Narrow Results

In this work we present a scalar field theory invariant under space-time anisotropic transformations with a dynamic exponent z. It is shown that this theory possesses symmetries similar to Hořava gravity and that in the limit z = 0 the equations of motion of the non-relativistic MOND theory are obtained. This result allow us to conjecture the existence of a Hořava type gravity that in the limit z = 0 is consistent with MOND.

A permissible spectrum of transverse vibrations for the holographic screen modifies both a distribution of thermal energy over bits at low temperatures and the law of gravitation at small accelerations of free fall in agreement with observations of flat rotation curves in spiral galaxies. This modification relates holographic screen parameters in de Sitter spacetime with the Milgrom acceleration in MOND.

The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of r^-2 force law. However, recently the interest in alternative gravities has emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an r^-α force law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent α, with small values of α corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.

We first show that the MOND concept is very unlikely: nonbaryonic dark matter exists. We then discuss dwarf special galaxies that in some cases appear to be nearly pure dark matter systems. The search for dark matter particles can be carried out from space (sterile neutrinos neutralino annihilation) or on the Earth (direct detection). We describe progress in these areas and focus on the progress of the ZEPLIN II detector now taking data.^1,2.

We summarize an interesting set of solar system predictions that we have recently derived for modified Newtonian dynamics (MOND). Specifically, we find that strong MOND behavior may become evident near the saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizable oblate ellipsoid around the saddle point. While strong MOND behavior would be a spectacular "backyard" vindication of the theory, pinpointing the MOND bubbles in the setting of the realistic solar system may be difficult. Space missions such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region.

A proposal is made to test Newton's inverse-square law using the perihelion shift of test masses (planets) in free fall within a spacecraft located at the Earth–Sun L2 point. Such an artificial planetary system in space (APSIS) will operate in a drag-free environment with controlled experimental conditions and minimal interference from terrestrial sources of contamination. We demonstrate that such a space experiment can probe the presence of a "hidden" fifth dimension on the scale of a micron, if the periapsis shift of a "planet" can be measured to sub-arc-second accuracy. Some suggestions for spacecraft design are made.

We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speed-up problem, laboratory and solar system tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

Cosmological models that invoke warm or cold dark matter cannot explain observed regularities in the properties of dwarf galaxies, their highly anisotropic spatial distributions, nor the correlation between observed mass discrepancies and acceleration. These problems with the standard model of cosmology have deep implications, in particular in combination with the observation that the data are excellently described by Modified Newtonian Dynamics (MOND). MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems, and in the universe at large, without invoking 'dark' entities. MOND introduces a new universal constant of nature with the dimensions of acceleration, a₀, such that the pre-MONDian dynamics is valid for accelerations a ≫ a₀, and the deep MONDian regime is obtained for a ≪ a₀, where spacetime scale invariance is invoked. Remaining challenges for MOND are (i) explaining fully the observed mass discrepancies in galaxy clusters, and (ii) the development of a relativistic theory of MOND that will satisfactorily account for cosmology. The universal constant a₀ turns out to have an intriguing connection with cosmology: ā₀ ≡ 2πa₀ ≈ cH₀ ≈ c²(Λ/3)^1/2. This may point to a deep connection between cosmology and internal dynamics of local systems.

The Modified Newtonian Dynamics (MOND) paradigm to the missing mass problem requires introducing a functional that is to be identified through observations and experiments. We consider the aquadratic Lagrangian theory as a realization of the MOND. We show that the accurate value of the Earth GM measured by the lunar laser ranging measurements and that by various artificial Earth satellites, including the accurate tracking of the LAGEOS satellites, constrain this functional such that some of the chosen/proposed functional are refuted.

I analyze the possibility of reproducing MONDian dark matter effects by using a nonlocal model of gravity. The model was used before in order to recreate screening effects for the cosmological constant (Λ) value. Although the model in the weak-field approximation (in static coordinates) can reproduce the field equations in agreement with the AQUAL Lagrangian, the solutions are scale dependent and cannot reproduce the same dynamics in agreement with MOND.

