f（R）引力宇宙学
Cosmography of f(R) gravity
摘要：
现在公认宇宙正在经历一个加速膨胀的阶段，正如哈勃Ia型超新星（SNeIa）图和几个LSS观测所证明的那样。未来的SNeIa调查和其他探测器将有可能更好地描述宇宙的动力学状态，重新引起对宇宙学的兴趣，这使得对距离-红移关系的模型独立分析成为可能。另一方面，四阶引力理论，也被称为$f(R)$引力，吸引了很多人的兴趣，因为他们可以解释加速膨胀没有任何暗能量。我们在这里展示了如何有可能将宇宙学参数（即减速$q_0$，急动$j_0$，快照$s_0$和lerk $l_0$参数）与$f(R)$及其衍生物$f^{(n)}(R) = d^nf/dR^n$（与$n = 1, 2, 3$）的当前值联系起来，从而提供了一种新的工具来约束这种高阶模型。因此，我们的分析提供了一种可能性，将来自宇宙学的独立于模型的结果与$f(R)$宇宙学的理论假设联系起来。
英文摘要：
It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better characterize the dynamical state of the universe renewing the interest in cosmography which allows a model independent analysis of the distance - redshift relation. On the other hand, fourth order theories of gravity, also referred to as $f(R)$ gravity, have attracted a lot of interest since they could be able to explain the accelerated expansion without any dark energy. We show here how it is possible to relate the cosmographic parameters (namely the deceleration $q_0$, the jerk $j_0$, the snap $s_0$ and the lerk $l_0$ parameters) to the present day values of $f(R)$ and its derivatives $f^{(n)}(R) = d^nf/dR^n$ (with $n = 1, 2, 3$) thus offering a new tool to constrain such higher order models. Our analysis thus offers the possibility to relate the model independent results coming from cosmography to the theoretically motivated assumptions of $f(R)$ cosmology.
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