arXiv subjects

Mordehai Milgrom

Publications and source records attributed to Mordehai Milgrom.

At least 19 recordsLinked to original sources

arXiv2026

Bimetric MOND as a framework for variable-$G$ theories -- local systems and cosmology

Bimetric MOND (BIMOND) is used as a platform for variable-$G$ theories that have MOND-specific idiosyncrasies. E.g., MOND premises dictate return to standard dynamics in the high-acceleration limit, predicting the standard value of $G$ for high-acceleration systems. This automatically ensures compliance of such theories with all the constraints on inconstancy of $G$ that emerge from the study of high-acceleration systems: geophysics, solar system, pulsars, supernovae, stellar evolution, emission of gravitational waves, etc. In MOND, constraints deduced from such phenomena have no bearing on possible $G$ variability in cosmology. My guiding motivation is to see if such theories may account for some roles of dark matter in cosmology; e.g., in accounting for the expansion history of the Universe in the matter-dominated era, by having a $G_e\approx 2πG$ govern the later stages of the expansion, instead of invoking matter density $\approx 2π\times$ baryon density. Without adding degrees of freedom, or new dimensionful constants, BIMOND can be extended to a class of theories that entail what is best described as phenomenon-dependence of Newton's constant, $G$. I cannot yet present a consistent model that complies with all the observations in cosmology, including the expansion history, with all its details. Instead, I describe some examples of theories in the class that predict different values of $G_e$ in different circumstances, including one where $G$ takes its standard value for all subcosmological systems -- even if they are deep in the MOND regime. I also discuss scenarios in which $G_e\approx G$ in the early Universe, as required by constraints from big-bang nucleosynthesis, but with $G_e> G$ setting in at later times, where it can affect the expansion history during the matter-dominated era.

astro-ph.CO↗

arXiv2025

Broader view of bimetric MOND

All existing treatments of bimetric MOND (BIMOND) -- a class of relativistic versions of MOND -- have dealt with a rather restricted sub-class: The Lagrangian of the interaction between the gravitational degrees of freedom -- the two metrics -- is a function of a certain {\it single} scalar argument built from the difference in connections of the two metrics. I show that the scope of BIMOND is much richer: The two metrics can couple through several scalars to give theories that all have a "good" nonrelativistic (NR) limit -- one that accounts correctly, a-la MOND, for the dynamics of galactic systems, {\it including gravitational lensing}. This extended-BIMOND framework exhibits a qualitative departure from the way we think of MOND at present, as encapsulated, in all its aspects, by one "interpolating function" of one acceleration variable. After deriving the general field equations, I pinpoint the subclass of theories that satisfy the pivotal requirement of a good NR limit. These involve three independent, quadratic scalar variables. In the NR limit these scalars all reduce to the same acceleration scalar, and the NR theory then does hinge on one function of a {\it a single} acceleration variable -- representing the NR MOND "interpolating function", whose form is largely dictated by the observed NR galactic dynamics. However, these scalars behave differently, in different relativistic contexts. So, the full richness of the multi-variable Lagrangian, as it enters cosmology, for example, is hardly informed by what we learn from observations of galactic dynamics. In this paper, I present the formalism, with some generic examples. I also consider some cosmological solutions where the two metrics are small departures from one Friedman-Lemaitre-Robertson-Walker metric. This may offer a framework for describing cosmology within the extended BIMOND.

gr-qc↗

arXiv2025

The deep-MOND limit -- a study in Primary vs secondary predictions

In default of a fundamental MOND theory -- a FUNDAMOND -- I advocate that, alongside searching for one, we should try to identify predictions that follow from wide classes of MOND theories, if not necessarily from all. In particular, predictions that follow from only the basic tenets of MOND -- ``primary predictions'' -- are shared by all MOND theories, and are especially valuable. Such predictions permit us to test the MOND paradigm itself, or at least large parts of it, without yet having a FUNDAMOND. Concentrating on the deep-MOND limit, I discuss examples of either type of predictions. For some examples of primary predictions, I demonstrate how they follow from the basic tenets (which I first formulate). I emphasize that even predictions that pertain to the deep-MOND limit - namely, those that concern gravitating systems that have low accelerations everywhere -- require the full set of MOND tenets, including the existence of a Newtonian limit close to the deep-MOND regime. This is because Newtonian dynamics is a unique theory that all MOND theories must tend to in the limit of high accelerations, and it strongly constrains aspects of the deep-MOND regime, if the transition between the limits is fast enough, which is one of the MOND tenets.

