Future for our Sun: Ultraviolet image of the planetary nebula NGC 7293 also known as the Helix Nebula. It is the nearest example of what happens to a star, like our own Sun, as it approaches the end of its life when it runs out of fuel, expels gas outward and evolves into a much hotter, smaller and denser white dwarf star. Image Credit: NASA/JPL-Caltech/SSC

In the future, the average density of matter in the universe (both ordinary matter and dark matter) will continue to drop in proportion to the increasing spatial volume as the universe expands ever more rapidly. The dark energy density, however, behaves differently. Dark energy is an irreducible property of even empty space, so as new space is created, the dark energy density remains the same; it is believed to not only take the same value in all portions of space at a given time, but to also have had the same value (per unit volume) for many billions of years.

Since around 5 billion years ago, when the universe was 9 billion years old, the dark energy has dominated over both types of matter (ordinary and dark) and this dominance is only increasing with the universe’s continued expansion. Today it is 73% of the total mass-energy density and it will approach close to 100% in the future. The assumption is made that the cosmological constant or dark energy term that we measure today remains constant into the future. However it cannot be ruled out that it is changing very slowly or might change suddenly at some future date.

In the cosmological constant case, the scale factor for the size of the universe grows exponentially with time. This is known as the de Sitter solution to the equations of general relativity, and it indicates that the expansion of the universe is accelerating into a runaway condition. There is a single parameter, a timescale. Cosmological measurements indicate that the value is such that the size of the universe for each spatial dimension will double and redouble every 11 billion years (the volume will thus grow by 8 times each 11 billion years).

When the universe is 25 billion years old (now it’s 14 billion years old), distant galaxies will be about twice as far away as today (and 4 times fainter). Well before that time we’ll need to evacuate the Earth as the Sun will go into its red giant phase some 5 billion years from now, followed by a white dwarf phase – as shown in the image of the Helix planetary nebula above. When the universe is around 124 billion years old, distant galaxies on average will be 1000 times farther away from us than now. And after 234 billion years they will be an incredible million times farther away than now!

Year                                    Relative Distance                        Relative Brightness

14 billion (Now)                        1                                                1

25 billion                                    2                                                1/4

124 billion                                  1000                                         one-millionth

234 billion                                  1,000,000                               one-trillionth

The distant galaxies that we detect with the Hubble telescope and large Earth-bound telescopes will become invisible since their apparent luminosity will drop as the square of the increasing distance. For example at the time of 124 billion years, they will be 1 million times fainter (1000 squared). At the time of 234 billion years they will be a trillion times fainter (one million squared). Actually it will be worse than this since their light will be redshifted (stretched out by the cosmological expansion) by the same relative distance factor, so light emitted in the visible will be detected in the millimeter radio region when the universe is 100+ billion years old. This is without considering the evolution in their stellar populations, but only their lower mass, fainter stars will survive, further aggravating the situation.

Galaxies themselves are not changing very much in their size or in internal density, rather it is the spacing between galaxies that is on average growing rapidly. Galaxy groups and clusters that are today gravitationally bound will remain bound. Our home, the Milky Way galaxy, and its large neighbor the Andromeda galaxy, will stay together since they are gravitationally bound, and they may very well merge in several billion years due to tidal effects. All of the 40 or so galaxies and dwarf galaxies in our gravitationally bound Local Group may coalesce after 1 trillion years have passed.

Our light cone horizon, which determines which galaxies are even theoretically visible to us, is shrinking in relative terms. Sufficiently distant galaxies are already receding faster than the speed of light from our vantage point and are entirely hidden from us; if the inflationary model is correct as seems to be the case, the universe is immensely larger than what we are able to detect. This is possible and indeed happening because there are no constraints in special relativity or general relativity on the expansion rate of space itself; only the objects within space are constrained to moving at less than the speed of light relative to their local frames of reference.

An intelligent society in the very distant future, possibly our descendants who have moved to a planet in orbit around another star, would observe only one galaxy, namely their own. This would be a larger galaxy formed from the Milky Way and other members of the Local Group. All other galaxies would no longer be visible, first they would become too distant and too faint, and then they would be entirely beyond our light horizon. These descendants or other observers would believe their galaxy to be the only one in the universe, unless they had access to (and a willingness to believe in) very ancient research publications.

We are fortunate to live in this epoch – despite dark matter, dark energy, and dark gravity, the universe is young, and we are immersed in light.

References:

http://spiff.rit.edu/classes/phys240/lectures/future/future.html

The Five Ages of the Universe, Fred Adams and Greg Laughlin, Simon and Schuster, 1999

The Runaway Universe, Donald Goldsmith, Perseus Books, 2000

Dark Matter, Dark Energy, Dark Gravity, Stephen Perrenod, 2011, https://darkmatterdarkenergy.wordpress.com/where-to-find/