We argue that dark matter (DM)and dark energy phenomena associated with galactic rotation curves (RC’s), X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit the HI nearby galaxy survey (THINGS) RC data rivaling modified Newtonian dynamics, Roentgen Satellite/Advanced Satellite for Cosmology and Astrophysics (ROSAT/ASCA) X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling $\mathrm{\Lambda }$CDM without nonbaryonic DM or a cosmological constant. In the case of DM, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein–de Sitter cosmology. Therefore, the phenomena of DM and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.

For Newtonian dynamics to hold over galactic scales, large amounts of dark matter (DM) are required which would dominate cosmic structures. Accounting for the strong observational evidence that the universe is accelerating requires the presence of an unknown dark energy (DE) component constituting about 70% of the matter. Several ingenious ongoing experiments to detect the DM particles have so far led to negative results. Moreover, the comparable proportions of the DM and DE at the present epoch appear unnatural and not predicted by any theory. For these reasons, alternative ideas like MOND and modification of gravity or general relativity over cosmic scales have been proposed. It is shown in this paper that these alternate ideas may not be easily distinguishable from the usual DM or DE hypotheses. Specific examples are given to illustrate this point that the modified theories are special cases of a generalized DM paradigm.

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory.

(i) Investigations of stellar systems known as wide binaries suggest that Newton’s law of gravitation breaks down at low accelerations. This can be explained by proposing a fifth force with $U(1)$ gauge symmetry, whose corresponding gauge boson is the sought for dark matter candidate. (ii) Relativistic causality (i.e. no faster than light signalling) permits nonlocal correlations stronger than those permitted by quantum mechanics. Can this be explained if our universe possesses a second 4D spacetime with a signature opposite to ours? (iii) Such a fifth force, and a second spacetime, arise naturally in a recently proposed theory of unification based on an $E_8\times E_8$ symmetry. Our spacetime arises from breaking of an $SU{(2)}_R\times U{(1)}_{Y\mathrm{\text{DEM}}}$ symmetry, and the second spacetime arises from broken electroweak symmetry.

We review and emphasize the importance of the Satellite Test of the Equivalence Principle (STEP) in probing one of the most successful and popular alternative theories to dark matter known as Modified Newtonian Dynamics (MOND), on Earth. This would be achieved with no modification of STEP’s current design and sensitivity and if MOND exists STEP could in principle easily detect it.

Birkhoff’s theorem (1923) states that in the framework of General Relativity the only solution to the central symmetric gravitational field in vacuum is the Schwarzschild metric. This result has crucial consequences in the resolution of the dark matter problem. This problem can only be solved through the discovery of a new type of matter particles, or by the introduction of a new theory of gravitation which supplants General Relativity. After reviewing Birkhoff’s theorem, it was discovered that by starting the calculation of the metric from an indeterminate metric whose coefficients are locally defined, we obtain a solution containing two arbitrary functions. In general, these functions do not induce any difference between this solution and the Schwarzschild metric. However, it can be seen that if we choose a triangular signal for these functions, the situation changes dramatically: (1) the metric is broken down into four distinct metrics that replace each other cyclically over time, (2) for two of these four metrics, the coordinate differentials dr and dt switch their spatial/temporal role cyclically, (3) the four metrics are not separable: they form a single logical set that we call a 4-metric and (4) this 4-metric cannot be transformed into the Schwarzschild metric by any coordinate change. According to these findings, there is a second solution in the spherical space, in addition to the Schwarzschild metric, and thus, Birkhoff’s theorem is incomplete. In the 4-metric, the orbital velocity of a massive particle does not depend on the radial distance. This 4-metric is thus in agreement with the baryonic Tully–Fisher relation (BTFR), (consequently BTFR is in agreement with a solution of General Relativity without presence of dark matter and without hypothesis on the distribution of stars in galaxies). By combining the 4-metric with the Schwarzschild metric, another 4-metric in agreement with the observed galaxy rotation curve can been obtained. The calculation of the light deflection in this space is also exposed in this paper.