gr-qc↗

arXiv2025

Is MOND necessarily nonlinear?

The iconic, deep-MOND-limit (DML) relation between acceleration and mass, $a\sim (M\mathcal{A}_0)^{1/2}/r$, implies that, in MOND, accelerations cannot be linear in the mass distribution ($\mathcal{A}_0\equiv Ga_0$ is the DML constant, and $a_0$ the MOND acceleration). This leads to important idiosyncracies of MOND, such as a breakdown of the strong equivalence principle, and the resulting ``external-field effect''. I show that the DML axioms are, in themselves, consistent with a, possibly unique, nonrelativistic, action-based, linear formulation of the DML. This model suffers from important drawbacks, which may make it unacceptable as a basis for a full-fledged MOND theory. The model is unique among MOND theories propounded to date not only in being linear -- hence not exhibiting an external-field effect, for example -- but in constituting a modification of both Newtonian inertia and Newtonian gravity. This linear and time-local model inspires and begets several, one-parameter families of models. One family employs nonlinear, time-nonlocal kinetic terms, but still linear gravitational-field equations. Other families generalize the DMLs of AQUAL and QUMOND, modifying gravity as well as inertia. All families employ fractional time derivatives and possibly fractional Laplacians. At present, I cannot base some acceptable MOND theory on these models -- for example, I cannot offer a sensible umbrella theory that interpolates between these DML models and Newtonian dynamics. They are, however, quite useful in elucidating various matter-of-principle aspects of MOND; e.g., they help to understand which predictions follow from only the basic tenets of MOND -- so-called primary predictions -- and which are secondary, i.e., theory dependent. The models may also show the way to a wider class of MOND theories. (Abridged.)

gr-qc↗

arXiv2024

Central-surface-densities correlation in general MOND theories

It is shown that the foundational axioms of MOND alone predict a strong correlation between a bulk measure of the baryonic surface density, $Σ_B$, and the corresponding dynamical one, $Σ_D$, of an isolated object, such as a galaxy. The correlation is encapsulated by its high- and low-$Σ_B$ behaviors. For $Σ_B\ggΣ_M\equiv a_0/2πG$ ($Σ_M$ is the critical MOND surface density) one has $Σ_D\approxΣ_B$. Their difference -- which would be interpreted as the contribution of dark matter -- is $Σ_P=Σ_D-Σ_B\simΣ_M\llΣ_B$. In the deep-MOND limit, $Σ_B\llΣ_M$, one has $Σ_D\sim (Σ_MΣ_B)^{1/2}$. This is a primary prediction of MOND, shared by all theories that embody its basic tenets. Sharper correlations, even strict algebraic relations, $Σ_D(Σ_B)$, are predicted in specific MOND theories, for specific classes of mass distribution -- e.g., pure discs, or spherical systems -- and for specific definitions of the surface densities. I proceed to discuss such tighter correlations for the central surface densities of axisymmetric galactic systems, $Σ^0_B$ and $Σ^0_D$. Past work has demonstrated such relations for pure discs in the AQUAL and QUMOND theories. Here I consider them in broader classes of MOND theories. For most observed systems, $Σ^0_D$ can not be determined directly at present, but, in many cases, a good proxy for it is the acceleration integral $\mathcal{G}\equiv\int_0^\infty g_r d\ln~r$, where $g_r$ is the radial acceleration along a reflection-symmetry plane of a system, such as a disc galaxy. $\mathcal{G}$ can be determined directly from the rotation curve. I discuss the extent to which $\mathcal{G}$ is a good proxy for $Σ^0_D$, and how the relation between them depends on system geometry, from pure discs, through disc-plus-bulge ones, to quasi-spherical systems.

