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 < g0 , 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 small to large scale. At early times MOND drives 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 CDM power-spectrum. MOND with the standard value g0 = 10 −8cm s−2, yields a high clustering amplitude that can match the observed galaxy distribution only with strong (anti-) biasing. A value of g0 ≈ 10−9cm s−2, however, gives results similar to Newtonian dynamics and can be consistent with the observed large scale structure.