A Baseline model for Modified Newtonian Mechanics I: The Early Universe

Abstract

In modelling galaxy structure formation, neither Cold Dark Matter (CDM) nor canonical Modified Newtonian Dynamics (MOND) (Milgrom [1]) can easily accommodate the appearance of massive galaxies at early times [2]. As a baseline We propose a new single-metric universe which fits within the MOND frame in that there is no new matter in the stress-momentum tensor, to reset the cosmological time scale at which cold dark matter may have a role. The metric interpolates smoothly between the Schwarzschild metric of central masses at small scales and the Friedmann Lemaitre Robertson Walker (FLRW) metric of an expanding universe at large scales without discrete boundaries. Within the framework of interpolations proposed by Baker [3] it is unique where the Newtonian free fall velcoity plays the role of peculiar velocity in an expanding background. Our model looks old-fashioned in that it superficially resembles a vacuole model wtih all the artificialities that this implies, but whereas traditional vacuole models do their best to hide boundary effects, all the new physics in our model arises from the smooth early-universe transitioning of one regime to the other. This metric inherits from MOND the existence of an acceleration scale a0 below which Newtonian gravity is modified. This is no longer the constant of traditional MOND [1] but depends on the background density, most simply as a0 ~1/2 H^2 r, where r is the relevant distance scalce. As a result, there are additional strong forces at high red-shifts sufficient at galactic scales, we believe, to trigger galaxy formation with needing to invoke the fimailar targets of LCDM searches. We have largely restricted ourselves here to galaxy and galaxy-cluster distances. We are agnostic as to whether we need further ingredients at large scales but, if we do, the metric provides a solid baseline.