“彩虹”宇宙中的扰动问题

在广义相对论的基础上，可以研究宇宙的时空演化。宇宙的极早期会有一个暴胀时期，在这个时期内会产生影响宇宙大尺度结构的密度扰动。本论文讨论彩虹引力下的暴胀模型，导出了度规场和标量场的扰动方程，分析了密度扰动随时间变化的性质。通过求解功率谱，发现彩虹宇宙里功率谱的标度不变性依然保持。谱指数与标准暴胀型中一致，但是其功率谱的幅值缺与探测粒子的能量有关。

The Perturbations in "Rainbow" Universe

It is possible to discuss the structure of spacetime and the evolution of the universe by General Relativity proposed by Einstein in 1915.It is believed that there is a stage of inflation in the very early epoch of the universe.The inflationary paradigm generates density perturbations as seeds for large scale structure in the universe.In recent years,rainbow gravity as a semi-classical and effective theory of quantum gravity has been proposed by Maguejio and Smolin.In this paper,we discuss the perturbations of inflation in the rainbow universe and derive the power spectrum.It turns out that the scale invariance of the power spectrum is preserved and the power spectrum index is unchanged.However,the magnitude of the spectrum depends on the energy of probes.