Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND)

Employing a thermodynamic interpretation of gravity based on the holographic principle and assuming underlying particle statistics, fermionic or bosonic, for the excitations of the holographic screen leads to Modified Newtonian Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in MOND and the Fermi energy of the holographic fermionic degrees of freedom is obtained. In this formulation the physics of MOND results from the quantum-classical crossover in the fermionic specific heat. However, due to the dimensionality of the screen, the formalism is general and applies to two dimensional bosonic excitations as well. It is shown that replacing the assumption of the equipartition of energy on the holographic screen by a standard quantum-statistical-mechanics description wherein some of the degrees of freedom are frozen out at low temperatures is the physical basis for the MOND interpolating function ${\tilde \mu}$. The interpolating function ${\tilde \mu}$ is calculated within the statistical mechanical formalism and compared to the leading phenomenological interpolating functions, most commonly used. Based on the statistical mechanical view of MOND, its cosmological implications are re-interpreted: the connection between $a_0$ and the Hubble constant is described as a quantum uncertainty relation; and the relationship between $a_0$ and the cosmological constant is better understood physically

A new perspective on MOND

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_0/2\pi; 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.Comment: 16 pages, 3 figures, substantial overlap with arXiv:1211.1625; one arithmetic correction made, subsection 4.1 rewritten; accepted for publication by the Canadian Journal of Physic

On the separation between baryonic and dark matter: evidence for phantom dark matter?

The recent years have seen combined measurements of X-ray and (weak) lensing contours for colliding galaxy clusters such as, for instance, the famous "Bullet" cluster. These observations have revealed offsets in the peaks of the baryonic and (dominant) gravitational matter component of order ~(100-200) kpc. Such discrepancies are difficult to explain using modified theories for gravity other than dark matter. Or are they not? Here we use the concept of "phantom dark matter" that is based upon a Newtonian interpretation of the MONDian gravitational potential. We show that this idea is in fact capable of producing substantial offsets in idealistic density configurations, involving a uniform external field. However, when analysed in a MONDian cosmological framework we deduce that the size (and probablity) of the effect is too small to explain the observed offsets found in the most recent observations, at least in the simplest incarnation of phantom dark matter as discussed here. The lensing centers in merging galaxy clusters are likely very close to the centers of true mass even in a MONDian cosmology. This gives the support to the idea that neutrino-like non-collisional matter might be responsible for the observed offsets of lensing and X-ray peaks.Comment: 6 pages, 5 figures, accepted for publication in Ap

Modified Newtonian Dynamics of Large Scale Structure

We examine the implications of Modified Newtonian Dynamics (MOND) on the large scale structure in a Friedmann-Robertson-Walker universe. We employ a ``Jeans swindle'' to write a MOND-type relationship between the fluctuations in the density and the gravitational force, \vg. In linear Newtonian theory, |\vg| decreases with time and eventually becomes $<g_0$, the threshold below which MOND is dominant. If the Newtonian initial density field has a power-law power-spectrum of index $n<-1$, then MOND domination proceeds from small to large scale. At early times MOND tends to drive the density power-spectrum towards $k^{-1}$, independent of its shape in the Newtonian regime. We use N-body simulations to solve the MOND equations of motion starting from initial conditions with a CDM power-spectrum. MOND with the standard value $g_0=10^{-8} cm s^{-2}$, yields a high clustering amplitude that can match the observed galaxy distribution only with strong (anti-) biasing. A value of $g_0 \approx 10^{-9}cm s^{-2}$, however, gives results similar to Newtonian dynamics and can be consistent with the observed large scale structure.Comment: Version accepted for publication in the MNRAS. Results of more simulations are include

Gravitation in the fractal D=2 inertial universe: New phenomenology in spiral discs and a theoretical basis for MOND

