Characterizing gravitational wave detector networks: from A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mrow/><mml:mo>♯</mml:mo></mml:msup></mml:mrow></mml:math>to cosmic explorer

Abstract Gravitational-wave observations by the laser interferometer gravitational-wave observatory (LIGO) and Virgo have provided us a new tool to explore the Universe on all scales from nuclear physics to the cosmos and have the massive potential to further impact fundamental physics, astrophysics, and cosmology for decades to come. In this paper we have studied the science capabilities of a network of LIGO detectors when they reach their best possible sensitivity, called A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:msup><mml:mrow/><mml:mo>♯</mml:mo></mml:msup></mml:mrow></mml:math> , given the infrastructure in which they exist and a new generation of observatories that are factor of 10 to 100 times more sensitive (depending on the frequency), in particular a pair of L-shaped cosmic explorer (CE) observatories (one 40 km and one 20 km arm length) in the US and the triangular Einstein telescope with 10 km arms in Europe. We use a set of science metrics derived from the top priorities of several funding agencies to characterize the science capabilities of different networks. The presence of one or two A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:msup><mml:mrow/><mml:mo>♯</mml:mo></mml:msup></mml:mrow></mml:math> observatories in a network containing two or one next generation observatories, respectively, will provide good localization capabilities for facilitating multimessenger astronomy (MMA) and precision measurement of the Hubble parameter. Two CE observatories are indispensable for achieving precise localization of binary neutron star events, facilitating detection of electromagnetic counterparts and transforming MMA. Their combined operation is even more important in the detection and localization of high-redshift sources, such as binary neutron stars, beyond the star-formation peak, and primordial black hole mergers, which may occur roughly 100 million years after the Big Bang. The addition of the Einstein Telescope to a network of two CE observatories is critical for accomplishing all the identified science metrics including the nuclear equation of state, cosmological parameters, the growth of black holes through cosmic history, but also make new discoveries such as the presence of dark matter within or around neutron stars and black holes, continuous gravitational waves from rotating neutron stars, transient signals from supernovae, and the production of stellar-mass black holes in the early Universe. For most metrics the triple network of next generation terrestrial observatories are a factor 100 better than what can be accomplished by a network of three A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"><mml:mrow><mml:msup><mml:mrow/><mml:mo>♯</mml:mo></mml:msup></mml:mrow></mml:math> observatories.