Constraining f(R) Gravity via Structure Formation of the Universe

我們研究f(R)重力理論，一個替代暗能量去解釋晚期宇宙加速膨脹的理論，這之下的宇宙微擾演化，。使用GR 當作計算f(R)重力下的宇宙微擾的早期近似是一個常規的方法，對於晚期宇宙，則使用辻川(稱作Tsu)提出的近似方程去計算物質密度微擾。用GR 加上Tsu 去計算物質密度微擾及物質功率譜是常規的方法。在這篇論文中我們提出一個新的近似，「雙重微擾」(稱作DP)，去計算早期宇宙微擾，而在晚期，我們使用Tsu。對不同的f(R)設計者模型和不同傅立葉模式下，我們研究其在方法I(GR 加上Tsu)和方法II(DP 加上Tsu)之間物質密度微擾與物質功率譜之差異。我們發現早期f(R)重力的重力修正效應或許不可忽略。因此，我們的近似可以改善常規的方法。We investigate the evolution of the cosmological perturbations in f(R) gravity, an alternative to dark energy for explaining the late-time cosmic acceleration. It is conventional to use GR as the approximation to calculate cosmological perturbations in f(R) gravity at early times. For the late-time universe, it is to use the approximate formula proposed by Tsujikawa (termed Tsu) to calculate the matter density perturbation. The method with GR and Tsu is conventional to calculate the matter density perturbation and the matter power spectrum. In this thesis we propose a new approach, “double perturbation” (DP), to calculate cosmological perturbations at early times. For the late times, we use Tsu. For different designer f(R) models, we study the difference between Method I (GR+Tsu) and Method II (DP+Tsu) in matter density perturbations and matter power spectra for different Fourier modes. For the shorter-wavelength Fourier modes we find that the effect of the gravity modification at early times in f(R) gravity may not be negligible. We conclude that to be self-consistent, in the f(R) theory one should employ the approximation presented in this thesis instead of that of GR in the treatment of the early-time evolution