Tell me, where are we going?

Abstract: Extracting cosmological information from observables is a daunting task. In particular, the peculiar velocity of the observer affects a large set of observables, including redshift, time intervals, angles, solid angles and specific intensities. In the first part of my talk, I will give an overview of what has led to a confident measurement of the observer’s peculiar velocity, when it really is an expectation, which can and should be tested. In a second part, I shall describe an alternative measurement of the observer’s peculiar velocity with quasar number counts, which gives a discrepant answer. I will provide a potential solution, with different crosschecks that can be performed. Finally, I will describe an application to time-delay cosmography with strongly lensed quasars and discuss optical evidence for a supermassive black hole binary, potentially observable with gravitational wave in the pulsar timing array band.