  Any successful alternative gravity theory that obviates the need for dark
matter must fit our cosmological observations. Measurements of microwave
background polarization trace the large-scale baryon velocity field at
recombination and show very strong, $O(1)$, baryon acoustic oscillations.
Measurements of the large-scale structure of galaxies at low redshift show much
weaker features in the spectrum. If the alternative gravity theory's dynamical
equations for the growth rate of structure are linear, then the density field
growth can be described by a Green's function: $\delta(\vec x,t) = \delta(\vec
x,t')G(x,t,t')$. We show that the Green function, $G(x,t,t')$, must have
dramatic features that erase the initial baryon oscillations. This implies an
acceleration law that changes sign on the $\sim 150$ Mpc scale. On the other
hand, if the alternative gravity theory has a large nonlinear term that couples
modes on different scales, then the theory would predict large-scale
non-Gaussian features in large-scale structure. These are not seen in the
distribution of galaxies nor in the distribution of quasars. No proposed
alternative gravity theory for dark matter seems to satisfy these constraints.