An interpretation of Mach's Principle led us to consider if it was possible to have a globally inertial universe that was irreducibly associated with a non-trivial global matter distribution, Roscoe (GRG,2002,34,5,577-602, astro-ph/0107397). This question received a positive answer, subject to the condition that the global matter distribution is necessarily fractal, D=2. The purpose of the present paper is to show how general gravitational processes arise in this universe. We illustrate the theory by using it to model an idealized spiral galaxy. One particular subclass of solutions, corresponding to logarithmic spirals, has already been extensively tested in Roscoe A&A,1999,343,788-800 (astro-ph/0107305), and shown to resolve dynamical data over large samples of ORCs with a very high degree of statistical precision. However, this latter analysis led directly to the discovery of a major new phenomenology in spiral discs - that of discrete dynamical classes - comprehensively confirmed in Roscoe A&A,2002,385,431-453 (astro-ph/0107300) over four large independent samples of ORCs. In this paper, we analyse the theory to show how the discrete dynamical classes phenomenology has a ready explanation in terms of an algebraic consistency condition which must necessarily be satisfied. Of equal significance, we apply the theory with complete success to the detailed modelling of a sample of eight Low Surface Brightness spirals (LSBs) which, hitherto, have been succesfully modelled only by Milgrom's MOND algorithm. We are able to conclude that the essence of the MOND algorithm must be contained within the presented theory.Comment: 35 pages, 13 figures. Accepted for publication in GRG (General Relativity and Gravitation

Testing MOND gravity in the shell galaxy NGC 3923

Context. The elliptical galaxy NGC 3923 is surrounded by numerous stellar shells that are concentric arcs centered on the galactic core. They are very likely a result of a minor merger and they consist of stars in nearly radial orbits. For a given potential, the shell radii at a given time after the merger can be calculated and compared to observations. The Modified Newtonian Dynamics (MOND) is a theory that aims to solve the missing mass problem by modifying the laws of classical dynamics in the limit of small accelerations. Hernquist & Quinn(1987) claimed that the shell distribution of NGC 3923 contradicted MOND, but Milgrom(1988) found several substantial insufficiencies in their work. Aims. We test whether the observed shell distribution in NGC 3923 is consistent with MOND using the current observational knowledge of the shell number and positions and of the host galaxy surface brightness profile, which supersede the data available in the 1980s when the last (and negative) tests of MOND viability were performed on NGC 3923. Methods. Using the 3.6 um bandpass image of NGC 3923 from the Spitzer space telescope we construct the mass profile of the galaxy. The evolution of shell radii in MOND is then computed using analytical formulae. We use 27 currently observed shells and allow for their multi-generation formation, unlike the Hernquist & Quinn one-generation model that used the 18 shells known at the time. Results. Our model reproduces the observed shell radii with a maximum deviation of 5% for 25 out of 27 known shells while keeping a reasonable formation scenario. A multi-generation nature of the shell system, resulting from successive passages of the surviving core of the tidally disrupted dwarf galaxy, is one of key ingredients of our scenario supported by the extreme shell radial range. The 25 reproduced shells are interpreted as belonging to three generations.Comment: 8 pages, 3 figures, Accepted for publication in A&

A New interpretation of MOND based on Mach principle and an Unruh like effect

A new interpretation is introduced for MOND based on the Sciama's interpretation of Mach principle and an Unruh like effect, in the context of a generalized equivalence principle. It is argued that in a locally accelerated frame with acceleration $a$ the appearance of a Rindler horizon may give rise to a constant acceleration $a_0$ as the local properties of cosmological horizon or Hubble length. The total gravitational acceleration inside this frame becomes the combination of $a$ with $a_0$. For $a\gg a_0$, the conventional gravitational mass $m_g$ interacts with the dominant acceleration as $m_g a$ and application of Sciama's interpretation leads to the standard Newtonian dynamics. For $a\ll a_0$, however, a reduced gravitational mass $\bar{m}_g$ interacts with the dominant acceleration as $\bar{m}_g a_0$ and the application of Sciama's interpretation on this reduced gravitational mass leads to MOND. This introduces a third proposal for MOND: {\it The modification of gravitational mass}.Comment: 11 pages, throughout revisio