Large black-hole scalar charges induced by cosmology in Horndeski theories

The regularity of black-hole solutions, embedded in an expanding universe, is studied in a subclass of Horndeski theories, namely the sum of the simplest quadratic, cubic, and quintic actions. We find that in the presence of a time derivative of the scalar field, driven by the cosmological expansion, this regularity generically imposes large scalar charges for black holes, even when assuming strictly no direct coupling of matter to the scalar field. Such charges cause a significant accretion of the scalar field by the black holes, driving its local time derivative to a small value. This phenomenon, together with the Vainshtein screening typical of these theories, strongly suppresses observable scalar effects. We show that this full class of models is consistent with LIGO/Virgo detections of gravitational waves, but that the LISA mission should be able to constrain the coefficient of the quintic term at the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>30</a:mn></a:mrow></a:msup></a:math> level in a self-acceleration scenario, an improvement by 16 orders of magnitude with respect to what is imposed by the speed of gravitational waves.