10 pages, 4 figures, Based on a talk at `BonnGravity2019 -- The functioning of galaxies: challenges for Newtonian and Milgromian dynamics', Bonn, September 2019
I limelight and review a potentially crucial aspect of MOND: The near equality of the MOND acceleration constant, $a_0$ -- as deduced from local, galactic phenomena -- and cosmological parameters. To wit, $a_0\sim c H_0\sim c^2Λ^{1/2}\sim c^2/\ell_U$, where $H_0$ is the present value of the Hubble-Lemaître constant, $Λ$ is the `cosmological constant', and $\ell_U$ is a cosmological characteristic length; e.g., the Hubble distance, or the de Sitter radius associated with $Λ$. In itself, this near equality has some important phenomenological consequences, such as the impossibility of black holes, and of cosmological strong lensing, in the MOND regime. More importantly perhaps, this `coincidence' may be a pointer to the `FUNDAMOND' -- the more basic theory underlying MOND phenomenology. The manners in which such a relation emerges in existing, underlying scheme of MOND are also reviewed, interlaced with examples of similar relations in other physical systems, between apparently-fundamental velocity, length, and acceleration constants. Such analogies may point the way to explanation of the MOND `coincidence'.
The statistics of high speed satellite galaxies, as reported in the recent literature, can be a powerful diagnosis of the depth of the potential well of the host halo, and hence discriminate between competing gravitational theories. Naively one expects that high speed satellites are more common in Modified Newtonian Dynamics (MOND) than in cold dark matter (CDM) since an isolated MONDian system has an infinite potential well, while CDM halos have finite potential wells. In this \textit{Letter} we report on an initial test of this hypothesis in the context of the first generation of cosmologica…
McGaugh et al. (2016) have used their extensive SPARC sample to update the well-known mass-discrepancy-acceleration relation (MDAR), which is one of the major predicted "MOND laws". This is not a newly discovered relation. Rather, it improves on the many previous studies of it, with more and better data. Like its precedents, it bears crucial ramifications for the observed dynamical anomalies in disc galaxies, and, in particular, on their resolution by the MOND paradigm. Their result, indeed, constitute a triumph for MOND. However, unlike previous analyses of the MDAR, McGaugh et al. have chose…
A general account of MOND theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration -- below an acceleration constant a0 -- where dynamics become scale invariant. I list some of the salient predictions of these tenets. The special role of a0 and its significance are then discussed. In particular, I stress its coincidence with cosmologically relevant accelerations. The deep-MOND limit and the consequences of its scale invariance are considered in some detail. General aspects of MOND theories are then described, after wh…
Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate to explain the observed discrepancy between the dynamics and the distribution of the visible matter in the Universe. The Modified Newtonian Dynamics (MOND) proposal aims at solving the problem by postulating that Newton's second law of motion is modified for accelerations smaller than ~10^{-10}m/s^2. This simple amendment, has had tremendous success in explaining galactic rotation curves. However, be…
The debate in cosmology concerning LambdaCDM and MOND depends crucially on their respective ability of modelling across scales, and dealing with some of the specific problems that arise along the way. The main upshot of this article is to present three main problems facing multi-scale modelling in contemporary cosmology. The LambdaCDM model, which is the standard and by far most successful current cosmological model, faces what I call the downscaling problem when it comes to explain some recalcitrant evidence at the scale of individual galaxies, such as the mass-discrepancy acceleration relati…
A novel interpretation of MOND is presented. For galactic data, in addition to Newtonian acceleration, there is an attractive acceleration peaking at Milgrom's parameter a_0. The peak lies within experimental error where a_0 = cH_0/2π; H_0 is the present-time value of the Hubble constant and c the velocity of light. The physical interpretation of this relation and its connection to Dark Energy are discussed.
Galactic systems, and the Universe at large, exhibit large dynamical anomalies: The observed matter in them falls very short of providing enough gravity to account for their dynamics. The mainstream response to this conundrum is to invoke large quantities of `dark matter' -- which purportedly supplies the needed extra gravity -- and also of `dark energy', to account for further anomalies in cosmology, such as the observed, accelerated expansion. The MOND paradigm offers a different solution: a breakdown of standard dynamics (gravity and/or inertia) in the limit of low accelerations -- below so…
I describe a heuristic model where MOND dynamics emerge in a universe viewed as a nearly spherical brane embedded in a higher-dimensional flat space. The brane, described by $ξ(Ω)$, is of density $σ$ ($ξ$ and $Ω$ are the radial and angular coordinates in the embedding space). The brane and matter -- confined to the brane and of density $ρ(Ω)\llσ$ -- are coupled to a potential $\varepsilon(ξ)$. I restrict myself to shallow perturbations, $ξ(Ω)=\ell_0+ζ(Ω)$, $|ζ|\ll\ell_0$. A balanced brane implies $\hat a_0\equiv\varepsilon'(\ell_0)\sim T/σ\ell_0$, $T$ is the brane tension, yielding for the vel…
MOND has limelighted the fact that Newtonian dynamics (ND) and general relativity (GR) have not been verified at accelerations below MOND's $a_0$. In particular, we do not know that all the principles underlying ND or GR apply below $a_0$. I discuss possible breakdown of general covariance (GC) in this limit. This resonates well with MOND, which hinges on accelerations. Relaxing GC affords more freedom in constructing MOND theories. I exemplify this with a simplified theory whose gravitational Lagrangian is $\mathcal{L}_M\propto \ell_M^{-2}\mathcal{F}(\ell_M^{2}\mathcal{R})$, where $\mathcal{R…
Genzel et al. have recently published the rotation curves of six high-redshift disc galaxies ($z\sim 0.9-2.4$), which they find to be `baryon dominated' within the studies radii. While not up to the standard afforded by data available for analysis in the nearby Universe, these data are valuable in constraining cosmological evolution of either DM scenarios, or -- as I discuss here -- $z$-dependence of MOND. Indeed, these results, if taken at face value, teach us useful lessons in connection with MOND. a. The dynamical accelerations at the half-light radii, found by Genzel et al., are rather hig…
This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss's law for gravity as well as other fundamental classical laws are extended to a $D$-dimensional metric space, where $D$ can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical structures without requirin…
In this work we study the cosmological simulations as a tool to understand the formation of large-scale structure of the universe, for this, we show the equivalence of Newtonian cosmology with Poisson gauge and we study the solution of the Einstein's field equations for this gauge. The simulations are essential for taking account the results of the cosmological model, allowing to compare the results with observational data. The N-bodies simulations have been used from systems of few bodies to the evolution and formation of nonlinear large scale structure as filaments and galactic halos.
