Dark Matter in the Standard Model Extension in Non-Commutative Geometry (NCG)

It is for the most part expected that dark matter is important to clarify the rotation of the galaxy, It has effectively been seen that the non-commutative geometry background can achieve this objective similarly. The objective of this study is to investigate a relationship between non-commutative geometry and certain aspect of dark matter. We are relying on a basic mathematical expression argument that indicates that the appearance of dark matter in galaxies and galaxy clusters with regard to flat rotation curves is similarly a result of non commutative geometry.

Can a tensorial analogue of gravitational force explain away the galactic rotation curves without dark matter?

The dark matter problem is one of the most pressing problems in modern physics. As there is no well-established claim from a direct detection experiment supporting the existence of the illusive dark matter that has been postulated to explain the flat rotation curves of galaxies, and since the whole issue of an alternative theory of gravity remains controversial, it may be worth to reconsider the familiar ground of general relativity (GR) itself for a possible way out. It has recently been discovered that a skew-symmetric rank-three tensor field — the Lanczos tensor field — that generates the Weyl tensor differentially, provides a proper relativistic analogue of the Newtonian gravitational force. By taking account of its conformal invariance, the Lanczos tensor leads to a modified acceleration law which can explain, within the framework of GR itself, the flat rotation curves of galaxies without the need for any dark matter whatsoever.

Is non-particle dark matter equation of state parameter evolving with time?

Recently, the so-called Hubble Tension, i.e. the mismatch between the local and the cosmological measurements of the Hubble parameter, has been resolved when non-particle dark matter is considered which has a negative equation of state parameter ($$\omega \approx -\,0.01$$ ω ≈ - 0.01 ). We investigate if such a candidate can successfully describe the galactic flat rotation curves. It is found that the flat rotation curve feature puts a stringent constraint on the dark matter equation of state parameter $$\omega $$ ω and $$\omega \approx -\,0.01$$ ω ≈ - 0.01 is not consistent with flat rotational curves, observed around the galaxies. However, a dynamic $$\omega $$ ω of non-particle dark matter may overcome the Hubble tension without affecting the flat rotation curve feature.

Galactic Orbital Effects on Pulsar Timing

In the currently accepted paradigm, dark matter is hypothesized as an explanation of the flat rotation curves of galaxies under the assumption of virialized orbits. The use of millisecond pulsar timing as a probe of Galactic dark matter content is explored as a means of relaxing this assumption. A method of inference of the Galactic potential using the frequency derivative $\dot{\nu }$ is produced, and an estimate for a virialized Galactic rotation curve is given through direct observation of acceleration. The data set used includes 210 pulsars with known $\dot{\nu }$ and astrometric properties, a subset of which also have measured $\ddot{\nu }$. In principle, this enables the exploration of kinematic effects, but in practice, $\ddot{\nu }$ values are found to be too imprecise at present to adequately constrain radial velocities of pulsars. Additionally, surface magnetic field strengths are inferred from $\dot{\nu }$ and the magnetic spin-down contribution to $\ddot{\nu }$ is estimated. For several pulsars the radial velocity is known, and the kinematic contribution to $\ddot{\nu }$ is estimated accordingly. The binary orbital periods of PSR J1713+0747 and other binary pulsars are also used to constrain Galactic mass density models.

Flat Rotation Curves of z ∼ 1 Star-Forming Galaxies

We investigate the shape of the Rotation Curves (RCs) of z ∼ 1 Star-Forming Galaxies (SFGs) and compare them with local SFGs. For this purpose, we have used 344 galaxies from the K-band Multi-Object Spectrograph (KMOS) for Redshift One Spectroscopic Survey (KROSS). This sample covers the redshift range 0.57 ≤ z ≤ 1.04, the effective radii 0.69 ≤ Re [kpc] ≤ 7.76, and the stellar masses 8.7 ≤ log (M* [M⊙]) ≤ 11.32. Using 3DBAROLO, we extract the Hα kinematic maps and corresponding RCs. The main advantage of 3DBAROLO is that it incorporates the beam smearing in the 3D observational space, which provide us with the intrinsic rotation velocity even in the low spatial resolution data. We have corrected the RCs for pressure support, which seems to be a more dominant effect than beam smearing in high-z galaxies. Only a combination of the three techniques (3D-kinematic modelling + 3D-beam smearing correction + pressure gradient correction ) yields the intrinsic RC of an individual galaxy. Further, we present the co-added and binned RCs constructed out of 256 high-quality objects. We do not see any change in the shape of RCs with respect to the local SFGs. Moreover, we notice a significant evolution in the stellar-disk length (RD) of the galaxies as a function of their circular velocity. Therefore, we conclude that the stellar disk of SFGs evolves over cosmic time (from z ∼ 1) while the total mass stays constant (within ∼20 kpc).

