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arXiv 2004.10815gr-qc
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暖膨胀模型中随机波动方程和扩散方程的功率谱

Power spectrum of stochastic wave and diffusion equations in the warm inflation models

Z. Haba

摘要:

我们讨论耗散随机波和扩散方程的暴胀子与环境的相互作用,在一个外部的扩展度规。我们证明了扩散方程在强摩擦极限下很好地逼近了波动方程。在扰动随时间缓慢变化且几乎是指数展开的假设下,我们计算了波动方程的长波功率谱。在假设噪声在坐标变换下具有形式不变性的条件下,我们得到了接近尺度不变性的功率谱。在扩散近似中,我们超越了慢变假设。我们精确地计算了指数膨胀和多项式势模型以及幂律膨胀和指数势模型的功率谱。

英文摘要:

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.

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