Mohamad-Ziad Charif - Antares

From these equations we can derive the Friedmann equation (eq 2.5 & 2.6) withH(t) = ȧ(t)a(t) and ˙ρ tot being the time derivative of ρ tot .H 2 (t) = 8π 3 ρ tot − k a 2 + Λ 3(2.5)˙ρ tot = −3H(ρ tot + p tot ) (2.6)The Friedman equation can sometimes be written in the following form in equation2.7 as function of the normalized densities of all ingredients of the universe,where Ω R is the density of radiation in the universe, Ω M is the density of all typesof matter, Ω K is the curvature of space. At our time now (a=1) the equation isreduced to 2.8.Ω M can also be written as the sum of Ω c + Ω b , where Ω c is the density of darkmatter and Ω b as the density of baryonic matter.H 2H02= Ω R a −4 + Ω M a −3 + Ω k a −2 + Ω Λ (2.7)1 = Ω R + Ω M + Ω k + Ω Λ (2.8)The best measured value for these parameters above come from the combinationof WMAP survey[21], baryon acoustic oscillations[18].Ω b = 0.0456 ± 0.00015(fig 2.5) the density of baryonic matter which is in agreement with predictionsfrom primordial nucleosynthesis[22], Ω c = 0.227±0.014 the density of dark matter,Ω Λ = 0.728 +0.015−0.016 the cosmological constant (fig 2.5) , Ω R = 4.97 · 10 −5 thedensity of radiation. The results indicate that we have about 50 times more darkmatter in the Universe than baryonic matter (consistent with observations).2.1.6.1 Dark matter in ΛCDMDark matter can either be explained as actual matter (baryonic or not) or as lawsof gravity being different at the large scales[12] such as the MOND (MOdifiedNewtonian Dynamcics) model. With major models for modified laws of gravitybeing disfavored in face of matter models [10, 11], the remaining part is to seewhether this matter is baryonic or not. The major candidate for baryonic darkmatter is MACHOs or Massive Compact Halo Objects. MACHOs mainly consistsof large and condensed objected such black holes, neutron stars, and otherthat have from barely to non-existing electromagnetic signatures. The contributionof these objects has already been constrained and ruled out as a dark mattercandidate[23, 24, 25].What remains are the non-baryonic candidates, which can be divided into threecategories:11