No Run Gravity

Abstract

Considering the dark energy/gravity landscape if next generation surveys of galaxies, cosmic microwave background radiation, and gravitational waves do not find clear modification of gravity, we develop No Run Gravity as a counterexample to the conclusion that this would imply general relativity with an expansion history described by an equation of state $w(z)$. No Run Gravity is a cubic Horndeski theory with a constant Planck mass, no gravitational slip, and no modification of gravitational waves, but a rich phenomenology beyond $w(z)$. We calculate the evolution of gravitational strength, sound speed, and cosmic growth within the theory and project sensitivities for upcoming DESI redshift space distortion data.