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Any successful alternative gravity theory that obviates the need for darkmatter must fit our cosmological observations. Measurements of microwavebackground polarization trace the large-scale baryon velocity field atrecombination and show very strong, $O(1)$, baryon acoustic oscillations.Measurements of the large-scale structure of galaxies at low redshift show muchweaker features in the spectrum. If the alternative gravity theory's dynamicalequations for the growth rate of structure are linear, then the density fieldgrowth can be described by a Green's function: $\delta(\vec x,t) = \delta(\vecx,t')G(x,t,t')$. We show that the Green function, $G(x,t,t')$, must havedramatic features that erase the initial baryon oscillations. This implies anacceleration law that changes sign on the $\sim 150$ Mpc scale. On the otherhand, if the alternative gravity theory has a large nonlinear term that couplesmodes on different scales, then the theory would predict large-scalenon-Gaussian features in large-scale structure. These are not seen in thedistribution of galaxies nor in the distribution of quasars. No proposedalternative gravity theory for dark matter seems to satisfy these constraints.

What is the price of abandoning dark matter? Cosmological constraints on alternative gravity theories