Vacuum polarization instead of "dark matter" in a galaxy

Abstract

We considered a vacuum polarization inside a galaxy in the eikonal approximation and found that two possible types of polarization exist. The first type is described by the equation of state $p=\rho/3$, similar to radiation. Using the conformally-unimodular metric allows constructing a nonsingular solution for this vacuum ``substance'', if a compact astrophysical object exists in the galaxy's center. As a result, a ``dark'' galactical halo appears that increases the rotation velocity of a test particle as a function of the distance from a galactic center. The second type of vacuum polarization has a more complicated equation of state. As a static physical effect, it produces renormalization of the gravitational constant, thus, causing no static halo. However, a nonstationary polarization of the second type, resulting from an exponential increase (or decrease) of the galactic nuclei mass with time in some hypothetical time-dependent process, produces a gravitational potential looking like a dark matter halo.