Interpretation of Rotation Curves of Spiral Galaxies in Modified Teleparallel Gravity

There is a significant difference between the calculation based on the theory of general relativity and observation of rotation curves of spiral galaxies. To describe this discrepancy, two distinct theories have been proposed so far： existence of dark matter and modification of underlying gravitational theory. In the absence of dark matter, it is assumed that the theory of general relativity on galactic scales needs to be modified. This letter is devoted to explaining this difference in a modified teleparMIeI gravity. We show that modified teleparallel gravity favors flatness of rotation curves of spiral galaxies much in the same way as observation shows.     

Comparing dark matter models,modified Newtonian dynamics and modified gravity in accounting for galaxy rotation curves

We compare six models(including the baryonic model,two dark matter models,two modified Newtonian dynamics models and one modified gravity model) in accounting for galaxy rotation curves.For the dark matter models,we assume NFW profile and core-modified profile for the dark halo,respectively.For the modified Newtonian dynamics models,we discuss Milgrom's MOND theory with two different interpolation functions,the standard and the simple interpolation functions.For the modified gravity,we focus on Moffat's MSTG theory.We fit these models to the observed rotation curves of 9 high-surface brightness and 9 low-surface brightness galaxies.We apply the Bayesian Information Criterion and the Akaike Information Criterion to test the goodness-of-fit of each model.It is found that none of the six models can fit all the galaxy rotation curves well.Two galaxies can be best fitted by the baryonic model without involving nonluminous dark matter.MOND can fit the largest number of galaxies,and only one galaxy can be best fitted by the MSTG model.Core-modified model fits about half the LSB galaxies well,but no HSB galaxies,while the NFW model fits only a small fraction of HSB galaxies but no LSB galaxies.This may imply that the oversimplified NFW and core-modified profiles cannot model the postulated dark matter haloes well.     

Modified Newton's gravity in Finsler space as a possible alternative to dark matter hypothesis

A modified Newton's gravity is obtained as the weak field approximation of the Einstein's equation in Finsler space. It is found that a specified Finsler structure makes the modified Newton's gravity equivalent to the modified Newtonian dynamics (MOND). In the framework of Finsler geometry, the flat rotation curves of spiral galaxies can be deduced naturally without invoking dark matter.     

The Carmeli Metric Correctly Describes Spiral Galaxy Rotation Curves

The metric by Carmeli accurately produces the Tully-Fisher type relation in spiral galaxies, a relation showing the fourth power of the rotation speed proportional to the mass of the galaxy. And therefore it is claimed that it is also no longer necessary to invoke dark matter to explain the anomalous dynamics in the arms of spiral galaxies. An analysis is presented here showing Carmeli’s 5 dimensional space-time-velocity metric can also indeed describe the rotation curves of spiral galaxies based on the properties of the metric alone.     

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

An explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy in the context of gravitation. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode—the transverse-tensor graviton—the metric comprises a compression mode—the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in empty space, except possibly for the origin, is studied. A three-parameter solution describing a new static space structure—the dark lacuna—is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and putative asphericity or rotation.     

Balance of dark and luminous mass in rotating galaxies

A fine balance between dark and baryonic mass is observed in spiral galaxies. As the contribution of the baryons to the total rotation velocity increases, the contribution of the dark matter decreases by a compensating amount. This poses a fine-tuning problem for galaxy formation models, and may point to new physics for dark matter particles or even a modification of gravity.     

Extended theories of gravity and their cosmological and astrophysical applications

Astrophysical observations are pointing out huge amounts of “dark matter” and “dark energy” needed to explain the observed large scale structure and cosmic dynamics. The emerging picture is a spatially flat, homogeneous Universe undergoing the today observed accelerated phase. Despite of the good quality of astrophysical surveys, commonly addressed as Precision Cosmology, the nature and the nurture of dark energy and dark matter, which should constitute the bulk of cosmological matter-energy, are still unknown. Furthermore, up to now, no experimental evidence has been found, at fundamental level, to explain such mysterious components. The problem could be completely reversed considering dark matter and dark energy as “shortcomings” of General Relativity in its simplest formulation (a linear theory in the Ricci scalar R, minimally coupled to the standard perfect fluid matter) and claiming for the “correct” theory of gravity as that derived by matching the largest number of observational data, without imposing any theory a priori. As a working hypothesis, accelerating behavior of cosmic fluid, large scale structure, potential of galaxy clusters, rotation curves of spiral galaxies could be reproduced by means of extending the standard theory of General Relativity. In other words, gravity could acts in different ways at different scales and the above “shortcomings” could be due to incorrect extrapolations of the Einstein gravity, actually tested at short scales and low energy regimes. After a survey of what is intended for Extended Theories of Gravity in the so called “metric” and “Palatini” approaches, we discuss some cosmological and astrophysical applications where the issues related to the dark components are addressed by enlarging the Einstein theory to more general f (R) Lagrangians, where f (R) is a generic function of Ricci scalar R, not assumed simply linear. Obviously, this is not the final answer to the problem of “dark-components” but it can be considered as an operative scheme whose aim is to avoid the addition of unknown exotic ingredients to the cosmic pie.     

