Aims: We outline the Bayesian approach to inferring f_NL, the level of non-Gaussianity of local type. Phrasing f_NL inference in a Bayesian framework takes advantage of existing techniques to account for instrumental effects and foreground contamination in CMB data and takes into account uncertainties in the cosmological parameters in an unambiguous way.
Methods: We derive closed form expressions for the joint posterior of f_NL and the reconstructed underlying curvature perturbation, Phi, and deduce the conditional probability densities for f_NL and Phi. Completing the inference problem amounts to finding the marginal density for f_NL. For realistic data sets the necessary integrations are intractable. We propose an exact Hamiltonian sampling algorithm to generate correlated samples from the f_NL posterior. For sufficiently high signal-to-noise ratios, we can exploit the assumption of weak non-Gaussianity to find a direct Monte Carlo technique to generate independent samples from the posterior distribution for f_NL. We illustrate our approach using a simplified toy model of CMB data for the simple case of a 1-D sky.
Results: When applied to our toy problem, we find that, in the limit of high signal-to-noise, the sampling efficiency of the approximate algorithm outperforms that of Hamiltonian sampling by two orders of magnitude. When f_NL is not significantly constrained by the data, the more efficient, approximate algorithm biases the posterior density towards f_NL = 0.
Probing the baryon mass fraction in IGM and its redshift evolution with fast radio bursts using Bayesian inference method
利用红移范围$f_\mathrm{IGM}$内的18个定域FRB研究了星系际介质中重子质量分数。我们构造了一个五参数的贝叶斯推断模型，适当地考虑了IGM和宿主星系色散测度的概率分布。为了检验可能的红移演化，我们将$f_\mathrm{IGM}$参数化为红移的温和演化函数$f_\mathrm{IGM}=f_\mathrm{IGM,0}[1+αz/(1+z)]$。通过同时约束5个参数，得到了主星系DM的中值为$\exp(μ)=72.49^{+33.31}_{-25.62}~{\rm pc ~ cm ^ {-3}}$的$f_\mathrm{IGM,0} = 0.92^{+0.06}_{-0.12}$和$α= 0.49^{+0.59}_{-0.47}$。通过固定两个可以与其他观测值独立约束的参数，我们得到了三参数拟合中的$α=0.11^{+0.24}_{-0.27}$，它在$1σ$不确定度范围内与零一致。蒙特卡罗模拟表明，即使300个FRB也不足以同时严格约束五个参数。这主要是由参数之间的相关性造成的。只有当两个参数固定时，才需要100个FRB来实现对其余参数的无偏约束。
Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data
a Service de Physique Th\'eorique, Brussels Laboratory of the Universe BLU-ULB, Universit\'e Libre de Bruxelles, Boulevard du Triomphe, CP225, 1050 Brussels, Belgium
Probing late-time deviations from $Λ$CDM with a quadratic dark energy expansion
Plaksha University（普拉克斯哈大学）；Universidade Federal do Paraná（巴拉那联邦大学）；Federal University of Latin American Integration (UNILA)（拉丁美洲联邦大学）；Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学）；Instituto Nacional de Pesquisas Espaciais（国家空间研究所）
Probing potential redshift-dependent systematics in the Hubble tension: Model-independent $H_0$ constraints from DESI R2
School of Physics and Optoelectronic, Yangtze University（长江大学物理与光电工程学院）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理学院）；Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University（北京师范大学天文与前沿科学研究院）；Department of Physics, and Collaborative Innovation Center for Quantum Effects and Applications, Hunan Normal University（湖南师范大学物理与信息科学学院）
A fast deep-learning approach to probing primordial black hole populations in gravitational wave events
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学学院）；Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University（重庆大学物理系强耦合物理重庆市重点实验室）；International Center for Theoretical Physics Asia-Pacific, Beijing/Hangzhou, China（亚太理论物理中心）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), UCAS（中国科学院大学太极引力波宇宙实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
