Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions

Methodological reflections on the MOND/dark matter debate

The paper re-examines the principal methodological questions, arising in the debate over the cosmological standard model's postulate of Dark Matter vs. rivalling proposals that modify standard (Newtonian and general-relativistic) gravitational theory, the so-called Modified Newtonian Dynamics (MOND) and its subsequent extensions. What to make of such seemingly radical challenges of cosmological orthodoxy? In the first part of our paper, we assess MONDian theories through the lens of key ideas of major 20th century philosophers of science (Popper, Kuhn, Lakatos, and Laudan), thereby rectifying widespread misconceptions and misapplications of these ideas common in the pertinent MOND-related literature. None of these classical methodological frameworks, which render precise and systematise the more intuitive judgements prevalent in the scientific community, yields a favourable verdict on MOND and its successors-contrary to claims in the MOND-related literature by some of these theories' advocates; the respective theory appraisals are largely damning. Drawing on these insights, the paper's second part zooms in on the most common complaint about MONDian theories, their ad-hocness. We demonstrate how the recent coherentist model of ad-hocness captures, and fleshes out, the underlying-but too often insufficiently articulated-hunches underlying this critique. MONDian theories indeed come out as severely ad hoc: they do not cohere well with either theoretical or empirical-factual background knowledge. In fact, as our complementary comparison with the cosmological standard model's Dark Matter postulate shows, with respect to ad-hocness, MONDian theories fare worse than the cosmological standard model.

From Modified Newtonian Dynamics to Superfluid Vacuum Theory

Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a recent alternative based on the Superfluid Vacuum Theory (SVT) with a nonlinear logarithmic Schrödinger equation (LogSE) which reconciles both approaches, retains the essential success of MOND and the Superfluid nature but does not necessitate the hypothesis of processes including dark matter. We conclude with the implications of this SVT alternative on quantum theory itself.

Asymmetry in Galaxy Spin Directions—Analysis of Data from DES and Comparison to Four Other Sky Surveys

The paper shows an analysis of the large-scale distribution of galaxy spin directions of 739,286 galaxies imaged by DES. The distribution of the spin directions of the galaxies exhibits a large-scale dipole axis. Comparison of the location of the dipole axis to a similar analysis with data from SDSS, Pan-STARRS, and DESI Legacy Survey shows that all sky surveys exhibit dipole axes within 52° or less from each other, well within 1σ error, while non-random distribution is unexpected, the findings are consistent across all sky surveys, regardless of the telescope or whether the data were annotated manually or automatically. Possible errors that can lead to the observation are discussed. The paper also discusses previous studies showing opposite conclusions and analyzes the decisions that led to these results. Although the observation is provocative, and further research will be required, the existing evidence justifies considering the contention that galaxy spin directions as observed from Earth are not necessarily randomly distributed. Possible explanations can be related to mature cosmological theories, but also to the internal structure of galaxies.

From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity

Astronomical observations reveal a major deficiency in our understanding of physics—the detectable mass is insufficient to explain the observed motions in a huge variety of systems given our current understanding of gravity, Einstein’s General theory of Relativity (GR). This missing gravity problem may indicate a breakdown of GR at low accelerations, as postulated by Milgromian dynamics (MOND). We review the MOND theory and its consequences, including in a cosmological context where we advocate a hybrid approach involving light sterile neutrinos to address MOND’s cluster-scale issues. We then test the novel predictions of MOND using evidence from galaxies, galaxy groups, galaxy clusters, and the large-scale structure of the universe. We also consider whether the standard cosmological paradigm (LCDM) can explain the observations and review several previously published highly significant falsifications of it. Our overall assessment considers both the extent to which the data agree with each theory and how much flexibility each has when accommodating the data, with the gold standard being a clear a priori prediction not informed by the data in question. Our conclusion is that MOND is favoured by a wealth of data across a huge range of astrophysical scales, ranging from the kpc scales of galactic bars to the Gpc scale of the local supervoid and the Hubble tension, which is alleviated in MOND through enhanced cosmic variance. We also consider several future tests, mostly at scales much smaller than galaxies.

