MOND Gravity Research Articles

Deep-MOND polytropes

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. 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 $\zeta(y)$ is (for $\gamma\not=1$) $[\int_0^y \zeta \bar y^2 d\bar y]^{1/2}=-yd(\zeta^{\gamma-1})/dy$. Or, $\theta^n(y)=y^{-2}[(y\theta')^2]'$, where $\theta=\zeta^{\gamma-1}$, and $n\equiv (\gamma-1)^{-1}$. 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 $n<\infty$ ($\gamma>1$) 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 $\gamma$) between the total mass, $M$, and the mass-average velocity dispersion $\sigma$: $MGa_0=(9/4)\sigma^4$. However, the relation between $M$ and other measures of the velocity dispersion, such as the central, projected one, $\bar\sigma$, does depend on $n$ (but not $\mathcal{K}$), defining a `fundamental surface' in the $[M,~\bar\sigma,~n]$ space. I also describe the generalization to anisotropic polytropes, which also all have a finite radius (for $\gamma>1$), and all satisfy the above universal $M-\sigma$ 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.

Matter and twin matter in bimetric MOND

Bimetric MOND (BIMOND) theories, propounded recently, predict peculiar gravitational interactions between matter and twin matter (TM). Twin matter is hypothetical matter that might couple directly only to the second metric of the theory. Considerations of cosmology in the BIMOND framework suggest that such TM might exist and copy matter in its attributes. Here I investigate the indirect interactions that BIMOND theories predict between nonrelativistic masses of matter and TM. The most salient result is that in the deep-MOND regime of the matter-TM-symmetric theories, TM behaves as if it has a negative gravitational mass. To wit, interaction within each sector is attractive MOND gravity, but between matter and TM it is repulsive MOND gravity. In the high-acceleration regime, the interaction depends on a parameter, beta. For the favored value beta=1, matter and TM do not interact in this regime; for beta<1 they attract; and for beta>1 they repel each other. Such interactions may have substantial ramifications for all aspects of structure formation, such as matter distribution, peculiar velocities, and effects on the CMB. The repulsive interactions probably lead to segregation of matter and TM structures, leading, in turn, to intermeshing of the respective cosmic webs, with high-density nodes of one sector residing in the voids of the other (possibly conducing to efficient evacuation of the voids). Weak lensing by TM seems the best way to constrain its attributes. In the MOND regime a TM body acts on matter photons as a diverging lens. Strong lensing occurs in the high acceleration regime, and thus depends on the value of beta. For beta=1 no strong lensing effects of TM are expected. I also discuss briefly asymmetric theories (abridged).

DARK FLUID: A UNIFIED FRAMEWORK FOR MODIFIED NEWTONIAN DYNAMICS, DARK MATTER, AND DARK ENERGY

Empirical theories of Dark Matter like MOND gravity and of Dark Energy like f(R) gravity were motivated by astronomical data. But could these theories be branches rooted from a more general hence natural framework? Here we propose the natural Lagrangian of such a framework based on simple dimensional analysis and co-variant symmetry requirements, and explore various outcomes in a top-down fashion. Our framework preserves the co-variant formulation of GR, but allows the expanding physical metric be bent by a single new species of Dark Fluid flowing in space-time. Its non-uniform stress tensor and current vector are simply functions of a vector field of variable norm, resembling the 4-vector electromagnetic potential description for the photon fluid, but is dark (e.g., by very early decoupling from the baryon-radiation fluid). The Dark Fluid framework naturally branches into a continuous spectrum of theories with Dark Energy and Dark Matter effects, including the $f(R)$ gravity, TeVeS-like theories, Einstein-Aether and $\nu\Lambda$ theories as limiting cases. When the vector field degenerates into a pure Higgs-like scalar field, we obtain the physics for inflaton and quintessence. In this broad setting we emphasize the non-constant dynamical field behind the cosmological constant effect, and highlight plausible corrections beyond the classical MOND predictions. Choices of parameters can be made to pass BBN, PPN, and causality constraints. The Dark Fluid is inspired to unify/simplify the astronomically successful ingredients of previous constructions: the desired effects of inflaton plus quintessence plus Cold DM particle fields or MOND-like scalar field(s) are shown largely achievable by one vector field only.

An f(R) gravitation for galactic environments

We propose an action-based f(R) modification of Einstein's gravity that admits a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the Newtonian potential. A test star moving in such a spacetime acquires a constant asymptotic speed at large distances. This speed, calibrated empirically, is proportional to the fourth root of the mass of the central body in compliance with the Tully-Fisher relation. A variance of MOND's gravity emerges as an inevitable consequence of the proposed formalism. It has also been shown (Mendoza et al. 2006, [arXiv:astroph/8618398]) that a) the gravitational waves in this spacetime propagate with the speed of light in vacuum and b) there is a lensing effect added to what one finds in the classic GR.

An $\mathsf{f(R)}$ gravitation for galactic environments

We propose an action-based modification of Einstein's gravity that admits a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the Newtonian potential. A test star moving in such a spacetime acquires a constant asymptotic speed at large distances. This speed, calibrated empirically, is proportional to the fourth root of the mass of the central body in compliance with the Tully-Fisher relation. A variance of MOND's gravity emerges as an inevitable consequence of the proposed formalism. It has also been shown (Mendoza et al. [CITE], [arXiv:astroph/0610390]) that a) the gravitational waves in this spacetime propagate with the speed of light in vacuum and b) there is a lensing effect added to what one finds in the classic GR.

An f(R) gravitation for galactic environments

AbstractWe propose an action-based f(R) modification of Einstein's gravity which admits of a modified Schwarzschild-deSitter metric. In the weak field limit this amounts to adding a small logarithmic correction to the Newtonian potential. A test star moving in such a spacetime acquires a constant asymptotic speed at large distances. This speed turns out to be proportional to the fourth root of the mass of the central body in compliance with the Tully-Fisher relation. A variance of MOND's gravity emerges as an inevitable consequence of the proposed formalism.