Modified Newtonian dynamics of large-scale structure

We examine the implications of modified Newtonian dynamics (MOND) on the large-scale structure in a Friedmann-Robertson-Walker universe. We employ a `Jeans swindle' to write a MOND-type relationship between the fluctuations in the density and the gravitational force, g . In linear Newtonian theory, | g | decreases with time and eventually becomes <g ₀ , the threshold below which MOND is dominant. If the Newtonian initial density field has a power-law power spectrum of index n <-1, then MOND-domination proceeds from the small to the large scale. At early times MOND tends to drive the density power spectrum towards k ^-1 , independent of its shape in the Newtonian regime. We use N -body simulations to solve the MOND equations of motion, starting from initial conditions with a cold dark matter (CDM) power spectrum. MOND with the standard value g ₀ =10^-8 cms^-2 yields a high clustering amplitude that can match the observed galaxy distribution only with strong (anti-) biasing. A value of g ₀ ~10^-9 cms^-2 , however, gives results similar to Newtonian dynamics and can be consistent with the observed large-scale structure.