A stochastic gravitational wave background causes the apparent positions of distant sources to fluctuate, with angular deflections of order the characteristic strain amplitude of the gravitational waves. These fluctuations may be detectable with high precision astrometry, as first suggested by Braginsky et al. in 1990. Several researchers have made order of magnitude estimates of the upper limits obtainable on the gravitational wave spectrum Ω_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future space-based optical interferometry missions GAIA and SIM, and for VLBI interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6 quasars over a time of T ~ 1 yr with an angular accuracy of Δθ~ 10 μas would yield a sensitivity level of Ω_gw ~ (Δθ)^2/(N T^2 H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we take a first step toward firming up these estimates by computing in detail the statistical properties of the angular deflections caused by a stochastic background. We compute analytically the two point correlation function of the deflections on the sphere, and the spectrum as a function of frequency and angular scale. The fluctuations are concentrated at low frequencies (for a scale invariant stochastic background), and at large angular scales, starting with the quadrupole. The magnetic-type and electric-type pieces of the fluctuations have equal amounts of power.
Astrometric constraints on stochastic gravitational wave background with neural networks
Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Observatoire astronomique de Strasbourg, CNRS, Université de Strasbourg（斯特拉斯堡天文台）；Department of Physics and Astrophysics, Nagoya University（名古屋大学物理学与天体物理学系）
First astrometric constraints on parity-violation in the gravitational wave background
Observatoire astronomique de Strasbourg, CNRS, Université de Strasbourg（斯特拉斯堡天文台）；Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；Department of Physics, Nagoya University（名古屋大学物理学系）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo（东京大学宇宙物质前沿研究中心）；Center for Particle Cosmology, Department of Physics and Astronomy, University of Pennsylvania（宾夕法尼亚大学粒子宇宙学中心）
Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
Physics Department, Swansea University（斯旺西大学物理系）；Dipartimento di Fisica e Astronomia, Università di Bologna, INFN, Sezione di Bologna, I.S. FLAG（博洛尼亚大学物理与天文学系，意大利国家核物理研究所博洛尼部分所，FLAG研究所）
COSMOGRAIL: the COSmological MOnitoring of GRAvItational Lenses X. Modeling based on high-precision astrometry of a sample of 25 lensed quasars: consequences for ellipticity, shear, and astrometric anomalies
