Cosmic star-formation decline, the first galaxies and early black holes from the energy cascade of dark matter and gas

Abstract Three puzzles in galaxy evolution follow from the energy cascade in haloes and galaxy centres: the steep decline of cosmic star formation since $z\simeq2$, the excess of UV-bright galaxies at $z>10$, and over-massive early black holes. Haloes of fixed mass collapse at a fixed density contrast until a crossover at $a_*\simeq0.5$--0.64, then grow denser. Gas instead radiates its random energy; if it keeps a fixed contrast, the cascade rate shared by all galaxy cores rises as $(1+z)^{5/2}$. Like haloes, galaxies have two levels: cores share a rate and boundaries a contrast, so the rate at the effective radius lies below the core rate by $F\propto M^{-2/3}$, about 1 in spheroids and $\sim10^2$ in low-mass discs. (i) \emph{Late decline.} Infalling gas reaches the galaxy only if the core radiates its heat fast enough. After $a_*$ this cooling fraction falls as $(1+z)^{5/4}$, steepening the local slope of the star-formation density from 1.5 to 2.7 with no added parameter. (ii) \emph{First galaxies.} Core densities at a given scale are the same in every host, so the threshold for feedback-free star formation is crossed in all haloes at once. A sharp onset at $z\simeq10.5$ fits the JWST densities and luminosity functions better than bursty or feedback-free alternatives ($\Delta{\rm AIC}\ge42$). (iii) \emph{Black holes.} Luminosity is limited by the pressure of the dense core gas, which rises with redshift, rather than by electron scattering. The resulting ceiling, $L/L_{\rm Edd}\propto(1+z)^2M_{\rm BH}^{-1/5}$, encloses all but 24 of $1.5\times10^5$ quasars\fix{ and the little red dots with revised masses}{}. Because the core sets the black hole, $M_{\rm BH}/\sigma^5$ stays constant, while dynamical masses at the effective radius of disc-dominated hosts lie a factor $F\simeq70$--90 below the core level, nearly cancelling the rise of the core rate, $(1+z)^{5/2}\simeq88$ at $z\simeq5$. This is why JADES black holes lie 1--2 dex above the local relation with stellar mass but near those with dispersion and dynamical mass. Against local disc hosts measured alike, the JADES hosts lie higher in $\sigma^3/R_e$ by $+1.18$ dex at fixed $\sigma$ and $+1.98$ dex at fixed dynamical mass, as predicted.