Modified Newtonian dynamics of large-scale structure

Abstract

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 go = 10 - 8 cm s - 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 cm s - 2 , however, gives results similar to Newtonian dynamics and can be consistent with the observed large-scale structure.