A Possible Explanation of Dark Matter and Dark Energy Involving a Vector Torsion Field

A simple gravitational model with torsion is studied, and it is suggested that it could explain the dark matter and dark energy in the universe. It can be reinterpreted as a model using the Einstein gravitational equations where spacetime has regions filled with a perfect fluid with negative energy (pressure) and positive mass density, other regions containing an anisotropic substance that in the rest frame (where the momentum is zero) has negative mass density and a uniaxial stress tensor, and possibly other “luminal” regions where there is no rest frame. The torsion vector field is inhomogeneous throughout spacetime, and possibly turbulent. Numerical simulations should reveal whether or not the equations are consistent with cosmological observations of dark matter and dark energy.

Crossover in Extended Newtonian Gravity Emerging from Thermodynamics

Recently, it has been discovered that a scalar field coupled to a fluid and allowed to be a thermodynamic variable in consistency with the second law of thermodynamics is only of gravity, and, accordingly, the emergence of extended Newtonian gravity has been predicted. The resulting field equation for the potential of this emergent force is nonlinear and admits the logarithmic potential as a singular solution, suggesting its relevance to the dark matter conundrum. Here, a general analysis of the nonlinear field equation is performed. It is found that the emergent force field exhibits an unsharp crossover between the 1/r and 1/r2 forces outside the fluid, depending on a spatial scale characteristic of the present theory to be observationally tested in the context of the dark matter conundrum. Then, the action functional is constructed for the potential of the emergent field, and the field energy is shown to be free from an infrared divergence. A comment is also made on the difference of the present theory to MOND (modified Newtonian dynamics).

Weyl Conformal Symmetry Model of the Dark Galactic Halo

The postulate of universal conformal (local Weyl scaling) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) generates an effective cosmological constant that fits the observed accelerating Hubble expansion for redshifts z≤1 (7.33 Gyr) accurately with only one free parameter. Growth of a galaxy is modeled by the central accumulation of matter from an enclosing empty spherical halo whose radius expands with depletion. Details of this process account for the nonclassical, radial centripetal acceleration observed at excessive orbital velocities in galactic haloes. There is no need for dark matter.

The Cusp–Core Problem in Gas-Poor Dwarf Spheroidal Galaxies

This review deals with the inconsistency of inner dark matter density profiles in dwarf galaxies, known as the cusp–core problem. In particular, we aim to focus on gas-poor dwarf galaxies. One of the most promising solutions to this cold dark matter small-scale issue is the stellar feedback, but it seems to be only designed for gas-rich dwarfs. However, in the regime of classical dwarfs, this core mechanism becomes negligible. Therefore, it is required to find solutions without invoking these baryonic processes as dark matter cores tend to persist even for these dwarfs, which are rather dark-matter-dominated. Here, we have presented two categories of solutions. One consists of creating dark matter cores from cusps within cold dark matter by altering the dark matter potential via perturbers. The second category gathers solutions that depict the natural emergence of dark matter cores in alternative theories. Given the wide variety of solutions, it becomes necessary to identify which mechanism dominates in the central region of galaxies by finding observational signatures left by them in order to highlight the true nature of dark matter.

Are Disks of Satellites Comprised of Tidal Dwarf Galaxies?

It was found that satellites of nearby galaxies can form flattened co-rotating structures called disks of satellites or planes of satellites. Their existence is not expected by the current galaxy formation simulations in the standard dark matter-based cosmology. On the contrary, modified gravity offers a promising alternative: the objects in the disks of satellites are tidal dwarf galaxies, that is, small galaxies that form from tidal tails of interacting galaxies. After introducing the topic, we review here our work on simulating the formation of the disks of satellites of the Milky Way and Andromeda galaxies. The initial conditions of the simulation were tuned to reproduce the observed positions, velocities and disk orientations of the galaxies. The simulation showed that the galaxies had a close flyby 6.8 Gyr ago. One of the tidal tails produced by the Milky Way was captured by Andromeda. It formed a cloud of particles resembling the disk of satellites at Andromeda by its size, orientation, rotation and mass. A hint of a disk of satellites was formed at the Milky Way too. In addition, the encounter induced a warp in the disk of the simulated Milky Way that resembles the real warp by its magnitude and orientation. We present here, for the first time, the proper motions of the members of the disk of satellites of Andromeda predicted by our simulation. Finally, we point out some of the remaining open questions which this hypothesis, for the formation of disks of satellites, brings up.

