We examine the question as to whether the Palatini f(R) gravity theories permit space-times in which the causality is violated. We show that every perfect-fluid Gödel-type solution of Palatini f(R) gravity with density $ρ$ and pressure $p$ that satisfy the weak energy condition $ρ+p \geq 0$ is necessarily isometric to the Gödel geometry, demonstrating therefore that these theories present causal anomalies in the form of closed time-like curves. This result extends a theorem on Gödel-type models to the framework of Palatini f(R) gravity theory. We concretely examine the Gödel-type perfect-fluid solutions in specific $f(R) = R - α/R^{n}$ Palatini gravity theory, where the free parameters $α$ and $n$ have been recently constrained by a diverse set of observational data. We show that for positive matter density and for $α$ and $n$ within the interval permitted by the observational data, this theory does not admit the Gödel geometry as a perfect-fluid solution of its field equations. In this sense, this theory remedies the causal pathology in the form of closed time-like curves which is allowed in general relativity. We derive an expression for a critical radius $r_c$ (beyond which the causality is violated) for an arbitrary Palatini f(R) theory, thus making apparent that the violation of causality depends on the form of f(R) and on the matter content components. We also examine the violation of causality of Gödel-type by considering a single scalar field as the matter content. For this source we show that Palatini f(R) gravity gives rise to a unique Gödel-type solution with no violation of causality.
Statefinder diagnostic and constraints on the Palatini f(R) gravity theories
本文利用Palatini形式下的一系列$f(R)$引力理论，研究了平坦Friedmann-Robertson-Walker（FRW）宇宙产生晚时加速度的概率.我们应用statefinder诊断这些宇宙学模型选择的一系列参数，看看他们是否彼此区分。诊断涉及状态查找器对$\{r,s\}$，其中$r$是从比例因子$a$及其相对于宇宙时间$t$的高阶导数导出的，并且$s$由$r$和减速参数$q$表示。总之，我们发现，虽然两种类型的$f(R)$理论：（i）$f(R) = R + αR^m - βR^{-n}$和（ii）$f(R) = R + α\ln R - β$可以导致晚时间加速，它们在$r-s$和$r-q$平面的演化轨迹显示出不同的演化特性，这当然证明了状态发现诊断的优点。此外，我们利用观测哈勃参数数据（OHD）来约束这些模型的$f(R)$重力。结果，除了（i）情况的$m=n=1/2$之外，（i）情况和（ii）情况的$α=0$允许$Λ$ CDM模型存在于1个$σ$置信区域中。对最佳拟合模型进行状态发现器诊断后发现，所有最佳拟合模型都能经历减速/加速过渡阶段，且加速时刻较晚，并且在未来都将转向de-Sitter点（$\{r,s\}=\{1,0\}$）。同时，这些模型之间的演化差异是明显的，特别是在$r-s$平面，这使得状态发现诊断更可靠的判别宇宙学模型。
The habitability of the Universe through 13 billion years of cosmic time
天体生物学领域在模拟银河系尺度的宜居带方面取得了巨大的进展，这些宜居带为生命的形成和复杂的进化提供了稳定的环境。最近，这个想法已经扩展到宇宙学尺度，通过对局部宇宙的可居住性进行整体建模的研究（例如Dayal et al. 2015; Li & Zhang 2015）。然而，所有这些研究都只集中在估计II型超新星（SNII）或伽马射线暴（GRB）的潜在有害影响，忽略了Ia型超新星（SNIa）和活动星系核（AGN）的贡献。在这项研究中，我们遵循两种不同的方法，基于（i）有害辐射的幅度和（ii）有害辐射照射的总行星托管体积。我们同时跟踪整个宇宙的关键天体物理源（SNII，SNIa，AGN和GRB）的贡献，以确定其在138亿年宇宙时间内的可居住性。我们发现SNII在任何宇宙时期的总辐射收支和有害辐射照射量中占主导地位，紧随其后的是SNIa（贡献为SNII的一半），GRB和AGN占微不足道的部分（<1%）。其次，由于恒星的总质量（或行星的总数）随着时间的推移而缓慢增加，而总的有害辐射密度和受影响的体积在最初的30亿年后下降，我们发现宇宙的可居住性在宇宙时间内稳步增加。我们发现，根据确切的模型假设，与40亿年前生命首次出现在地球上时相比，今天的宇宙可居住性是2.5到20倍。我们发现，这种可居住性的增加将持续到最后的恒星在接下来的数千亿年内消亡。
