Cosmological tests of gravity with latest observations

We perform observational tests of modified gravity on cosmological scales following model-dependent and model-independent approaches using the latest astronomical observations, including measurements of the local Hubble constant, cosmic microwave background, the baryonic acoustic oscillations and redshift space distortions derived from galaxy surveys including the SDSS BOSS and eBOSS, as well as the weak lensing observations performed by the CFHTLenS team. Using all data combined, we find a deviation from the prediction of general relativity in both the effective Newton's constant, $\mu(a,k)$, and in the gravitational slip, $\eta(a,k)$. The deviation is at a $3.1\sigma$ level in the joint $\{\mu(a,k),\eta(a,k)\}$ space using a two-parameter phenomenological model for $\mu$ and $\eta$, and it reaches a $3.7\sigma$ level if a general parametrisation is used. This signal, which may be subject to unknown observational systematics, or a sign of new physics, is worth further investigating with forthcoming observations.Comment: 12 pages, 8 figures; ApJ accepte

Efficient Numerical Evaluation of Feynman Integral

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with $\mathcal{O}(10^{-3})$ accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.Comment: 8 pages, 5 figures, published in Chinese Physics