Review on Indirect Dark Matter Searches with Neutrino Telescopes

The search for dark matter is one of the hottest topics in Physics today. The fact that about 80% of the matter of the Universe is of unknown nature has triggered an intense experimental activity to detect this kind of matter and a no less intense effort on the theory side to explain it. Given the fact that we do not know the properties of dark matter well, searches from different fronts are mandatory. Neutrino telescopes are part of this experimental quest and offer specific advantages. Among the targets to look for dark matter, the Sun and the Galactic Center are the most promising ones. Considering models of dark matter densities in the Sun, neutrino telescopes have put the best limits on spin-dependent cross section of proton-WIMP scattering. Moreover, they are competitive in the constraints on the thermally averaged annihilation cross-section for high WIMP masses when looking at the Galactic Centre. Other results are also reviewed.

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations.

Relativistic Fractional-Dimension Gravity

This paper presents a relativistic version of Newtonian Fractional-Dimension Gravity (NFDG), an alternative gravitational model recently introduced and based on the theory of fractional-dimension spaces. This extended version—Relativistic Fractional-Dimension Gravity (RFDG)—is based on other existing theories in the literature and might be useful for astrophysical and cosmological applications. In particular, in this work, we review the mathematical theory for spaces with non-integer dimensions and its connections with the non-relativistic NFDG. The Euler–Lagrange equations for scalar fields can also be extended to spaces with fractional dimensions, by adding an appropriate weight factor, and then can be used to generalize the Laplacian operator for rectangular, spherical, and cylindrical coordinates. In addition, the same weight factor can be added to the standard Hilbert action in order to obtain the field equations, following methods used for scalar-tensor models of gravity, multi-scale spacetimes, and fractional gravity theories. We then apply the field equations to standard cosmology and to the Friedmann-Lemaître-Robertson-Walker metric. Using a suitable weight vtt, depending on the synchronous time t and on a single time-dimension parameter αt, we extend the Friedmann equations to the RFDG case. This allows for the computation of the scale factor at for different values of the fractional time-dimension αt and the comparison with standard cosmology results. Future additional work on the subject, including studies of the cosmological late-time acceleration, type Ia supernovae data, and related dark energy theory will be needed to establish this model as a relativistic alternative theory of gravity.

New Relativistic Theory for Modified Newtonian Dynamics

We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

ΛCDM and MOND: A debate about models or theory?

The debate between ΛCDM and MOND is often cast in terms of competing gravitational theories. However, recent philosophical discussion suggests that the ΛCDM-MOND debate demonstrates the challenges of multiscale modeling in the context of cosmological scales. I extend this discussion and explore what happens when the debate is thought to be about modeling rather than about theory, offering a model-focused interpretation of the ΛCDM-MOND debate. This analysis shows how a model-focused interpretation of the debate provides a better understanding of challenges associated with extension to a different scale or domain, which are tied to commitments about explanatory fit.

Testing galaxy formation and dark matter with low surface brightness galaxies

Galaxies are the basic structural element of the universe; galaxy formation theory seeks to explain how these structures came to be. I trace some of the foundational ideas in galaxy formation, with emphasis on the need for non-baryonic cold dark matter. Many elements of early theory did not survive contact with observations of low surface brightness galaxies, leading to the need for auxiliary hypotheses like feedback. The failure points often trace to the surprising predictive successes of an alternative to dark matter, the Modified Newtonian Dynamics (MOND). While dark matter models are flexible in accommodating observations, they do not provide the predictive capacity of MOND. If the universe is made of cold dark matter, why does MOND get any predictions right?