astro-ph.GA↗

arXiv2023

MOND as manifestation of modified inertia

Practically all the full-fledged MOND theories propounded to date are of the modified-gravity (MG) type: they modify only the Newtonian, Poisson action of the gravitational potential, or the general-relativistic Einstein-Hilbert action, leaving other terms (inertia) intact. Here, I discuss the interpretation of MOND as modified inertia (MI). My main aim is threefold: (a) to advocate exploring MOND theories beyond MG, and appreciating their idiosyncrasies, (b) to highlight the fact that secondary predictions of such theories can differ materially from those of MG theories, (c) to demonstrate some of this with specific MI models. I discuss some definitions and generalities concerning MI. I then present instances of MI in physics, and the lessons we can learn from them for MOND. I then concentrate on a specific class of nonrelativistic, MOND, MI models, and contrast their predictions with those of the two workhorse, MG theories -- AQUAL and QUMOND. The MI models predict possibly a stronger external-field effect -- e.g. on low acceleration systems in the solar neighborhood -- such as very wide binary stars -- and on vertical motions in disc galaxies. More generally, the workings of the effect are rather different, and depend in different ways on dimensionless characteristics of the system, such as frequency ratios of the external and internal fields, eccentricity of trajectories, etc. These models predict a {\it much} weaker effect of the Galactic field in the inner Solar System than is predicted by AQUAL/QUMOND. I also show how noncircular motions -- such as those perpendicular to the disc -- modify the standard, algebraic mass-discrepancy-acceleration relation (aka RAR) that is predicted by MI for exactly circular orbits. These differences, and more that are discussed, can potentially offer ways to distinguish between theories.

astro-ph.GA↗

arXiv2023

Generalizations of Quasilinear MOND (QUMOND)

I present a class of theories that generalize quasilinear MOND (QUMOND). Like QUMOND, these GQUMOND theories require solving only the linear Poisson equation (twice). Unlike QUMOND, their Lagrangian depends on higher derivatives of the Newtonian potential. They thus dictate different "phantom" densities as virtual sources in the Poisson equation for the MOND potential. These theories might open new avenues to more fundamental theories, and have much heuristic value. I use them to demonstrate that even within limited classes of modified-gravity formulations of MOND, theories can differ substantially on lower-tier MOND predictions. Such GQUMOND theories force, generically, the introduction of dimensioned constants other than the MOND acceleration, $a_0$, such as a length, a frequency, etc. As a result, some of these theories reduce to QUMOND itself only, e.g., on length scales (or, in other versions, dynamical times) larger than some critical value. But in smaller systems (or, alternatively, in ones with shorter dynamical times), MOND effects are screened, even if their internal accelerations are smaller than $a_0$. In such theories it is possible that MOND (expressed as QUMOND) applies on galactic scales, but its departures from Newtonian dynamics are substantially suppressed in some subgalactic systems -- such as binary stars, and open, or globular star clusters. The same holds for the effect of the galactic field on dynamics in the inner solar system, which can be greatly suppressed compared with what QUMOND predicts. Tidal effects of a galaxy on smaller subsystems are the same as in QUMOND, for the examples I consider. I also describe briefly versions that do not involve dimensioned constants other than $a_0$, and yet differ from QUMOND in important ways.