On the plausible origins of the spiral character of galaxies

We here-in demonstrate that the proposed hitherto unknown gravitomagnetic dark-force that hypothetically explains the Flat Rotation Curves of Spiral Galaxies — this same force, explains very well, the logarithmic and as-well, the barred spiral shapes of spiral galaxies. That is, much in line with Edward Arthur Milne (1896-1950)’s 1946 ideas — albeit, on a radically and asymptotically different philosophical train of thought, the galactic disk is here assumed to be in a state of free-fall around the central bulge with the hypothetical gravitomagnetic dark-force being the dominant force determining all gravity-related dynamics of the disk, thus leading to logarithmic and barred spiral orbits, hence the shape of spiral galaxies.

MONG: An extension to Galaxy Clusters

The presence of dark matter, though well established by indirect evidence is yet to be observed directly. Various dark matter detection experiments running for several years have yielded no positive results so far. In view of these negative results, we had earlier proposed alternate models by postulating a minimum gravitational field strength (minimum curvature) and also a minimum acceleration. These postulates led to the modified Newtonian dynamics and modified Newtonian gravity (MONG). The observed flat rotation curves of galaxies had also been accounted for through these postulates. Here we extend these postulates to galaxy clusters and model the dynamical velocity-distance curves for such large-scale structures. The velocity-distance curve of the Virgo cluster, plotted with this model is found to be in accordance with that observed.

A Unified Electro-Gravity Theory to Model Spiral Galaxies without Dark Matter

A unified electro-gravity (UEG) theory, which has been successfully used for modeling an elementary particle, is applied in this paper to model gravitation in spiral galaxies. The new UEG model would explain the "flat rotation curves'' commonly observed in the spiral galaxies, without need for any hypothetical dark matter. The UEG theory is implemented in a somewhat different manner for a spiral galaxy, as compared to the simple application of the UEG theory to an elementary particle. This is because the spiral galaxy, unlike the elementary particle, is not spherically symmetric. The UEG constant $\gamma$, required in the new model to support the galaxies' flat rotation speeds, is estimated using measured data from a galaxy survey, as well as for a selected galaxy for illustration. The estimates are compared with the $\gamma$ derived from the UEG model of an elementary particle. The UEG model for the galaxy is shown to explain the empirical Tully-Fisher Relationship (TFR), is consistent with the Modified Newtonian Dynamics (MOND), and is also independently supported by measured trends of galaxy thickness with surface brightness and rotation speed. The UEG theory may similarly be extended to emulate the hypothetical dark matter in galaxy clusters as well as in cosmology.

Intrinsic Nature of Dark Matter in the Galactic Halo

We obtain more straightforwardly the main intrinsic features of dark matter distribution in the halos of galaxies by considering the spherically symmetric space-time, which satisfies the flat rotational curve condition, and the geometric equation of state resulting from the modified gravity theory. In order to measure the equation of state for dark matter in the galactic halo, we provide a general formalism taking into account the modified f(X) gravity theories. Here, f(X) is a general function of X∈{R,G,T}, where R,G and T are the Ricci scalar, the Gauss-Bonnet scalar and the torsion scalar, respectively. These theories yield that the flat rotation curves appear as a consequence of the additional geometric structure accommodated by those of modified gravity theories. Constructing a geometric equation of state wX≡pX/ρX and inspiring by some values of the equation of state for the ordinary matter, we infer the properties of dark matter in galactic halos of galaxies.