强透镜约束下Palatini形式的$f(R)$引力理论
$f(R)$ gravity theories in the Palatini Formalism constrained from strong lensing
摘要：
$f(R)$引力能够驱动宇宙的晚期加速，正在成为暗能量的一个有希望的替代品。各种$f(R)$重力模型已经针对膨胀历史的探测器进行了深入的测试，包括Ia型超新星（SNIa）、宇宙微波背景（CMB）和重子声学振荡（BAO）。在本文中，我们建议使用统计透镜样本从斯隆数字巡天类星体透镜搜索数据发布3（SQLS DR 3）约束$f(R)$重力模型。该样品可探测高达$z\sim2.2$的扩增历史，高于当前SNIa和BAO数据探测的扩增历史。我们采用一个典型的参数化形式$f(R)=R-αH^2_0(-\frac{R}{H^2_0})^β$与$α$和$β$常数。对于$β=0$（$Λ$ CDM），我们获得了参数$α=-4.193$的最佳拟合值，其95%置信区间为[-4.633，-3.754]。$α$的最佳拟合值对应于物质密度参数$Ω_{m0}=0.301$，与其他探头的约束一致。如果允许$β$是自由的，则最适合的参数是$(α, β)=(-3.777, 0.06195)$。因此，我们给出了$Ω_{m0}=0.285$和减速参数$q_0=-0.544$。在95%的置信水平下，$α$和$β$分别被约束为[-4.67，-2.89]和[-0.078，0.202]。显然，鉴于目前有限的样本量，我们只能将$β$限制在$Δβ\sim 0.1$的准确度范围内，因此无法区分$Λ$ CDM和$f(R)$具有高度显著性的重力，实际上，前者位于68%的置信度范围内。我们预计，将SQLS DR 3镜头样本扩展到SDSS DR 5和SDSS-II将使模型的约束更加严格。
英文摘要：
$f(R)$ gravity, capable of driving the late-time acceleration of the universe, is emerging as a promising alternative to dark energy. Various $f(R)$ gravity models have been intensively tested against probes of the expansion history, including type Ia supernovae (SNIa), the cosmic microwave background (CMB) and baryon acoustic oscillations (BAO). In this paper we propose to use the statistical lens sample from Sloan Digital Sky Survey Quasar Lens Search Data Release 3 (SQLS DR3) to constrain $f(R)$ gravity models. This sample can probe the expansion history up to $z\sim2.2$, higher than what probed by current SNIa and BAO data. We adopt a typical parameterization of the form $f(R)=R-αH^2_0(-\frac{R}{H^2_0})^β$ with $α$ and $β$ constants. For $β=0$ ($Λ$CDM), we obtain the best-fit value of the parameter $α=-4.193$, for which the 95% confidence interval that is [-4.633, -3.754]. This best-fit value of $α$ corresponds to the matter density parameter $Ω_{m0}=0.301$, consistent with constraints from other probes. Allowing $β$ to be free, the best-fit parameters are $(α, β)=(-3.777, 0.06195)$. Consequently, we give $Ω_{m0}=0.285$ and the deceleration parameter $q_0=-0.544$. At the 95% confidence level, $α$ and $β$ are constrained to [-4.67, -2.89] and [-0.078, 0.202] respectively. Clearly, given the currently limited sample size, we can only constrain $β$ within the accuracy of $Δβ\sim 0.1$ and thus can not distinguish between $Λ$CDM and $f(R)$ gravity with high significance, and actually, the former lies in the 68% confidence contour. We expect that the extension of the SQLS DR3 lens sample to the SDSS DR5 and SDSS-II will make constraints on the model more stringent.
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