论文标题
温暖通货膨胀模型中随机波和扩散方程的功率谱
Power spectrum of stochastic wave and diffusion equations in the warm inflation models
论文作者
论文摘要
我们讨论了由于充气量与外部扩展度量中环境的相互作用而产生的耗散随机波和扩散方程。我们表明，扩散方程很好地近似于强摩擦极限。在假设扰动逐渐变化并且扩展几乎是指数级的假设下，我们计算了波方程的长波功率谱。在假设噪声在坐标转换下具有不变的形式的假设，我们获得了接近刻度不变的功率谱。在扩散近似中，我们超出了缓慢的变化假设。我们在具有指数膨胀和多项式电势以及幂律膨胀和指数势的模型中精确计算功率谱。
We discuss dissipative stochastic wave and diffusion equations resulting from an interaction of the inflaton with an environment in an external expanding metric. We show that a diffusion equation well approximates the wave equation in a strong friction limit. We calculate the long wave power spectrum of the wave equation under the assumption that the perturbations are slowly varying in time and the expansion is almost exponential. Under the assumption that the noise has a form invariant under coordinate transformations we obtain the power spectrum close to the scale invariant one. In the diffusion approximation we go beyond the slow variation assumption. We calculate the power spectrum exactly in models with exponential inflation and polynomial potentials and with power-law inflation and exponential potentials.
