膨胀弹性固体中微扰的量子化
Quantization of Perturbations in an Inflating Elastic Solid
摘要：
一个足够刚性的相对论弹性固体可以在负压值下保持稳定，因此能够驱动一个加速膨胀的阶段。如果一个相对论性弹性固体在早期宇宙中推动了一个暴胀阶段，量子力学激发的扰动将在介质中产生。我们研究了线性标量和张量扰动，并研究了具有这种暴胀周期的观测结果。我们发现，缓慢变化的声速的扰动和缓慢变化的固体状态方程可以产生一个轻微的红色倾斜的标量功率谱，符合目前的观测数据。即使在没有非绝热压力的情况下，由于固体内部的剪应力，扰动也会在超视界尺度上演化。因此，扰动谱一般对通货膨胀结束的细节很敏感，我们描述了这种依赖性。有趣的是，我们在这里发现了（1 + P/ρ）显著大于0的弹性固体的加速解，但它们具有几乎标度不变的标量谱和张量谱。除了理论上的兴趣，这可能允许可行的暴胀现象相对远离德西特政权的可能性。
英文摘要：
A sufficiently rigid relativistic elastic solid can be stable for negative pressure values and thus is capable of driving a stage of accelerated expansion. If a relativistic elastic solid drove an inflationary stage in the early Universe, quantum mechanically excited perturbations would arise in the medium. We quantize the linear scalar and tensor perturbations and investigate the observational consequences of having such an inflationary period. We find that slowly varying sound speeds of the perturbations and a slowing varying equation of state of the solid can produce a slightly red-tilted scalar power spectrum that agrees with current observational data. Even in the absence of nonadiabatic pressures, perturbations evolve on superhorizon scales, due to the shear stresses within the solid. As such, the spectra of perturbations are in general sensitive to the details of the end of inflation and we characterize this dependence. Interestingly, we uncover here accelerating solutions for elastic solids with (1 + P/ρ) significantly greater than 0 that nevertheless have nearly scale-invariant scalar and tensor spectra. Beyond theoretical interest, this may allow for the possibility of viable inflationary phenomenology relatively far from the de Sitter regime.
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