发表机构
ICRANet; Sapienza University of Rome; INFN, Sezione di Perugia; University of Chinese Academy of Sciences（国际相对论天体物理中心; 罗马第一大学; 意大利国家核物理研究所佩鲁加分部; 中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从复标量场推导出含时变宇宙学项的宇宙速率方程闭合方程组，给出粒子对产生与能量交换机制，并应用于暴胀、再加热及标准宇宙学。
AI 中文摘要
在具有时变宇宙学项的弗里德曼宇宙中，重粒子-反粒子对的产生及其与时空真空的能量交换由宇宙速率方程描述：$\dot\rho_M+3H\rho_M=\Gamma_M(\rho_M^H-\rho_M)-\Gamma_M^{\rm de}\rho_M$。该方程与弗里德曼方程、时变宇宙学项的能量平衡方程以及辐射的再加热方程一起，构成一个由四个独立背景方程组成的闭合方程组。我们从具有全局U(1)对称性并与曲率非最小耦合的复标量场推导出该方程组。在绝热情况下，非相对论模式的占据数给出$\rho_M^H=2\chi m^2H^2$。基于与时空真空涨落的成对耦合$\xi R|\Phi|^2$的动力学方程给出弛豫率$\Gamma_M$，而汤川耦合给出衰变率$\Gamma_M^{\rm de}$。在快速振荡情况下，哈勃函数以两倍于对质量的频率振荡并与对锁定相位，因此与它们没有净能量交换。所产生的对的能量由宇宙学项在时间演化中的减少提供：$-\dot\rho_\Lambda=[(3-2\epsilon) H+\Gamma_M^{\rm de}]\rho_M^H$。对快速时间取平均，得到细致平衡区域$\Gamma_M\gg H$中的宇宙速率方程。在该区域，闭合方程组具有精确的幂律解，其中$\epsilon=-\dot H/H^2=\chi m^2/m_{\rm pl}^2$。我们讨论了该闭合方程组在暴胀、再加热和标准宇宙学中的应用。
英文摘要
In a Friedmann universe with a time-varying cosmological term, the production of massive particle--antiparticle pairs and their exchange of energy with the spacetime vacuum are described by a cosmic rate equation, $\dotρ_M+3Hρ_M=Γ_M(ρ_M^H-ρ_M)-Γ_M^{\rm de}ρ_M$. Together with the Friedmann equations, an energy-balance equation for the time-varying cosmological term, and a reheating equation for the radiation, it forms a closed set of four independent background equations. We derive this set from a complex scalar field with a global U(1) symmetry and a non-minimal coupling to curvature. In the adiabatic case, the occupation of non-relativistic modes gives $ρ_M^H=2χm^2H^2$. A kinetic equation, based on the pairwise coupling $ξR|Φ|^2$ to fluctuations of the spacetime vacuum, gives the relaxation rate $Γ_M$, and a Yukawa coupling gives the decay rate $Γ_M^{\rm de}$. In the fast-oscillating case, the Hubble function oscillates at twice the pair mass and locks in phase with the pairs, so that it exchanges no net energy with them. The energy of the created pairs is supplied instead by the decrease of the cosmological term in the time evolution, $-\dotρ_Λ=[(3-2ε) H+Γ_M^{\rm de}]ρ_M^H$. Averaging over the fast time gives the cosmic rate equation in the detailed-balance regime $Γ_M\gg H$. In this regime the closed set has an exact power-law solution with $ε=-\dot H/H^2=χm^2/m_{\rm pl}^2$. We discuss the application of the closed set to inflation, reheating and standard cosmology.
Comments31 pages, 5 figures