Modified Newtonian Gravity, Wide Binaries and the Tully-Fisher Relation

A recent study of a sample of wide binary star systems from the Hipparcos and Gaia catalogues has found clear evidence of a gravitational anomaly of the same kind as that appearing in galaxies and galactic clusters. Instead of a relative orbital velocity decaying as the square root of the separation, ΔV∝r−1/2, it was shown that an asymptotic constant velocity is reached for distances of order 0.1 pc. If confirmed, it would be difficult to accommodate this breakdown of Kepler’s laws within the current dark matter (DM) paradigm because DM does not aggregate in small scales, so there would be very little DM in a 0.1 pc sphere. In this paper, we propose a simple non-Newtonian model of gravity that could explain both the wide binaries anomaly and the anomalous rotation curves of galaxies as codified by the Tully-Fisher relation. The required extra potential can be understood as a Klein-Gordon field with a position-dependent mass parameter. The extra forces behave as 1/r on parsec scales and r on Solar system scales. We show that retrograde anomalous perihelion precessions are predicted for the planets. This could be tested by precision ephemerides in the near future.

Status, Challenges and Directions in Indirect Dark Matter Searches

Indirect searches for dark matter are based on detecting an anomalous flux of photons, neutrinos or cosmic-rays produced in annihilations or decays of dark matter candidates gravitationally accumulated in heavy cosmological objects, like galaxies, the Sun or the Earth. Additionally, evidence for dark matter that can also be understood as indirect can be obtained from early universe probes, like fluctuations of the cosmic microwave background temperature, the primordial abundance of light elements or the Hydrogen 21-cm line. The techniques needed to detect these different signatures require very different types of detectors: Air shower arrays, gamma- and X-ray telescopes, neutrino telescopes, radio telescopes or particle detectors in balloons or satellites. While many of these detectors were not originally intended to search for dark matter, they have proven to be unique complementary tools for direct search efforts. In this review we summarize the current status of indirect searches for dark matter, mentioning also the challenges and limitations that these techniques encounter.

Dark Matters on the Scale of Galaxies

The cold dark-matter model successfully explains both the emergence and evolution of cosmic structures on large scales and, when we include a cosmological constant, the properties of the homogeneous and isotropic Universe. However, the cold dark-matter model faces persistent challenges on the scales of galaxies. Indeed, N-body simulations predict some galaxy properties that are at odds with the observations. These discrepancies are primarily related to the dark-matter distribution in the innermost regions of the halos of galaxies and to the dynamical properties of dwarf galaxies. They may have three different origins: (1) the baryonic physics affecting galaxy formation is still poorly understood and it is thus not properly included in the model; (2) the actual properties of dark matter differs from those of the conventional cold dark matter; (3) the theory of gravity departs from General Relativity. Solving these discrepancies is a rapidly evolving research field. We illustrate some of the solutions proposed within the cold dark-matter model, and solutions when including warm dark matter, self-interacting dark matter, axion-like particles, or fuzzy dark matter. We also illustrate some modifications of the theory of gravity: Modified Newtonian Dynamics (MOND), MOdified Gravity (MOG), and f(R) gravity.

Predictions and Outcomes for the Dynamics of Rotating Galaxies

A review is given of a priori predictions made for the dynamics of rotating galaxies. One theory—MOND—has had many predictions corroborated by subsequent observations. While it is sometimes possible to offer post hoc explanations for these observations in terms of dark matter, it is seldom possible to use dark matter to predict the same phenomena.

The Scale-Invariant Vacuum (SIV) Theory: A Possible Origin of Dark Matter and Dark Energy