Impact of a global quadratic potential on galactic rotation curves

We present a conformal gravity fit to the 20 largest of a sample of 110 spiral galaxies. We identify the presence of a universal quadratic potential V(κ)(r)=-κc2r2/2 with κ=9.54×10??? cm?2 induced by cosmic inhomogeneities. When V(κ)(r) is taken in conjunction with both a universal linear potential V(γ?)(r)=γ?c2r/2 with γ?=3.06×10?3? cm?1 generated by the homogeneous cosmic background and the contribution generated by the local luminous matter in galaxies, the theory then accounts for the rotation curve systematics observed in the entire 110 galaxies, without the need for any dark matter whatsoever. Our study suggests that using dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With V(κ)(r) being negative, galaxies can only support bound orbits up to distances of order γ?/κ=100kpc, with global physics imposing a limit on the size of galaxies.     

Can cosmic structure form without dark matter?

One of the prime pieces of evidence for dark matter is the observation of large overdense regions in the Universe. To account for this observation, perturbations had to have grown since recombination by a factor greater than (1+z*) approximately 1180 where z* is the epoch of recombination. This enhanced growth does not happen in general relativity, and so dark matter is needed in the standard theory. We show here that enhanced growth can occur in alternatives to general relativity, in particular, in Bekenstein's relativistic version of modified Newtonian dynamics.     

Geometrical aspects on the dark matter problem

In the present paper we apply Nash’s theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space–time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements.     

LETTER: Gauge Choice and Geodetic Deflection in Conformal Gravity

Conformal gravity has been proposed as an alternative theory of gravity which can account for flat galactic rotation curves without recourse to copious quantities of dark matter. However it was shown that for the usual choice of the metric, the result is catastrophic for null or highly relativistic geodesics, the effect is exactly the opposite yielding an effective repulsion and less deflection in this case. It is the point of this paper, that any result for massive geodesics depends on the choice of conformal gauge, in contradistinction to the case of null geodesics. We show how it is possible to choose the gauge so that the theory is attractive for all geodesics.     

大尺度有效引力的E(2)规范理论模型

微波背景辐射的低l极矩的各向异性可能不能用微波背景辐射静止系boost到本动参考系来解释,我们推断boost对称性在宇宙学尺度上缺失,又由于单纯结合广义相对论和物质结构的标准模型不能解释星系以上尺度的引力现象,需要引入暗物质和暗能量.而迄今为止所有寻找暗物质粒子的实验给出的都是否定结果,暗能量的本质更是一个谜.因此,我们假设洛伦兹对称性是从星系以上尺度开始部分破缺,以非常狭义相对论对称群E(2)为例,用E(2)规范理论来构造大尺度有效引力理论,并分析了此规范理论的自洽性.从这些讨论中发现,当物质源即使为普通标量物质时,contortion也一般非零,非零contortion的存在会贡献一个等效能量动量张量的分布,它可能对暗物质效应给出至少部分的贡献.我们从对称性出发修改引力,有别于其他的修改引力理论.     

What is modified gravity and how to differentiate it from particle dark matter?

An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the curvature invariants is equivalent to general relativity in the presence of new fields that are gravitationally coupled to the energy-momentum tensor. We show that they can be shifted into a new energy-momentum tensor. There is no a priori reason to identify these new fields as gravitational degrees of freedom or matter fields. This leads to an equivalence between dark matter particles gravitationally coupled to the standard model fields and modified gravity theories designed to account for the dark matter phenomenon. Due to this ambiguity, it is impossible to differentiate experimentally between these theories and any attempt of doing so should be classified as a mere interpretation of the same phenomenon.     

