arXiv 1808.025392018-08hep-phastro-ph.COgr-qchep-th

后暴胀宇宙学中的粒子衰变

Particle decay in post inflationary cosmology

Nathan Herring, Brian Pardo, Daniel Boyanovsky, Andrew R. Zentner

备注：: more comments. published version
发表信息：: Phys. Rev. D 98, 083503 (2018)
DOI：: 10.1103/PhysRevD.98.083503

摘要：

我们研究了标准宇宙学模型中辐射和物质主导时期的标量粒子衰变。一个绝热近似是有效的自由度与典型的波长远小于粒子视界（$\propto$ ~哈勃半径）在给定的时间。我们实现了一个非微扰的方法，包括宇宙膨胀，并获得宇宙费米的黄金法则，使一个计算质量$m_1$的母粒子的衰变规律，随着建立的人口的子粒子的质量$m_2$。衰变粒子的存活概率为$P(t)=e^{-\widetildeΓ_k(t)\,t}$，其中$\widetildeΓ_k(t)$为\emph{effective momentum and time dependent decay rate}。它的特点是相对论和非相对论制度之间的过渡时间尺度$t_{nr}$和PDMATHAMT总是小于闵可夫斯基时空中的类似速率，作为（本地）时间膨胀和宇宙学红移的结果。对于$t \ll t_{nr}$的衰减规律是一个“拉伸指数”$P(t) = e^{-(t/t^*)^{3/2}}$，而对于非相对论阶段与$t \gg t_{nr}$，我们发现$P(t) = e^{-Γ_0 t}\,(t/t_{nr})^{Γ_0\,t_{nr}/2}$。哈勃时间尺度$\propto 1/H(t)$引入了能量不确定性$ΔE \sim H(t)$，其放松了运动学阈值的约束。这为$2πE_k(t) H(t) \gg 4m^2_2-m^2_1$打开了进入较重粒子的新衰变通道，$E_k(t)$是衰变粒子的（局部）共动能量。随着膨胀的进行，该通道关闭，并且通常的两个粒子阈值限制衰变运动学。

英文摘要：

We study scalar particle decay during the radiation and matter dominated epochs of a standard cosmological model. An adiabatic approximation is introduced that is valid for degrees of freedom with typical wavelengths much smaller than the particle horizon ($\propto$~Hubble radius) at a given time. We implement a non-perturbative method that includes the cosmological expansion and obtain a cosmological Fermi's Golden Rule that enables one to compute the decay law of a parent particle of mass $m_1$, along with the build up of the population of daughter particles of mass $m_2$. The survival probability of the decaying particle is $P(t)=e^{-\widetildeΓ_k(t)\,t}$ with $\widetildeΓ_k(t)$ being an \emph{effective momentum and time dependent decay rate}. It features a transition time scale $t_{nr}$ between the relativistic and non-relativistic regimes and for $k \neq 0$ is always smaller than the analogous rate in Minkowski spacetime, as a consequence of (local) time dilation and the cosmological redshift. For $t \ll t_{nr}$ the decay law is a "stretched exponential" $P(t) = e^{-(t/t^*)^{3/2}}$, whereas for the non-relativistic stage with $t \gg t_{nr}$, we find $P(t) = e^{-Γ_0 t}\,(t/t_{nr})^{Γ_0\,t_{nr}/2}$. The Hubble time scale $\propto 1/H(t)$ introduces an energy uncertainty $ΔE \sim H(t)$ which relaxes the constraints of kinematic thresholds. This opens new decay channels into heavier particles for $2πE_k(t) H(t) \gg 4m^2_2-m^2_1$, with $E_k(t)$ the (local) comoving energy of the decaying particle. As the expansion proceeds this channel closes and the usual two particle thresholds restrict the decay kinematics.

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