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&#39;&#39; to write a MOND-type relationship between the fluctuations in the density and the gravitational force, $\vg$. In linear Newtonian theory, $|\vg|$ 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 small to 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 CDM power-spectrum. MOND with the standard value $g_0=10^{-8} cm s^{-2}$, yields a high clustering amplitude that can match the observed galaxy distribution only with strong (anti-) biasing. A value of $g_0 \approx 10^{-9}cm s^{-2}$, however, gives results similar to Newtonian dynamics and can be consistent with the observed large scale structure.