astro-ph.GA↗

arXiv2023

Tripotential MOND theories

I present a new class of nonrelativistic, modified-gravity MOND theories. The three gravitational degrees of freedom of these ``TRIMOND'' theories are the MOND potential and two auxiliary potentials, one of which emerges as the Newtonian potential. Their Lagrangians involve a function of three acceleration variables -- the gradients of the potentials. So, the transition from the Newtonian to the MOND regime is rather richer than in the aquadratic-Lagrangian theory (AQUAL) and the quasilinear MOND theory (QUMOND), which are special cases of TRIMOND, each defined by a Lagrangian function of a single variable. In particular, unlike AQUAL and QUMOND whose deep-MOND limit (DML) is fully dictated by the required scale invariance, here, the scale-invariant DML still requires specifying a function of two variables. For one-dimensional (e.g., spherical) mass distributions, in all TRIMOND theories the MOND acceleration is a (theory specific, but system independent) function of the Newtonian acceleration; their variety appears in nonsymmetric situations. Also, they all make the salient, primary MOND predictions. For example, they predict the same DML virial relation as AQUAL and QUMOND, and thus the same DML $M-σ$ relation, and the same DML two-body force. Yet they can differ materially on secondary predictions. Such TRIMOND theories may be the nonrelativistic limits of scalar-bimetric relativistic formulations of MOND, such as BIMOND with an added scalar.

gr-qc↗

arXiv2022

Models of modified-inertia formulation of MOND

Models of "modified-inertia" formulation of MOND are described and applied to nonrelativistic many-body systems. They involve time-nonlocal equations of motion. Momentum, angular momentum, and energy are (nonlocally) defined, whose total values are conserved for isolated systems. The models make all the salient MOND predictions. Yet, they differ from existing "modified-gravity" formulations in some second-tier predictions. The models describe correctly the motion of a composite body in a low-acceleration field even when the internal accelerations of its constituents are high. They exhibit a MOND external field effect (EFE) that shows some important differences from what we have come to expect from modified-gravity versions: In one, simple example of the models, what determines the EFE, in the case of a dominant external field, is $μ(θ\langle a_{ex}\rangle/a_0)$, where $μ(x)$ is the MOND `interpolating function' that describes rotation curves, compared with $μ(a_{ex}/a_0)$ for presently-known modified-gravity formulations. The two main differences are that while $a_{ex}$ is the momentary value of the external acceleration, $\langle a_{ex}\rangle$ is a certain time average of it, and that $θ>1$ is an extra factor that depends on the frequency ratio of the external- and internal-field variations. Only ratios of frequencies enter, and $a_0$ remains the only new dimensioned constant. For a system on a circular orbit in a galaxy (such as the vertical dynamics in a disc galaxy), the first difference disappears, since $\langle a_{ex}\rangle=a_{ex}$. But the $θ$ factor can appreciably enhance the EFE in quenching MOND effects, over what is deduced in modified gravity. Some exact solutions are also described, such as for rotation curves, for an harmonic force, and the general, two-body problem, which in the deep-MOND regime reduces to a single-body problem.

astro-ph.GA↗

arXiv2022

Numerical Solutions of the External Field Effect on the Radial Acceleration in Disk Galaxies

In MOND (modified Newtonian dynamics)-based theories the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an "external field effect (EFE)". The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies the EFE can induce warps and modify the rotational speeds. Due to the non-linearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two non-relativistic Lagrangian theories of MOND: the `Aquadratic-Lagrangian' theory (AQUAL) and `Quasilinear MOND' (QUMOND). For AQUAL we consider only the axisymmetric field configurations with the external field along the disk axis, or a spherical galaxy with test-particle orbits inclined to the external field. For the more manageable QUMOND we calculate also the three-dimensional field configurations, with the external field inclined to the disk axis. We investigate particularly to what degree an external field modifies the quasi-flat part of rotation curves. While our QUMOND results agree well with published numerical results in QUMOND, we find that AQUAL predicts weaker EFE than published AQUAL results. However, AQUAL still predicts stronger EFE than QUMOND, which demonstrates current theoretical uncertainties. We also illustrate how the MOND prediction on the rising part of the rotation curve, in the inner parts, depends largely on disk thickness but only weakly on a plausible external field for a fixed galaxy model. Finally, we summarize our results for the outer parts as an improved, approximate analytic expression.

