Explaining the effects of dark matter using modified gravitational dynamics (MOND) has for decades been both an intriguing and controversial possibility. By insisting that the gravitational interaction that accounts for the Newtonian force also drives cosmic expansion, one may kinematically identify which cosmologies are compatible with MOND, without explicit reference to the underlying theory so long as the theory obeys Birkhoff’s law. We find that the critical acceleration $a_0$ must have a slight source-mass dependence ($a_0\sim M^{1/3}$) and that MOND cosmologies are naturally compatible with observed late-time expansion history. However, cosmologies that can produce enough density perturbations to account for structure formation are contrived and fine tuned. Even then, they may be marginally ruled out by evidence of early ($z\sim 20$) reionization.

• Received 16 October 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.131102