We review some of our recent results about the Radial Acceleration Relation (RAR) and its interpretation as either a fundamental or an emergent law. The former interpretation is in agreement with a class of modified gravity theories that dismiss the need for dark matter in galaxies (MOND in particular). Our most recent analysis, which includes refinements on the priors and the Bayesian test for compatibility between the posteriors, confirms that the hypothesis of a fundamental RAR is rejected at more than 5$σ$ from the very same data that was used to infer the RAR.
Verlinde (2016) has recently proposed that spacetime and gravity may emerge from an underlying microscopic theory. In a de Sitter spacetime, such emergent gravity (EG) contains an additional gravitational force due to dark energy, which may explain the mass discrepancies observed in galactic systems without the need of dark matter. For a point mass, EG is equivalent to Modified Newtonian Dynamics (MOND). We show that this equivalence does not hold for finite-size galaxies: there are significant differences between EG and MOND in the inner regions of galaxies. We confront theoretical prediction…
Modified Newtonian Dynamics has one free parameter and requires an interpolation function to recover the normal Newtonian limit. We here show that this interpolation function is unnecessary in a recently proposed covariant completion of Erik Verlinde's emergent gravity, and that Verlinde's approach moreover fixes the function's one free parameter. The so-derived correlation between the observed acceleration (inferred from rotation curves) and the gravitational acceleration due to merely the baryonic matter fits well with data. We then argue that the redshift-dependence of galactic rotation cur…
We present the results from the analysis of galaxy rotation curves with Verlinde's emergent gravity. We use the data in the SPARC (Spitzer Photometry and Accurate Rotation Curves) database, which contains a sample of 175 nearby disk galaxies with 3.6 $μ$m surface photometry and rotation curves. We compute the gravitational acceleration at different galactocentric radii expected from the baryon distribution of the galaxies with the emergent gravity, and compare it with the observed gravitational acceleration derived from galactic rotation curves. The predicted and observed accelerations agree w…
The equation of motion in the generally covariant modified gravity (MOG) theory leads, for weak gravitational fields and non-relativistic motion, to a modification of Newton's gravitational acceleration law. In addition to the metric $g_{μν}$, MOG has a vector field $ϕ_μ$ that couples with gravitational strength to all baryonic matter. The gravitational coupling strength is determined by the MOG parameter $α$, while parameter $μ$ is the small effective mass of $ϕ_μ$. The MOG acceleration law has been demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet Cluster and Train…
We consider specific deterministic quantum models of Cartan-Randers type and show how a dualized abelian gauge symmetry, diffeomorphism invariance, the Principle of Inertia, reversibility of phenomenological dynamics, maximal acceleration and maximal propagation speed for matter arise from such models in an phenomenological description. Two particular predictions are highlighted: the first is the value of maximal acceleration is universal and has the value of order 10^{52} m/s^2. The second prediction is that gauge symmetries in phenomenological models must come dualized and containing an abel…
We show that the radial acceleration relation for rotationally-supported galaxies may be explained, in the absence of cold dark matter, by a non-minimally coupled scalar field, whose fifth forces are partially screened on galactic scales by the symmetron mechanism. In addition, we show that sufficient energy is stored in the symmetron field to explain the dynamic stability of galactic disks.
The Navier-Stokes equations are considered by the use of the method of Lagrangians with covariant derivatives (MLCD) over spaces with affine connections and metrics. It is shown that the Euler-Lagrange equations appear as sufficient conditions for the existence of solutions of the Navier-Stokes equations over (pseudo) Euclidean and (pseudo) Riemannian spaces without torsion. By means of the corresponding (n-1)+ 1 projective formalism the Navier-Stokes equations for radial and tangential accelerations are found.
The central regions of nearby elliptical galaxies are dominated by baryons (stars) and provide interesting laboratories for studying the radial acceleration relation (RAR). We carry out exploratory analyses and discuss the possibility of constraining the RAR in the super-critical acceleration range $(10^{-9.5},\hspace{1ex}10^{-8})$~${\rm m}~{\rm s}^{-2}$ using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies including 24 ATLAS$^{\rm 3D}$ galaxies and 4201 SDSS galaxies covering a wide range of masses, sizes and luminosity density profiles. We consider a range of …
When a space-craft reaches a large radial velocity, we expand the time dependent radial distance to linear order in time. In the Schwarzschild metric this linear term in time leads to a significant un-modelled clock acceleration. For Pioneer 10, this acceleration is found to be about $40\%$ of the observed anomalous acceleration. As measured distances are geocentric distances instead of the heliocentric distances in the model, this un-modelled acceleration has an annual oscillation with amplitude close to observations. For Pioneer 11, we find that the un-modelled acceleration "On-Set" is cause…
The Radial Acceleration Relation confirms that a nontrivial acceleration scale can be found in the average internal dynamics of galaxies. The existence of such a scale is not obvious as far as the standard cosmological model is concerned, and it has been interpreted as a possible sign of modified gravity. The implications could be profound: it could in principle explain galactic dynamics without large amounts of yet-undetected dark matter and address issues that the standard cosmological model faces at galactic scales. Here, we consider 193 disk galaxies from the SPARC and THINGS databases and…
I address some problems encountered in the formulation of relativistic models encompassing the MOND phenomenology of radial acceleration. I explore scalar and vector theories with fractional kinetic terms and $f(R)$-type gravity, demanding that the energy density be bounded from below and that superluminal modes be absent, but also that some consistency constraints with observational results hold. I identify configurations whose energy is unbounded from below and formulate some no-go statements for vector field models and modified gravity theories. Finally, I discuss superfluid dark matter as …
Recent observations of anomalous line-of-sight velocity dispersions of two ultra-diffuse galaxies (UDGs) provide a stringent test for modified gravity theories. While NGC 1052-DF2 exhibits an extremely low dispersion value ($σ\sim 7.8_{-2.2}^{+5.6}$ km/s), the reported dispersion value for NGC 1052-DF44 is quite high ($σ\sim 41.0 \pm 8$ km/s). For DF2, the dynamical mass is almost equal to the luminous mass suggesting the galaxy have little to no `dark matter' in $Λ$CDM whereas DF4 requires a dynamical mass-to-light ratio of $\sim 30$ making it to be almost entirely consists of dark matter. It…
We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations of the radial velocity v_r of a typical S star orbiting the Supermassive Black Hole (SBH) hosted by the Galactic Center (GC) in Sgr A* caused by several dynamical effects. They are the general relativistic gravitoelectromagnetic (GEM) fields of the SBH, its quadrupole mass moment Q2, and a diffuse dark matter distribution around the SBH. All of them induce non-zero secular radial accelerations proportional to the eccentricity e of the orbit. By taking the S2 star, orbiting the SBH along a highly…
The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on n, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory n is proportional to the traversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits.