The Scale Invariant Vacuum (SIV) theory rests on the basic hypothesis that the macroscopic empty space is scale invariant. This hypothesis is applied in the context of the Integrable Weyl Geometry, where it leads to considerable simplifications in the scale covariant cosmological equations. After an initial explosion and a phase of braking, the cosmological models show a continuous acceleration of the expansion. Several observational tests of the SIV cosmology are performed: on the relation between H 0 and the age of the Universe, on the m − z diagram for SNIa data and its extension to z = 7 with quasars and GRBs, and on the H ( z ) vs. z relation. All comparisons show a very good agreement between SIV predictions and observations. Predictions for the future observations of the redshift drifts are also given. In the weak field approximation, the equation of motion contains, in addition to the classical Newtonian term, an acceleration term (usually very small) depending on the velocity. The two-body problem is studied, showing a slow expansion of the classical conics. The new equation has been applied to clusters of galaxies, to rotating galaxies (some proximities with Modifies Newtonian Dynamics, MOND, are noticed), to the velocity dispersion vs. the age of the stars in the Milky Way, and to the growth of the density fluctuations in the Universe. We point out the similarity of the mechanical effects of the SIV hypothesis in cosmology and in the Newtonian approximation. In both cases, it results in an additional acceleration in the direction of motions. In cosmology, these effects are currently interpreted in terms of the dark energy hypothesis, while in the Newtonian approximation they are accounted for in terms of the dark matter (DM) hypothesis. These hypotheses appear no longer necessary in the SIV context.

Excluded Volume for Flat Galaxy Rotation Curves in Newtonian Gravity and General Relativity

Using the classical vacuum solutions of Newtonian gravity that do not explicitly involve matter, dark matter, or the gravitational constant, subject to an averaging process, a form of gravity relevant to the flattening of galaxy rotation curves results. The latter resembles the solution found if the vacuum is simply assigned a gravitational field density, and a volume of the vacuum is then excluded, with no averaging process. A rationale then follows for why these terms would become important on the galactic scale. Then, a modification of General Relativity, motivated by the Newtonian solutions, that are equivalent to a charge void, is partially defined and discussed in terms of a least action principle.

A Modified Dynamical Model of Cosmology I Theory

Wheeler (1964) had formulated Mach’s principle as the boundary condition for general relativistic field equations. Here, we use this idea and develop a modified dynamical model of cosmology based on imposing Neumann boundary condition on cosmological perturbation equations. Then, it is shown that a new term appears in the equation of motion, which leads to a modified Poisson equation. In addition, a modified Hubble parameter is derived due to the presence of the new term. Moreover, it is proved that, without a cosmological constant, such a model has a late time-accelerated expansion with an equation of state converging to w < − 1 . Also, the luminosity distance in the present model is shown to differ from that of the Λ C D M model at high redshifts. Furthermore, it is found that the adiabatic sound speed squared is positive in radiation-dominated era and then converges to zero at later times. Theoretical implications of the Neumann boundary condition have been discussed, and it is shown that, by fixing the value of the conjugate momentum (under certain conditions), one could derive a similar version of modified dynamics. In a future work, we will confine the free parameters of the Neumann model based on hype Ia Supernovae, Hubble parameter data, and the age of the oldest stars.

Review of cosmic phase transitions: their significance and experimental signatures

The study of cosmic phase transitions are of central interest in modern cosmology. In the standard model of cosmology the Universe begins in a very hot state, right after at the end of inflation via the process of reheating/preheating, and cools to its present temperature as the Universe expands. Both new and existing physics at any scale can be responsible for catalyzing either first, second or cross over phase transition, which could be either thermal or non-thermal with a potential observable imprints. Thus this field prompts a rich dialogue between gravity, particle physics and cosmology. It is all but certain that at least two cosmic phase transitions have occurred-the electroweak and the QCD phase transitions. The focus of this review will be primarily on phase transitions above such scales, We review different types of phase transitions that can appear in our cosmic history, and their applications and experimental signatures in particular in the context of exciting gravitational waves, which could be potentially be constrained by LIGO/VIRGO, Kagra, LISA, and Decigo.

Gravitational Redshift Test Using Eccentric Galileo Satellites

We report on a new test of the gravitational redshift and thus of local position invariance, an integral part of the Einstein equivalence principle, which is the foundation of general relativity and all metric theories of gravitation. We use data spanning 1008 days from two satellites of Galileo, Europe's global satellite navigation system, which were launched in 2014, but accidentally delivered on elliptic rather than circular orbits. The resulting modulation of the gravitational redshift of the onboard atomic clocks allows the redshift determination with high accuracy. Additionally, specific laser ranging campaigns to the two satellites have enabled a good estimation of systematic effects related to orbit uncertainties. Together with a careful conservative modeling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be (0.19±2.48)×10^{-5} at 1 sigma, improving the best previous test by a factor 5.6. To our knowledge, this represents the first reported improvement on one of the longest standing results in experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment back in 1976.