astro-ph.GA↗

arXiv2021

MOND fiducial specific angular momentum of disc galaxies

It is pointed out that MOND defines a fiducial specific angular momentum (SAM) for a galaxy of total (baryonic) mass $\mathcal{M}$: $j_M(\mathcal{M})\equiv\mathcal{M}^{3/4}(G^3/a_0)^{1/4}\approx 383(\mathcal{M}/10^{10}M_\odot)^{3/4}{\rm kpc~km/s}$. It plays important roles in disc-galaxy dynamics and evolution: It underlies scaling relations in virialized galaxies that involve their angular-momentum. I show that the disc SAM should be $j_D\approx[\langle r\rangle/r_M(\mathcal{M})]j_M(\mathcal{M})=[Σ_M/\langle Σ\rangle]^{1/2}j_M(\mathcal{M})$, with $\langle r\rangle$ the mean radius of the disc, $\langle Σ\rangle=\mathcal{M}/2π\langle r\rangle^2$ some mean surface density of the galaxy, $r_M=(\mathcal{M} G/a_0)^{1/2}$ is the MOND radius of the galaxy, and $Σ_M=a_0/2πG$ is the (universal) MOND surface density. So, e.g., for a fixed $\langle Σ\rangle$, $j_D\propto \mathcal{M}^{3/4}$, while for a fixed $\langle r\rangle$, $j_D\propto \mathcal{M}^{1/4}$. Furthermore, $j_M(\mathcal{M})$ is a reference predictor of the type of galaxy a protogalaxy will settle into, if it evolves in isolation: A protogalaxy of mass $\mathcal{M}$, and SAM $j\gg j_M(\mathcal{M})$ should settle into a low-surface-density disc -- with mean acceleration $\langle a\rangle/a_0\approx j_M/j\ll 1$. While a protogalaxy with $j\lesssim j_M(\mathcal{M})$ should end up with a disc of mass $\mathcal{M}_D\approx j\mathcal{M}/j_M(\mathcal{M})$, having a SAM $j_D\approx j_M(\mathcal{M})$, which is tantamount to $\langle a\rangle\approx a_0$ (i.e., at the `Freeman limit'); it should also develop a low-SAM bulge, taking up the rest of the mass $\mathcal{M}_B\approx\mathcal{M}-\mathcal{M}_D$.

astro-ph.GA↗

arXiv2021

Deep-MOND polytropes

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}ρ^γ$. As self-consistent structures, such systems can serve as heuristic models for DML, astronomical systems, such as dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, and diffuse galaxy groups. They can also serve as testing ground for various theoretical MOND inferences. In dimensionless form, the equation satisfied by the radial density profile $ζ(y)$ is (for $γ\not=1$) $[\int_0^y ζ\bar y^2 d\bar y]^{1/2}=-yd(ζ^{γ-1})/dy$. Or, $θ^n(y)=y^{-2}[(yθ')^2]'$, where $θ=ζ^{γ-1}$, and $n\equiv (γ-1)^{-1}$. I discuss properties of the solutions, contrasting them with those of their Newtonian analogues -- the Lane-Emden polytropes. Due to the stronger MOND gravity, all DML polytropes have a finite mass, and for $n<\infty$ ($γ>1$) all have a finite radius. (Lane-Emden spheres have a finite mass only for $n\le 5$.) I use the DML polytropes to study DML scaling relations. For example, they satisfy a universal relation (for all $\mathcal{K}$ and $γ$) between the total mass, $M$, and the mass-average velocity dispersion $σ$: $MGa_0=(9/4)σ^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\barσ$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\barσ,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $γ>1$), and all satisfy the above universal $M-σ$ relation. This more extended class of models exhibits the central-surface-densities relation: a tight relation between the baryonic and the dynamical central surface densities predicted by MOND.

