We study the decay of a Higgs-like scalar Yukawa coupled to massless fermions in post-inflationary cosmology, combining a non-perturbative method with an adiabatic expansion. The renormalized survival probability $\mathcal{ P}_\Phi(t)$ of a (quasi) particle ``born'' at time $t_b$ and decaying at rest in the comoving frame, $\mathcal{ P}_\Phi(t) = \Big[\frac{ t}{ t_b}\Big]^{ -\frac{ Y^2}{ 8\pi^2}}~ e^{ \frac{ Y^2}{ 4\pi^2}\,\big(t/t_b\big)^{ 1/4} } \,e^{ -\Gamma_0\,(t-t_b)}~ \mathcal{ P}_\Phi(t_b) $, with $\Gamma_0$ the decay rate at rest in Minkowski space-time. For an ultrarelativistic particle we find $\mathcal{ P}_\Phi(t) = e^{ -\frac{ 2}{ 3}\Gamma_0\,t_{ nr}\,(t/t_{ nr})^{ 3/2}}~ \mathcal{ P}_\Phi(t_b)$ before it becomes non-relativistic at a time $t_{ nr}$ as a consequence of the cosmological redshift. For $t\gg t_{ nr}$ we find $\mathcal{ P}_\Phi(t) = \Big[\frac{ t}{ t_{ nr}}\Big]^{ -\frac{ Y^2}{ 8\pi^2}}~ e^{ \frac{ Y^2}{ 4\pi^2}\,\big(t/t_{ nr}\big)^{ 1/4} }~\Big[\frac{ t}{ t_{ nr}}\Big]^{ \Gamma_0 t_{ nr}/2} \,e^{ -\Gamma_0\,(t-t_{ nr})}~ \mathcal{ P}_\Phi(t_{ nr})$. The extra power is a consequence of the memory on the past history of the decay process. We compare these results to an S-matrix inspired phenomenological Minkowski-like decay law modified by an instantaneous Lorentz factor to account for cosmological redshift. Such phenomenological description \emph{ under estimates the lifetime of the particle}. For very long lived, very weakly coupled particles, we obtain an \emph{ upper bound} for the survival probability as a function of redshift $z$ valid throughout the expansion history $\mathcal{ P}_\Phi(z) \gtrsim e^{ -\frac{ \Gamma_0}{ H_0}\,\Upsilon(z,z_b)}\,\mathcal{ P}_\Phi(z_b)$, where $\Upsilon(z,z_b)$ only depends on cosmological parameters and $t_{ nr}$.
Categories: hep-ph astro-ph.CO gr-qc hep-th