Brief History of a Relativistic Century

More than one century is passed by the publication of special relativity and few less by the birth of general relativity. Despite the great experimental successes of these theories, the study of the universe, is plagued by numerous unsolved problems. For example one of the most problems in cosmology is the cosmological constant, which governs the expansion of the universe, also known as dark energy. A substantial portion, about 60%, of the mass-energy in the universe is in a form of mysterious energy that is pushing the cosmos apart at an accelerating rate. What is this energy, and where does it come from? Cosmologists have no real idea. Although given a similar name, there is another problem in cosmology, the so-called dark matter, which is actually unrelated to dark energy, except insofar as they involve things we don’t understand. About 90% of the mass in the universe is in an apparently invisible form of matter that we call dark matter. This dark matter can only be measured by the gravitational pull it has on objects around it, and all galaxies we observe contain large halos of it, often extending for hundreds of thousands of light years beyond the edge of luminous matter. Is this dark matter actual matter, such as weakly interacting massive particles, or perhaps it is just an observational artifact caused by an improper theory of gravity? Another mystery is why there is so much more matter than antimatter in the universe. According to physical theories, these forms of matter are essentially equivalent, but conventional matter is observed in much greater abundances than antimatter. In this paper we summarily introduce the principal alternative theories proposed during one century of relativity.     

Neutron stars in Scalar-Tensor-Vector Gravity

Scalar-Tensor-Vector Gravity (STVG), also referred as Modified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to describe Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman–Oppenheimer–Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.     

Periodic relativity: basic framework of the theory

An alternative gravity theory is proposed which does not rely on Riemannian geometry and geodesic trajectories. The theory named periodic relativity (PR) does not use the weak field approximation and allows every two body system to deviate differently from the flat Minkowski metric. PR differs from general relativity (GR) in predictions of the proper time intervals of distant objects. PR proposes a definite connection between the proper time interval of an object and gravitational frequency shift of its constituent particles as the object travels through the gravitational field. PR is based on the dynamic weak equivalence principle which equates the gravitational mass with the relativistic mass. PR provides very accurate solutions for the Pioneer anomaly and the rotation curves of galaxies outside the framework of general relativity. PR satisfies Einstein’s field equations with respect to the three major GR tests within the solar system and with respect to the derivation of Friedmann equation in cosmology. This article defines the underlying framework of the theory.     

Kerr–Newman-AdS black hole surrounded by perfect fluid matter in Rastall gravity

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to \(T^{\mu \nu }_{~~;\mu }=\lambda R^{,\nu }\). In this work, we derive the Kerr–Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman–Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy (\(\omega =-\,2/3\)) and the perfect fluid dark matter (\(\omega =-\,1/3\)). Firstly, the Rastall parameter \(\kappa \lambda \) could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity \(\alpha \), which depends on the black hole mass M and the Rastall parameter \(\kappa \lambda \). Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.     

Making the Case for Conformal Gravity

We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity being obtained because the theory is a PT symmetric rather than a Hermitian theory. We show that in the theory there can be no a priori classical curvature, with all curvature having to result from quantization. In the conformal theory gravity requires no independent quantization of its own, with it being quantized solely by virtue of its being coupled to a quantized matter source. Moreover, because it is this very coupling that fixes the strength of the gravitational field commutators, the gravity sector zero-point energy density and pressure fluctuations are then able to identically cancel the zero-point fluctuations associated with the matter sector. In addition, we show that when the conformal symmetry is spontaneously broken, the zero-point structure automatically readjusts so as to identically cancel the cosmological constant term that dynamical mass generation induces. We show that the macroscopic classical theory that results from the quantum conformal theory incorporates global physics effects that provide for a detailed accounting of a comprehensive set of 138 galactic rotation curves with no adjustable parameters other than the galactic mass to light ratios, and with the need for no dark matter whatsoever. With these global effects eliminating the need for dark matter, we see that invoking dark matter in galaxies could potentially be nothing more than an attempt to describe global physics effects in purely local galactic terms. Finally, we review some recent work by ’t Hooft in which a connection between conformal gravity and Einstein gravity has been found.     

Spiral galaxies rotation curves with a logarithmic corrected newtonian gravitational potential

We analyze the rotation curves of 10 spiral galaxies with a newtonian potential corrected with an extra logarithmic term. The logarithmic correction can have its origin from fundamental frameworks, like string theories or effective models of gravity due to quantum effects. There is also a connection with some toy models resulting from TeVeS. We represent the spiral galaxies as a thin disk. There is a new constant associated with the extra term in the potential. The rotation curve of the chosen sample of spiral galaxies is well reproduced for a narrow range of the new constant. The compatibility of this correction with local physics is discussed.     

A Kinetic Theory Approach to Quantum Gravity

We describe a kinetic theory approach to quantum gravity by which we mean a theory of the microscopic structure of space-time, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotty poles: quantum matter field on the right and space-time on the left. Each rung connecting the corresponding knots represents a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein–Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: (1) deduce the correlations of metric fluctuations from correlation noise in the matter field; (2) reconstituting quantum coherence—this is the reverse of decoherence—from these correlation functions; and (3) use the Boltzmann–Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding space-time counterparts. This will give us a hierarchy of generalized stochastic equations—call them the Boltzmann–Einstein hierarchy of quantum gravity—for each level of space-time structure, from the the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).