astro-ph.GA↗

arXiv2020

MOND vs. dark matter in light of historical parallels

MOND is a paradigm that contends to account for the mass discrepancies in the Universe without invoking `dark' components, such as `dark matter' and `dark energy'. It does so by supplanting Newtonian dynamics and General Relativity, departing from them at very low accelerations. Having in mind readers who are historians and philosophers of science, as well as physicists and astronomers, I describe in this review the main aspects of MOND -- its statement, its basic tenets, its main predictions, and the tests of these predictions -- contrasting it with the dark-matter paradigm. I then discuss possible wider ramifications of MOND, for example the potential significance of the MOND constant, $a_0$, with possible implications for the roots of MOND in cosmology. Along the way I point to parallels with several historical instances of nascent paradigms. In particular, with the emergence of the Copernican world picture, that of quantum physics, and that of relativity, as regards their initial advent, their development, their schematic structure, and their ramifications. For example, the interplay between theories and their corollary laws, and the centrality of a new constant with converging values as deduced from seemingly unrelated manifestations of these laws. I demonstrate how MOND has already unearthed a number of unsuspected laws of galactic dynamics (to which, indeed, $a_0$ is central) predicting them a priori, and leading to their subsequent verification. I parallel the struggle of the new with the old paradigms, and the appearance of hybrid paradigms at such times of struggle. I also try to identify in the history of those established paradigms a stage that can be likened to that of MOND today.

astro-ph.GA↗

arXiv2020

Fast-rotating galaxies do not depart from the MOND mass-asymptotic-speed relation

Ogle et al. have fallaciously argued recently that fast-rotating disc galaxies break with the predictions of MOND: the 6 fastest rotators of the 23 galaxies in their sample appear to have higher rotational speeds than is consistent with the MOND relation between the baryonic mass of a galaxy, $M$, and its `rotational speed', $V$. They interpret this departure as a break in the observed $M-V$ relation from a logarithmic slope near the MOND-predicted $4$, to a shallow slope of $\approx 0$. However, Ogle et al. use the MAXIMAL rotational speed of the galaxies, $V_{max}$, not the ASYMPTOTIC one, $V_\infty$, which appears in the MOND prediction, $V_\infty^4=MGa_0$. Plotting their $M$ vs. $V_{max}$ pairs on an $M$ vs. $V_\infty$ plot from Lelli et al. (2016), they arrive erroneously at the above tension with MOND. The $H_α$ rotation curves used by Ogle et al. are far too short reaching to probe the asymptotic regime, and determine $V_\infty$. However, it is well documented for fast rotators with observed, extended, HI rotation curves, that they can have $V_{max}$ considerably larger than the MOND-relevant $V_\infty$ [Noordermeer and Verheijen (NV) (2007) and others]. E.g., the fastest rotator in the NV sample has $V_{max}\approx 490{\rm ~km/s}$, but $V_\infty\approx 250{\rm ~km/s}$. NV also show that in a (MOND-irrelevant) $M-V_{max}$ plot the high-speed galaxies fall off the power-law line defined by the lower-speed ones, creating a break in the $M$ vs. $V$ relation, in just the way claimed by Ogle et al. But, when plotting the MOND-relevant $M$ vs. $V_\infty$ all galaxies fall near the same power-law relation, without a break.

astro-ph.GA↗

arXiv2020

The $a_0$ -- cosmology connection in MOND

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'.

