Exploring the Gravitational Wave Background with Photometric Surveys

The first detection by the LIGO/Virgo collaboration in 2015 has been a fundamental step in the search for gravitational waves (GWs), since they can provide a wealth of information about the Universe. One of the main targets is the detection of a Stochastic Gravitational Wave Background (SGWB). It is originated by the superposition of signals coming from recent astrophysical sources like Black Holes or Neutron Stars mergers (astrophysical background), but possibly also created by some physical processes that occurred in the very early Universe (cosmological background). In this work we further explore the possibility of characterizing the SGWB with photometric surveys. In fact, such surveys could be able to detect the angular deflections induced by the SGWB on the apparent position of distant stars. The expected signal has been characterized in the literature in terms of angular correlation functions and power spectra, assuming that the distance to the stars is much greater than the GW wavelength. We compute the correlation functions and power spectra in the general case without this assumption, showing how the expected signal varies at different distances and for different GW frequencies. Therefore we can be predictive on which photometric survey is best suited to probe a specific GW frequency, depending on the number of sources observed and their distances from Earth. In particular, we discuss possible applications of our results to an analysis of data provided by the Gaia mission. Following a similar procedure, we also compute the cross-correlation between the GW-induced deflection signal and the redshift measured by Pulsar Timing Array (PTA). We show how photo- metric surveys can help to cross-check PTA measurements, which have recently claimed a detection of the SGWB at a frequency of 1/yr. Finally, we discuss how current and future photometric surveys can bridge the frequency gap between existing interferometric, PTA and CMB polarization measurements.