Big Bang the size of the currently observable universe in years. Finally, a Poincaré recurrence could occur for the entire Universe, observable or not, assuming Linde's chaotic inflationary model with an inflaton whose mass is 10−6 Planck masses, in years.
In 101500 years, cold fusion occurring via quantum tunnelling should make the light nuclei in ordinary matter fuse into iron-56 nuclei (see isotopes of iron.) Fission and alpha-particle emission should make heavy nuclei also decay to iron, leaving stellar-mass objects as cold spheres of iron, called iron stars.
Quantum tunnelling should also turn large objects into black holes. Depending on the assumptions made, the time this takes to happen can be calculated as from years to years. Quantum tunnelling may also make iron stars collapse into neutron stars in around years.