This paper continues previous work on a novel alternative model of gravity, based on the theory of fractional-dimension spaces applied to Newton's law of gravitation. In particular, our Newtonian Fractional-Dimension Gravity is now applied to axially-symmetric structures, such as thin/thick disk galaxies described by exponential, Kuzmin, or other similar mass distributions. As in the case of spherically-symmetric structures, which was studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model,…
We present the radial distribution of the dark matter in two massive, X-ray luminous galaxy clusters, Abell~2142 and Abell~2319, and compare it with the quantity predicted as apparent manifestation of the baryonic mass in the context of the "Emergent Gravity" scenario, recently suggested from Verlinde (2016). Thanks to the observational strategy of the \xmm\ Cluster Outskirt Programme (X-COP), using the X-ray emission mapped with \xmm\ and the SZ signal in the Planck survey, we recover the gas density, temperature and thermal pressure profiles up to $\sim R_{200}$, allowing to constrain at unp…
The mysterious attractive constant radial force acted in the past on Pioneer spacecrafts - the so-called Pioneer anomaly - is considered within the context of Rindler acceleration. As an idea this is tempting since it is reminiscent of the cosmological constant. Fortunately the anomalous force acts radially toward the sun so that it differs from the mission of a cosmological constant. Without resorting to the physical source responsible for such a term we investigate the modified Schwarzschild geodesics. The Rindler acceleration naturally affects all massive / massless particle orbits. Stable …
Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal coordinate system constructed along its worldline, the particles in the swarm that move along the radial direction and are ultrarelativistic (that is, they have speeds above c/sqrt(2)) decelerate toward this terminal speed. On the other hand, the swarm particles that are ultrarelativistic and move in directions normal to the radial (jet) directions accelerate to almost the sp…
The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on $n$, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory $n$ is proportional to the transversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits. Here we give calculation details of the alternative II, discus…
The paper is devoted to an explanation of the accelerated rate of expansion of the Universe. Usually the acceleration of the Universe, which is described by FRW metric, is due to dark energy. It is shown that this effect may be considered as a manifestation of torsion tensor for a flat Universe in the realm of Teleparallel gravity. An observer with radial field velocity obey Hubble's Law. As a consequence it is established that this is radial acceleration in a flat Universe. In Eq. (\ref{24}) the acceleration is written in terms of the deceleration parameter, the Hubble's constant and the prop…
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-Lagrangi…
The dynamical mass of galaxies and the Newtonian acceleration generated from the baryons have been found to be strongly correlated. This correlation is known as 'Mass-Discrepancy Acceleration Relation' (MDAR). Further investigations have revealed a tighter relation - 'Radial Acceleration Relation' (RAR) - between the observed total acceleration and the (Newtonian) acceleration produced by the baryons. So far modified gravity theories have remained more successful than $Λ$CDM to explain these relations. However, a recent investigation has pointed out that, when RAR is expressed as a difference …
There is sufficient amount of internal evidence in the nature of gravitational theories to indicate that gravity is an emergent phenomenon like, e.g, elasticity. Such an emergent nature is most apparent in the structure of gravitational dynamics. It is, however, possible to go beyond the field equations and study the space itself as emergent in a well-defined manner in (and possibly only in) the context of cosmology. In the first part of this review, I describe various pieces of evidence which show that gravitational field equations are emergent. In the second part, I describe a novel way of s…
We investigate the contributions of the Friedmann-Lemaître-Robertson-Walker metric of the standard cosmology as an asymptotic boundary condition on the first-order approximation of the gravitational field in Moffat's theory of modified gravity (MOG). We also consider contributions due to the fact that the MOG theory does not satisfy the shell theorem or Birkhoff's theorem, resulting in what is known as the "external field effect" (EFE). We show that while both these effects add small contributions to the radial acceleration law, the result is orders of magnitude smaller than the radial acceler…
