用SN Ia研究运动学宇宙学的现状：JLA、Pantheon和用LSST研究未来的约束
Status of kinematic cosmology with SN Ia: JLA, Pantheon and future constraints with LSST
摘要：
在这项工作中，我们从Ia型超新星中获得了最先进的模型独立的宇宙学约束，通过测量纯运动学的$\left( q,j \right)$模型参数（其中$q$和$j$与哈勃参数的一阶和二阶导数有关）。对于SN Ia的JLA汇编，发现$Λ$ CDM期望的2 $σ$内的协议，其中最佳拟合的运动学参数是$q=-0.66 \pm 0.11$和$j=0.41 ^{+0.32}_{-0.33}$。对于$q=-0.73 \pm 0.13$和$j=0.76 ^{+0.41}_{-0.43}$，Pantheon样本显示出与$Λ$ CDM对$j=1$的预期比JLA更好的一致性，这暗示了较少的系统分类和/或更多的SN Ia缓解了紧张局势。对于未来，我们预测从LSST深度调查获得的SN Ia可达到的精度为$Δq \sim 0.05$和$Δj \sim 0.1$，这是系统性限制的，并且可能导致检测到与$Λ$ CDM（在$j$中）或当前测量的膨胀率（在$q$中）的偏差。相比之下，对于标准宇宙学参数，我们得到LSST的$ΔΩ_\mathrm{m}=0.01$和$Δw=0.07$。考虑到LSST预期的大量超新星Ia，可以限制多达500个天空区域的运动学参数，每个区域都有自己的哈勃图。对于每一个区域，在当前的系统水平上，可以达到百分之十的精度，与当今的全天巡天相当。这将决定宇宙膨胀的各向异性，或暗能量偶极子，在10 s的百分之十的水平在10 s的度尺度。
英文摘要：
In this work we derive state-of-the-art model-independent constraints on cosmology from SN Ia by measuring purely kinematical $\left( q,j \right)$ model parameters (where $q$ and $j$ are related to the first and second derivative of the Hubble parameter). For the JLA compilation of SN Ia an agreement within 2$σ$ of $Λ$CDM expectations is found, where best-fitting kinematical parameters are $q=-0.66 \pm 0.11$ and $j=0.41 ^{+0.32}_{-0.33}$. With $q=-0.73 \pm 0.13$ and $j=0.76 ^{+0.41}_{-0.43}$ the Pantheon sample shows even better agreement with the $Λ$CDM expectation of $j=1$ than JLA, hinting at less systematics and/or a higher number of SN Ia alleviating tensions. For the future we predict the precision achievable with SN Ia from the LSST deep survey as $Δq \sim 0.05$ and $Δj \sim 0.1$, which is systematics-limited and could lead to detect both deviations from $Λ$CDM (in $j$) or current expansion rates measured (in $q$). In comparison, for standard cosmological parameters we get $ΔΩ_\mathrm{m}=0.01$ and $Δw=0.07$ for LSST. Given the high number of SN Ia expected for LSST, kinematical parameters in up to 500 sky regions, each with their own individual Hubble diagram, can be constrained. For each region an individual precision at the 10s of percent level is within reach at current systematics-levels, comparable to present-day full-sky surveys. This will determine anisotropy in cosmic expansion, or the dark energy dipole, at the 10s of percent level at 10s of degree scales.
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