inflation as well as the branching ratio of the inflaton decay into the LSP. Here we see that this most likely requires the mass of the LSP, $m_{\rm LSP}$, to be in the TeV region. Such a small LSP mass may result from a cancellation of various contributions as a result of environmental selection associated with dark matter [@Hall:2011jd].

Let us first consider the case in which $T_R \gtrsim m_{\rm LSP}$. In this case, the LSP is thermalized and its abundance is roughly given by $$\Omega^{\rm th} h^2 \sim 10^{16} 
    \left( \frac{m_{\rm LSP}}{10^{12}~{\rm GeV}} \right)^2.
\label{eq:Omega-th}$$ This grossly overcloses the universe for $m_{\rm LSP} \sim O(\tilde{m})$. We now consider the case $T_R \ll m_{\rm LSP}$. In this case, thermal gas scattering and inflaton decay may still lead to a significant amount of the LSP abundance. From thermal scattering, we obtain the approximate LSP abundance of $$\Omega^{\rm sc} h^2 \sim 10^{21} 
    \left( \frac{T_R}{m_{\rm LSP}} \right)^7.
\label{eq:Omega-sc}$$ (A similar estimate in a different context can be found in Ref. [@Takayama:2007du].) Furthermore, if the mass of the inflaton $m_\phi$ is sufficiently larger than $m_{\rm LSP}$, the inflaton may directly decay into LSPs which do not effectively annihilate afterwards. The resulting LSP abundance is 