Scenario 1: The universe would continue accelerating forever. Therefore, the Milky Way of solar system would have led to gravitationally combined galaxies with very near. In order to exhaust material gas, there are no longer new stars in these galaxies. There are only leaving remnants of black holes and neutron stars, white dwarf stars.・・・10 ^ 18〜10 ^ '25 years after
＜If the universe is geometrically flat and dark energy is constant＞
ｋ（the geometry of space）＝０
Ω：the density parameter＝ρ／ρｃ
ρｃ：the critical density＝9×10＾-27（kg/㎥）＝3Ho＾2／8πG
π：the circumference of a circle divided＝3.1415…
Ｇ：Gravitational constant＝6.67×10＾−11 （m＾3 kg＾−1 s＾−2）
Scenario 2: Inflation would slow gradually, over time the expansion will stop. Furthermore, from which the universe starts to shrink, becomes very small and collapses. = "The Big Crunch". ・・・10＾27 years after
＜If the universe is analogous to a two-dimensional life-form on the surface of a sphere and dark energy decreases＞
π is small on large scales, parallel lines will ultimately meet, and the
interior angles of a triangle add up to more than 180 degrees.
Scenario 3: The acceleration of the universe may happen so quickly that galaxies, stars, and eventually atoms will be torn apart, in the so-called Big Rip.［2］・・・10＾18〜10＾25 years after
＜If the universe is analogous to a saddle-shape and infinite, and dark energy increases.＞
πis large on large scales, parallel lines diverge, and the interior angles of a triangle add up to less than 180 degrees.
○ Curvature of the universe・・・The Keyword is Friedman
• According to Friedman, curvature of the universe takes three values positive or zero or negative by the amount of materials and energy in the interior of the universe.
・In the three types of expansion of the universe that Friedman revealed, expansion speed becomes either "gradually slow" or "at the same rate". In the universe of negative curvature, finally expansion rate becomes constant, otherwise, the expansion rate will be slow due to gravity of matter inside the universe.
・Curvature of the universe can be obtained by precisely measuring the temperature fluctuations (non-uniformity of the signal strength) of the cosmic background radiation.
・According to observations of 2005, Ω is between 0.98 and 1.06. 
○ However, expansion of the universe has gently accelerated from six billion years ago(doubled over a period of several billion years: the second of inflation) . 
・Accelerated expansion is believed to be due to dark energy.
○Dark energy・・・We know only nature of it, that is accelerating the expansion of the universe.
Dark energy is the unknown energy to accelerate the expansion of the universe. It has similar properties as the cosmological term that introduced by Einstein to keep the static state of the universe without collapse by gravity. 
Its identity might be the energy of a mere vacuum as well as the cosmological term, or some potential energy (of the scalar field) that does not substantially change even in 10 billion years of time scale.
Others, it can be considered such scenarios that gravity theory which defines the cosmic expansion deviates from general relativity, or remnants of the high-dimensional cosmological such as membrane models have created an effective dark energy.
○In the case of scenario 1, it is necessary to escape from this universe after a few trillion years. 
[Expansion of the universe] 
○ For expansion of the universe is the expansion of space-time itself, so it is also possible to exceed the speed of light.
○Currently, the observable universe is expanding at 3.5 times of the speed of light. And expansion is accelerating.
: In the 18 billion light-years distant, the expansion velocity exceeds the speed of light. = We can not observe in the distance from it.
⇒After 2 trillion years it almost becomes invisible but one giant galaxy.
: We are living in special times!
○Outside of the observable universe is not known whether infinite or finite.
○ In any case, the observable universe is smaller than the whole universe, so we can not determine the structure of the entire universe by observation.
⇒ Therefore, in order to escape from our universe, rather than fly, it is necessary to exceed the time and space.
○But above is hypothesis and it is not intended validated. Moreover, the time requires 10 billion years. Don't worry!
○ Hypothesis over the future of the universe is a situation of "anything goes".
【Future of intelligence】
☆ The important thing for the intelligence is communication between the parallel universe rather than escape from the universe.
☆ Communication between the parallel universe would be done by GAI.
1. Chandra X-ray Observatory - NASA's flagship X-ray telescope
3. School of science the university of Tokyo
5. No.１６ Theory of Relativity
7. Michio Kaku / New York incandescent classroom " Amazing prophecy of "Theory of Everything;TOE"" 20150403
10. GAI ：Growing Artificial Intelligence No.35、No.40、No.41
11. 「気が遠くなる未来の宇宙のはなし(The story of the future of the universe mind-boggling)」Ktsuhiko Sato(2013)p.187〜