if T$_{R}$ ≥ M$_{1}$ ≥ 10 9 GeV, where M$_{1}$ is the lightest RH neutrino [333] $^{24}$. There exist various scenarios of non-thermal leptogenesis [336–340] which can work for T$_{R}$ ≤ M$_{N}$ . 3. Cold dark matter The WMAP data, galaxy clusters and large scale structure data pin down the dark matter abundance to be : Ω$_{DM}$ = 0 . 22 [274]. It is important to note that at the end of inflation right abundance of dark matter must be created. There are many well motivated particle physics candidates for cold dark matter [341, 342]. All the plausible candidates arise from beyond the SM physics. Within MSSM the lightest SUSY particle (LSP) is an excellent candidate by virtue of R-parity [31], the non-topological solitons such as Q-balls [91, 92], and Kaluza-Klein dark matter particles in theories with extra dimensions [342] are the most popular ones. The dark matter particles can be created via thermal scatterings in the case of thermal cold relics, and non-thermally in the process of decay of heavier particles. The thermal relic abundance is easy to calculate, the number density of dark matter X , n$_{X}$ , gets exponential suppression in comparison with the number density of relativistic degrees of freedom deter- mined by the freeze-out temperature, T$_{f}$ < m$_{X}$ . The abundance is calculated by solving the Boltzmann equation [96]: where σ is the total annihilation cross section, v is the velocity and bracket denotes thermally averaged quantities. In the case of heavy X , the cross section can be expanded with respect to the velocity in powers of v $^{2}$, 〈 σv 〉 = a + b 〈 v $^{2}$〉 + O ( 〈 v $^{4}$〉 ) + ... ≈ a + 6 b/x , where x = m$_{X}$/T and a, b $_{are expressed in GeV}$− $^{2}$. In the regime where the dark matter abundance is frozen- out for x ≫ x$_{f}$ ≡ m$_{X}$/T$_{f}$ , the relic density can be expressed in terms of the critical density: where $^{g}$∗ is the relativistic degrees of freedom and x$_{f}$ ∼ 25 − 30 (in the standard LSP case) are evaluated at the time of freeze-out. An approximate order of magnitude estimation of 24 Thermal leptogenesis can work below the reheat temperature T$_{R}$ < 10 9 GeV in the case of a resonant leptogenesis [334, 335]. 40 dn$_{X}$ dt + 3 Hn$_{X}$ = −〈 σv 〉 ( n 2 X − ( n eq $_{X}$) $^{2}$) , (80) Ω$_{X}$ h 2 ≈ 1 . 07 × 10 9 M$_{P}$ x$_{f}$ √ $^{g}$∗ ( a + 3 b/x$_{f}$ ) $_{GeV}$− $^{1}$, (81)