环境噪声下Starobinsky-Vilenkin随机通货膨胀的镇定
Stabilization of Starobinsky-Vilenkin stochastic inflation by an environmental noise
摘要：
我们讨论了暴胀子$ϕ$在相互作用中的无限数量的领域作为一个环境（噪音）与摩擦$γ^{2}>0$。在马尔可夫近似下，我们得到了一个随机波动方程（也出现在暖膨胀模型中）。在用白噪声代替环境后，如果$γ\neq 0$满足，则随机波动方程违反能量守恒。我们引入了一种暗能量作为暴胀子能量动量的补偿。我们在经典波动方程中加入Starobinsky-Vilenkin噪声，该噪声在慢滚近似中描述了膨胀度规中的量子涨落。我们研究由此产生的一致性爱因斯坦-克莱因-戈登系统在慢滚制度。在已知尺度因子$a$和哈勃变量$ H$对场$ϕ$的依赖关系的条件下，得到了暴胀子几率分布的Fokker-Planck方程.我们得到明确的固定的解决方案的福克-普朗克方程假设$a(ϕ)$和$H(ϕ)$可以近似地确定在一个慢滚制度，忽略噪音。我们将结果推广到多场D维位形空间。我们表明，在政权$a(ϕ)^{3}H(ϕ)^{5}\rightarrow \infty$的量子噪声决定的渐近行为的平稳分布。如果$a(ϕ)^{3}H(ϕ)^{5}$保持有限，则环境噪声确保平稳概率的可积性。在这种情况下，不需要引入边界条件来消除无限暴胀。$a(ϕ)^{3}H(ϕ)^{5}$的变化可以解释为从冷膨胀向暖膨胀过渡的标志。
英文摘要：
We discuss the inflaton $ϕ$ in an interaction with an infinite number of fields treated as an environment (noise) with a friction $γ^{2}>0$. In a Markovian approximation we obtain a stochastic wave equation (appearing also in the warm inflation models). After the replacement of the environment by the white noise, the stochastic wave equation violates the energy conservation if $γ\neq 0$. We introduce a dark energy as a compensation of the inflaton energy-momentum. We add to the classical wave equation the Starobinsky-Vilenkin noise which in the slow-roll approximation describes the quantum fluctuations in an expanding metric. We investigate the resulting consistent Einstein-Klein-Gordon system in the slow-roll regime. We obtain Fokker-Planck equation for the probability distribution of the inflaton assuming that the dependence of the scale factor $a$ and the Hubble variable $ H$ on the field $ϕ$ is known. We obtain explicit stationary solutions of the Fokker-Planck equation assuming that $a(ϕ)$ and $H(ϕ)$ can approximately be determined in a slow-roll regime with the neglect of noise. We extend the results to the multifield D-dimensional configuration space. We show that in the regime $a(ϕ)^{3}H(ϕ)^{5}\rightarrow \infty$ the quantum noise determines the asymptotic behaviour of the stationary distribution. If $a(ϕ)^{3}H(ϕ)^{5}$ stays finite then the environmental noise ensures the integrability of the stationary probability. In such a case there is no need to introduce boundary conditions with the purpose to eliminate infinite inflation. The variation of $a(ϕ)^{3}H(ϕ)^{5}$ could be interpreted as a sign of a transition from cold inflation to warm inflation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