Predictions for the Sky-Averaged Depth of the 21 cm Absorption Signal at High Redshift in Cosmologies with and without Nonbaryonic Cold Dark Matter

We consider the 21 cm absorption signal expected at high redshift in cosmologies with and without nonbaryonic cold dark matter. The expansion of the early Universe decelerates strongly with dark matter, but approximately coasts without it. This results in a different path length across the epochs when absorption is expected, with the consequence that the absorption is predicted to be a factor of ∼2 greater without dark matter than with it. Observation of such a signal would motivate consideration of extended theories of gravity in lieu of dark matter.

The Case for Nonlocal Modifications of Gravity

The huge amounts of undetected and exotic dark matter and dark energy needed to make general relativity work on large scales argue that we should investigate modifications of gravity. The only stable, metric-based and invariant alternative to general relativity is f(R) models. These models can explain primordial inflation, but they cannot dispense with either dark matter or dark energy. I advocate nonlocal modifications of gravity, not as new fundamental theories but rather as the gravitational vacuum polarization engendered by infrared quanta produced during primordial inflation. I also discuss some of the many objections which have been raised to this idea.

A Simple Model for Explaining Galaxy Rotation Curves

A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.

Interposing a Varying Gravitational Constant Between Modified Newtonian Dynamics and Weak Weyl Gravity

The Newtonian gravitational constant G obeys the dimensional relation [G][M][a] = [v]⁴, where M, a, and v denote mass, acceleration, and speed, respectively. Since the baryonic Tully-Fisher (BTF) and Faber-Jackson (BFJ) relations are observed facts, this relation implies that G a = constant. This result cannot be obtained in Newtonian dynamics which cannot explain the origin of the BTF and BFJ relations. An alternative, modified Newtonian dynamics (MOND) assumes that G = G ₀ is constant in space and derives naturally a characteristic constant acceleration a = a ₀, as well as the BTF and BFJ relations. This is overkill and it comes with a penalty: MOND cannot explain the origin of a ₀. A solid physical resolution of this issue is that G ∝ a ^-1, which implies that in lower-acceleration environments the gravitational force is boosted relative to its Newtonian value because G increases. This eliminates all problems related to MOND's empirical cutoff a ₀ and yields a quantitative method for mapping the detailed variations of G(a) across each individual galaxy as well as on larger and smaller scales. On the opposite end, the large accelerations produced by G(a) appear to be linked to the weak-field limit of the fourth-order theory of conformal Weyl gravity.

Galaxy rotation curves via conformal factors

We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in the Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other, the so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).

What makes the Universe accelerate? A review on what dark energy could be and how to test it

Explaining the origin of the acceleration of the expansion of the Universe remains as challenging as ever. In this review, we present different approaches from dark energy to modified gravity. We also emphasize the quantum nature of the problem and the need for an explanation which should violate Weinberg's no go theorem. This might involve a self-tuning mechanism or the acausal sequestering of the vacuum energy. Laboratory tests of the coupling to matter of nearly massless scalar fields, which could be one of the features required to explain the cosmic acceleration, are also reviewed.