According to these findings: (1) it is not necessary to introduce the notion of dark matter or the notion of distribution of stars in galaxies in order to find the observed galaxy rotation curve in the framework of General Relativity, (2) the modification of the metric with respect to the Schwarzschild metric appears to be due to the existence of a lower bound of the space-time curvature in galaxies (without external field effect), this phenomenon leading to a temporal oscillation of the space-time curvature, (3) an analysis of the external field effect for the Milky Way-Andromeda couple allows to model the rotation curve of the two galaxies beyond the plateau zone. The validation of these findings would be the first step toward challenging the standard model of cosmology ($\mathrm{\Lambda }$CDM), as the $\mathrm{\Lambda }$CDM model cannot be in agreement with the observed galaxy rotation curve without presence of dark matter. The second step would be the demonstration that there is no dark matter in intergalactic spaces (not included in this paper).

The GAIA DR3 measurement campaign has produced a MW rotation curve with significantly improved accuracy compared with previous campaigns. In 2023, several authors presented accurate rotation curves calculated from these measurements, within the framework of the dark matter hypothesis. They established new estimates of the Milky Way’s dynamical mass of around $2\times {10}^{11}{M}_{\odot }$. Some of these authors showed that, from a radial distance of around 18kpc, the Milky Way presents a significant Keplerian decay in the rotation curve, rather than a plateau zone. In this paper, we use a set of data tables from four different authors in a single database. Without making any assumptions about the existence or absence of dark matter, we analyze the observed radial acceleration as a function of the baryonic acceleration. We show that the observed acceleration is an accurate linear function of the baryonic acceleration, making the dark matter hypothesis problematic. Furthermore, we prove that the MW rotation curve can be calculated within the framework of General Relativity without dark matter, using the dynamic metric we published earlier in 2023: “On the incompleteness’ of Birkhoff’s theorem: A new approach to the central symmetric Gravitational Field in Vacuum Space.” In particular, this metric allows us to predict and model the Keplerian decay zone of the rotation curve. Our dynamical mass evaluation does not differ significantly from the value $2\times 10^{11}{M}_{\odot }$.

We summarize an interesting set of solar system predictions that we have recently derived for modified Newtonian dynamics (MOND). Specifically, we find that strong MOND behavior may become evident near the saddle points of the total gravitational potential. Whereas in Newtonian theory tidal stresses are finite at saddle points, they are expected to diverge in MOND, and to remain distinctly large inside a sizable oblate ellipsoid around the saddle point. While strong MOND behavior would be a spectacular “backyard” vindication of the theory, pinpointing the MOND bubbles in the setting of the realistic solar system may be difficult. Space missions such as the LISA Pathfinder, equipped with sensitive accelerometers, may be able to explore the larger perturbative region.

We first show that the MOND concept is very unlikely: nonbaryonic dark matter exists. We then discuss dwarf special galaxies that in some cases appear to be nearly pure dark matter systems. The search for dark matter particles can be carried out from space (sterile neutrinos neutralino annihilation) or on the Earth (direct detection). We describe progress in these areas and focus on the progress of the ZEPLIN II detector now taking data.^1,2

Cosmological models that invoke warm or cold dark matter can not explain observed regularities in the properties of dwarf galaxies, their highly anisotropic spatial distributions, nor the correlation between observed mass discrepancies and acceleration. These problems with the standard model of cosmology have deep implications, in particular in combination with the observation that the data are excellently described by Modified Newtonian Dynamics (MOND). MOND is a classical dynamics theory which explains the mass discrepancies in galactic systems, and in the universe at large, without invoking ‘dark’ entities. MOND introduces a new universal constant of nature with the dimensions of acceleration, a₀, such that the pre-MONDian dynamics is valid for accelerations a ≫ a₀, and the deep MONDian regime is obtained for a ≪ a₀, where space-time scale invariance is invoked. Remaining challenges for MOND are (i) explaining fully the observed mass discrepancies in galaxy clusters, and (ii) the development of a relativistic theory of MOND that will satisfactorily account for cosmology. The universal constant a₀ turns out to have an intriguing connection with cosmology: . This may point to a deep connection between cosmology and internal dynamics of local systems.