By Adnan Ghribi
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These calculations show that dark matter density decreased over the history of the Universe due to expansion of space and annihilation between dark matter particles and anti-particles. At some temperature in the early Universe, known as the freeze-out temperature, the density of dark matter decreased to the point that annihilation became negligible to the further evolution of the density, which is now dominated by expansion. What remains today is called the relic abundance, or relic density, of dark matter.
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101) that (+) f2 <0 and (−) f2 >0 (103) Then the stability condition (82) is obeyed for any value of R. As regards the (−)-case, there are two possibilities depending upon the sign of f 1 . Should f 1 be positive, all the remaining stability conditions are automatically satisﬁed, ie. in the case of both (−) f2 (−) > 0 and f 1 > 0. F() Supergravity and Early Universe: the Meeting Point F (R) Supergravity and Early Universe: the Meeting Point of Cosmology and High-Energy Physicsof Cosmology and High-Energy Physics 21 19 (−) Should f 1 be negative, f 1 < 0, we ﬁnd that the remaining stability conditions (100) and (102) are the same, as they should, while they are both given by 192 f 12 3 · 5 f 12 f = − − 32 0 ≡ Rins max f2 23 · 11 f 22 23 · 11 f 22 R < Rmax − (104) As regards the (+)-case, eq.