标题： 暴胀前反弹对$f(R)$引力理论中原初引力波的影响 显示英文标题

标题： Pre-Inflationary Bounce Effects on Primordial Gravitational Waves of $f(R)$ Gravity

摘要： 在本工作中，我们将研究我们宇宙可能的暴胀前情景以及这如何通过$f(R)$引力实现。具体来说，我们将引入一个情景，在暴胀前时期宇宙收缩直到达到最小幅度，随后膨胀，缓慢进入慢滚准德西特暴胀时期。这个暴胀前的反弹避免了宇宙奇点，并且在准德西特暴胀阶段前后时期，近似满足由弦理论提出的尺度因子对偶性$a(t)=a^{-1}(-t)$。我们研究哪些$f(R)$的近似形式可以实现这种无奇点的暴胀前情景，其准德西特部分由$R^2$引力描述，因此暴胀的结束得到了保证。此外，由于在弦理论的暴胀前大爆炸情景中会导致引力波能量谱的整体增强，我们详细考察了生成这种无奇点暴胀前反弹的$f(R)$引力的这一观点。正如我们所展示的，在$f(R)$引力情况下，原初引力波背景的能量谱也会被增强，但缺点是增强程度太小，无法被未来的高频干涉仪探测到。因此我们得出结论，就像单标量场理论的情况一样，$f(R)$引力无法产生可探测的随机引力波，可能需要标量和高阶曲率项的协同理论。 显示英文摘要

摘要： In this work we shall study a possible pre-inflationary scenario for our Universe and how this might be realized by $f(R)$ gravity. Specifically, we shall introduce a scenario in which the Universe in the pre-inflationary era contracts until it reaches a minimum magnitude, and subsequently expands, slowly entering a slow-roll quasi-de Sitter inflationary era. This pre-inflationary bounce avoids the cosmic singularity, and for the eras before and after the quasi-de Sitter inflationary stage, approximately satisfies the string theory motivated scale factor duality $a(t)=a^{-1}(-t)$. We investigate which approximate forms of $f(R)$ can realize such a non-singular pre-inflationary scenario, the quasi-de Sitter patch of which is described by an $R^2$ gravity, thus the exit from inflation is guaranteed. Furthermore, since in string theory pre-Big Bang scenarios lead to an overall amplification of the gravitational wave energy spectrum, we examine in detail this perspective for the $f(R)$ gravity generating this pre-inflationary non-singular bounce. As we show, in the $f(R)$ gravity case, the energy spectrum of the primordial gravitational waves background is also amplified, however the drawback is that the amplification is too small to be detected by future high frequency interferometers. Thus we conclude that, as in the case of single scalar field theories, $f(R)$ gravity cannot produce detectable stochastic gravitational waves and a synergistic theory of scalars and higher order curvature terms might be needed.