Title: Probing Modified Gravity Theories with ISW and CMB Lensing Show Chinese title

Title: 利用ISW和CMB透镜效应探测修正引力理论

Abstract: We use the optimised skew-spectrum as well as the skew-spectra associated with the Minkowski Functionals (MFs) to test the possibility of using the cross-correlation of the Integrated Sachs-Wolfe effect (ISW) and lensing of the cosmic microwave background (CMB) radiation to detect deviations in the theory of gravity away from General Relativity (GR). We find that the although both statistics can put constraints on modified gravity, the optimised skew-spectra are especially sensitive to the parameter $\rm B_0$ that denotes the the {\em Compton wavelength} of the scalaron at the present epoch. We investigate three modified gravity theories, namely: the Post-Parametrised Friedmanian (PPF) formalism; the Hu-Sawicki (HS) model; and the Bertschinger-Zukin (BZ) formalism. Employing a likelihood analysis for an experimental setup similar to ESA's Planck mission, we find that, assuming GR to be the correct model, we expect the constraints from the first two skew-spectra, $S_{\ell}^{(0)}$ and $S_{\ell}^{(1)}$, to be the same: $\rm B_0<0.45$ at $95%$ confidence level (CL), and $\rm B_0<0.67$ at $99%$ CL in the BZ model. The third skew-spectrum does not give any meaningful constraint. We find that the optimal skew-spectrum provides much more powerful constraint, giving $\rm B_0<0.071$ at $95%$ CL and $\rm B_0<0.15$ at $99%$ CL, which is essentially identical to what can be achieved using the full bispectrum. Show Chinese abstract

Abstract: 我们使用优化的偏斜光谱以及与米氏泛函（Minkowski Functionals, MFs）相关的偏斜光谱来检验利用宇宙微波背景（CMB）辐射的积分 Sachs-Wolfe 效应（ISW）和透镜效应之间的交叉相关性来探测偏离广义相对论（GR）的引力理论修正的可能性。 我们发现，尽管这两种统计方法都能够对修正引力施加限制，但优化的偏斜光谱对参数 $\rm B_0$ 特别敏感，该参数表示标量子在当前时代的 {\em 康普顿波长}。 我们研究了三种修正引力理论，即：后参数化弗里德曼（Post-Parametrised Friedmanian, PPF）形式主义；胡-索维奇（Hu-Sawicki, HS）模型；以及伯特辛格-祖金（Bertschinger-Zukin, BZ）形式主义。 利用类似于欧洲航天局 Planck 任务的实验装置进行可能性分析，我们发现，假设广义相对论（GR）是正确的模型，我们可以预期前两个偏度谱 $S_{\ell}^{(0)}$ 和 $S_{\ell}^{(1)}$ 的约束结果相同：在 $95%$ 置信水平 (CL) 下为 $\rm B_0<0.45$，在 $99%$ 置信水平下为 $\rm B_0<0.67$。在 BZ 模型中，第三个偏度谱没有给出有意义的约束。 我们发现，最优的斜谱提供了更强大的约束，在$95%$置信水平下得到$\rm B_0<0.071$，在$99%$置信水平下得到$\rm B_0<0.15$，这与使用完整三功率谱所能达到的结果基本相同。