Can $\Lambda$CDM model reproduce MOND-like behavior?

Abstract

It is usually believed that MOND can describe the galactic rotational curves with only baryonic matter and without any dark matter very well, while the $\Lambda$CDM model is expected to have difficulty in reproducing MOND-like behavior. Here, we use EAGLE's data to learn whether the $\Lambda$CDM model can reproduce MOND-like behavior. EAGLE's simulation result clearly reproduces the MOND-like behavior for $a_b\gtrapprox 10^{-12}\text{m/s}^2$ at $z=0$, although the acceleration constant, $a_0$, is a little larger than the observational data indicate. We find that $a_0$ increases with the redshift in a way different from what Milgrom proposed ($a_0\propto H$). Therefore, while galaxy rotation curves can be fitted by MOND's empirical function in the $\Lambda$CDM model, there is no clear connection between $a_0$ and the Hubble constant. We also find that $a_0$ at $z\gtrapprox 1$ is well separated from $a_0$ at $z=0$. Once we have enough galaxies observed at high redshifts, we will be able to rule out the modified gravity model based on MOND-like empirical function with a z-independent $a_0$.