We present the Iκ∊α model of galaxy formation, in which a galaxy's star formation rate is set by the balance between energy injected by feedback from massive stars and energy lost by the deepening of the potential of its host dark matter halo due to cosmological accretion. Such a balance is secularly stable provided that the star formation rate increases with the pressure in the star forming gas. The Iκ∊α model has four parameters that together control the feedback from star formation and the cosmological accretion rate onto a halo. Iκ∊α reproduces accurately the star formation rate as a function of halo mass and redshift in the EAGLE hydrodynamical simulation, even when all four parameters are held constant. It predicts the emergence of a star forming main sequence along which the specific star formation rate depends weakly on stellar mass with an amplitude that increases rapidly with redshift. We briefly discuss the emerging mass-metallicity relation, the evolution of the galaxy stellar mass function, and an extension of the model that includes feedback from active galactic nuclei (AGN). These self-regulation results are independent of the star formation law and the galaxy's gas content. Instead, star forming galaxies are shaped by the balance between stellar feedback and cosmological accretion, with accurately accounting for energy losses associated with feedback a crucial ingredient.