Surrounding matter theory

S.M.T. (Surrounding Matter Theory), an alternative theory to dark matter, is presented. It is based on a modification of Newton's law. This modification is done by multiplying a Newtonian potential by a given factor, which is varying with local distribution of matter, at the location where the gravitational force is exerted. With this new equation the model emphasizes that a gravitational force is roughly inversely proportional to mass density at the location where this force is applied. After presentation of the model, its dynamic is quickly applied to cosmology and galaxy structure. Some possible caveats of the model are identified. But the simple mechanism described above suggests the idea of a straightforward solution to the following issues: virial theorem mystery, the bullet cluster (“1E 0657-56” galaxy clusters) issue, the strong relative velocity of its subclusters, the value of cosmological critical density, the fine tuning issue, and expansion acceleration. Nucleosynthesis is not explained and would require a different model for radiation era. But a de Sitter Universe is predicted, this means that the spatial curvature, K, is 0, and today's deceleration parameter, q, is -1. The predicted time since last scattering is 68 h-1Gyr. With this value SMT explains heterogeneities of large scale structure and galaxy formation. Each kind of experimental speed profiles are retrieved by a simulation of a virtual galaxy. In the simulations, ring galaxies are generated by SMT dynamic itself, without the help of any particular external event. Those studies give motivation for scientific comparisons with experimental data.

Dynamical boson stars

The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called geons, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name boson stars. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.

Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves

In the weak-field limit of general relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of general relativity are supported by the observation of ultrahigh-energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of modified Newtonian dynamics, namely, the generalized Einstein-aether theory and bimetric modified Newtonian dynamics, display fatal inconsistencies with these observations.

Testing General Relativity with Stellar Orbits around the Supermassive Black Hole in Our Galactic Center

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.

Universal Modified Newtonian Dynamics Relation between the Baryonic and "Dynamical" Central Surface Densities of Disc Galaxies

I derive a new modified Newtonian dynamics (MOND) relation for pure-disc galaxies: The "dynamical" central surface density, Σ_{D}^{0}, deduced from the measured velocities, is a universal function of only the true, "baryonic'' central surface density, Σ_{B}^{0}: Σ_{D}^{0}=Σ_{M}S(Σ_{B}^{0}/Σ_{M}), where Σ_{M}≡a_{0}/2πG is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. S(y) is derived: S(y)=∫_{0}^{y}ν(y^{'})dy^{'}, with ν(y) being the interpolating function of the theory. The relation aymptotes to Σ_{D}^{0}=Σ_{B}^{0} for Σ_{B}^{0}≫Σ_{M}, and to Σ_{D}^{0}=(4Σ_{M}Σ_{B}^{0})^{1/2} for Σ_{B}^{0}≪Σ_{M}. This study was prompted by the recent finding of a correlation between related attributes of disc galaxies by Lelli et al.. The MOND central-surface-densities relation agrees very well with these results.

Satellite Test of the Equivalence Principle as a Probe of Modified Newtonian Dynamics

The proposed satellite test of the equivalence principle (STEP) will detect possible violations of the weak equivalence principle by measuring relative accelerations between test masses of different composition with a precision of one part in 10^{18}. A serendipitous by-product of the experimental design is that the absolute or common-mode acceleration of the test masses is also measured to high precision as they oscillate along a common axis under the influence of restoring forces produced by the position sensor currents, which in drag-free mode lead to Newtonian accelerations as small as 10^{-14}  g. This is deep inside the low-acceleration regime where modified Newtonian dynamics (MOND) diverges strongly from the Newtonian limit of general relativity. We show that MOND theories (including those based on the widely used "n family" of interpolating functions as well as the covariant tensor-vector-scalar formulation) predict an easily detectable increase in the frequency of oscillations of the STEP test masses if the strong equivalence principle holds. If it does not hold, MOND predicts a cumulative increase in oscillation amplitude which is also detectable. STEP thus provides a new and potentially decisive test of Newton's law of inertia, as well as the equivalence principle in both its strong and weak forms.

Gravitation-Wave Emission in Shift-Symmetric Horndeski Theories

Gravity theories beyond general relativity typically predict dipolar gravitational emission by compact-star binaries. This emission is sourced by "sensitivity" parameters depending on the stellar compactness. We introduce a general formalism to calculate these parameters, and show that in shift-symmetric Horndeski theories stellar sensitivities and dipolar radiation vanish, provided that the binary's dynamics is perturbative (i.e., the post-Newtonian formalism is applicable) and cosmological-expansion effects can be neglected. This allows one to reproduce the binary-pulsar-observed orbital decay.