Gravitational wave memory imprints on the CMB from populations of massive black hole mergers

Aims. Our aim is to showcase and characterise the rich phenomenology of temperature fluctuation patterns that are imprinted on the cosmic microwave background (CMB) by the gravitational wave memory (GWM) of massive black hole mergers. Methods. We analysed both individual binaries as well as populations of binaries, distributed in local cosmological boxes at a given redshift. Results. The magnitude of the temperature fluctuations scales primarily as a function of binary total mass and pattern angular scale, and accumulates as a random-walk process when populations of mergers are considered. Fluctuations of order ∼10−12 K are reached across scales of ∼1′ to ∼1° for realistic volumetric merger rates of 10−3 Mpc−3 Gyr−1, as is appropriate for massive galaxies at z = 1. We determined numerically that GWM temperature fluctuations result in a universal power spectrum with a scaling of P(k)∝k−2.7. Conclusions. While not detectable given the limitations of current all-sky CMB surveys, our work explicitly shows how every black hole merger in the Universe left us its unique faint signature.