astro-ph.GA↗

arXiv2019

Noncovariance at low accelerations as a route to MOND

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 $\mathcal{R}= g^{μν} (Γ^γ_{μν}Γ^λ_{λγ}-Γ^γ_{μλ} Γ^λ_{νγ})/2$. $Γ^γ_{μν}$ is the Levi-Civita connection of a metric, $g_{μν}$, and $\ell_M=c^2/a_0$ is the MOND length. Requiring $\mathcal{F}(z)\rightarrow z+ζ$, for $z\gg 1$ gives GR with a cosmological constant $ζc^{-4}a_0^2$ for high accelerations. In the MOND limit $\mathcal{F}'(z\ll 1)\propto z^{1/2}$. In the nonrelativistic limit the metric is of the form $g_{μν}\approx η_{μν}-2ϕδ_{μν}$, as in GR, but the potential $ϕ$ solves a MOND, nonlinear Poisson analog. This form of $g_{μν}$ also produces gravitational lensing as in GR only with the MOND potential. I show that this theory is a fixed-gauge expression of BIMOND, with the auxiliary metric constrained to be flat. The latter theory is thus a covariantized version of the former a-la Stückelberg. This theory is also a special case of so-called $f(\mathcal{Q})$ theories -- aquadratic generalizations of `symmetric, teleparallel GR', which are, in turn, also equivalent to constrained BIMOND-type theories. (Abridged.)

gr-qc↗

arXiv2019

MOND from a brane-world picture

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 velocity of small brane perturbations $c^2\sim T/σ\sim \ell_0\hat a_0$. But, $\hat a_0$ plays the role of the MOND acceleration constant in local gravitational dynamics; so $\hat a_0\sim c^2/\ell_0$. What we, in the brane, perceive as the gravitational potential is $ϕ\equiv\varepsilon[ξ(Ω)]\approx ϕ_0+\hat a_0ζ$. Aspects of MOND that may emerge naturally as geometrical properties are: a. The special role of acceleration in MOND, and why it is an acceleration, $a_0$, that marks the transition from the standard dynamics much above $a_0$ to scale-invariant dynamics much below $a_0$. b. The intriguing connection of $a_0$ with cosmology. c. The Newtonian limit corresponds to local departure $|ζ|\ll\ell_0$; i.e., $ϕ-ϕ_0\sim a_0ζ\ll a_0\ell_0\sim c^2$ - whereas relativity enters when $|ζ|\not\ll\ell_0$. The model also opens new vistas for extension, e.g., it points to possible dependence of $a_0$ on $ϕ$, and to $a_0$ losing its status and meaning altogether in the relativistic regime. The required global balance of the brane might solve the `old' cosmological-constant problem. I discuss possible connections with the nearly-de-Sitter nature of our Universe. (Abridged.)

gr-qc↗

arXiv2019

MOND in galaxy groups: a superior sample

Intermediate-richness galaxy groups are an important test ground for MOND. First, they constitute a distinct type of galactic systems, with their own evolution histories and underlying physical processes; secondly, they probe little-chartered regions of parameter space, as they have baryonic masses similar to massive galaxies, and similar velocity dispersions, but much larger sizes -- similar to cluster cores (or even to clusters), but much lower dispersions. Importantly in the context of MOND, they have the lowest internal accelerations reachable inside galactic systems. I analyze a sample of 56 medium-richness groups having a large number ($\ge 15$) of members with measured velocities. The groups obey the deep-MOND, baryonic-mass-velocity-dispersion relation, $M_MGa_0=(81/4)σ^4$, with individual, MOND $M_M/L_K$ ratios of order $1$ solar unit, with $(M_M/L_K)_{median}=0.7$ s.u. compared with the much larger Newtonian $M_d/L_K$ -- several tens s.u., and $(M_d/L_K)_{median}=37$ s.u. The same MOND relation describes dwarf spheroidals -- 2-3 orders smaller in size, and 7-8 orders lower in mass. The groups conformation to the MOND relation is equivalent to their lying on the deep-MOND branch of the `acceleration-discrepancy relation', $g\approx (g_N a_0)^{1/2}$, for $g$ as low as a few percents of $a_0$ ($g_N$ is the baryonic, Newtonian, gravitational acceleration, and $g$ the actual one). This argues against a breakdown of MOND at extremely low accelerations. This conformation also argues against the hypothesis that the remaining MOND conundrum in cluster cores bespeaks a breakdown of MOND on large-distance scales; our groups are as large as cluster cores, but do not show obvious disagreement with MOND. I also discuss the possible presence of the idiosyncratic, MOND external-field effect.

astro-ph.GA↗