Observational scalings testing modified gravity

We consider different observational effects to test a modified gravity approach involving the cosmological constant in the common description of dark matter and dark energy.We obtain upper limits for the cosmological constant by studying the scaling relations for 12 nearby galaxy clusters, the radiated power from gravitational waves and the Tully-Fisher relation for super spiral galaxies. Our estimations reveal that, for all these cases, the upper limits for Λ are consistent with its actual value predicted by cosmological observations.

Hints for a Gravitational Transition in Tully–Fisher Data

We use an up-to-date compilation of Tully–Fisher data to search for transitions in the evolution of the Tully–Fisher relation. Using an up-to-date data compilation, we find hints at ≈3σ level for a transition at critical distances Dc≃9 Mpc and Dc≃17 Mpc. We split the full sample in two subsamples, according to the measured galaxy distance with respect to splitting distance Dc, and identify the likelihood of the best-fit slope and intercept of one sample with respect to the best-fit corresponding values of the other sample. For Dc≃9 Mpc and Dc≃17 Mpc, we find a tension between the two subsamples at a level of Δχ2>17(3.5σ). Using Monte Carlo simulations, we demonstrate that this result is robust with respect to random statistical and systematic variations of the galactic distances and is unlikely in the context of a homogeneous dataset constructed using the Tully–Fisher relation. If the tension is interpreted as being due to a gravitational strength transition, it would imply a shift in the effective gravitational constant to lower values for distances larger than Dc by ΔGG≃−0.1. Such a shift is of the anticipated sign and magnitude but at a somewhat lower distance (redshift) than the gravitational transition recently proposed to address the Hubble and growth tensions (ΔGG≃−0.1 at the transition redshift of zt≲0.01 (Dc≲40 Mpc)).

Rotation curves and scaling relations of extremely massive spiral galaxies

We study the kinematics and scaling relations of a sample of 43 giant spiral galaxies that have stellar masses exceeding 1011 M⊙ and optical discs up to 80 kpc in radius. We use a hybrid 3D-1D approach to fit 3D kinematic models to long-slit observations of the Hα-$\rm{[N\, \small {II}]}$ emission lines and we obtain robust rotation curves of these massive systems. We find that all galaxies in our sample seem to reach a flat part of the rotation curve within the outermost optical radius. We use the derived kinematics to study the high-mass end of the two most important scaling relations for spiral galaxies: the stellar/baryonic mass Tully-Fisher relation and the Fall (mass-angular momentum) relation. All galaxies in our sample, with the possible exception of the two fastest rotators, lie comfortably on both these scaling relations determined at lower masses, without any evident break or bend at the high-mass regime. When we combine our high-mass sample with lower-mass data from the Spitzer Photometry & Accurate Rotation Curves catalog, we find a slope of α = 4.25 ± 0.19 for the stellar Tully-Fisher relation and a slope of γ = 0.64 ± 0.11 for the Fall relation. Our results indicate that most, if not all, of these rare, giant spiral galaxies are scaled up versions of less massive discs and that spiral galaxies are a self-similar population of objects up to the very high-mass end.

Gravitational lensing study of cold dark matter-led galactic halo

In this work, the spacetime geometry of the halo region in spiral galaxies is obtained considering the observed flat galactic rotation curve feature, invoking the Tully–Fisher relation and assuming the presence of cold dark matter in the galaxy. The gravitational lensing analysis is performed treating the so-obtained spacetime as a gravitational lens. It is found that the aforementioned spacetime as the gravitational lens can consistently explain the galaxy–galaxy weak gravitational lensing observations and the lensing observations of the well-known Abell 370 and Abell 2390 galaxy clusters.

Dynamical Gravity, Expanding Space and Stretching Gedesics

The gravitational natures of phenomena separately attributed to dark matter and dark energy and challenges encountered in identifying such sources motivate enquiry into the capabilities of the field, itself, to generate such phenomena. It is found that, in curvature-free Friedmann-Lemaître-Robertson-Walker and gravitationally perturbed Robertson-Walker spacetimes, gravity has an equation of state parameter w = -1 and negative pressures. Expanding space is proposed as the form of a growing cosmic gravitational field. The gravitational-spatial expansion is locally isobaric. Barotropic gravitational dynamics yield the Hubble-Lemaître law. The expansion results from the induction of gravity by matter, radiation and by itself. Gravitational auto-induction is a dynamical feedback process that produces an isotropic spatial expansion with an invariant Hubble parameter like a ‘cosmological constant’ of density 2H2/κ or, equivalently, of a density parameter of 2/3. The Planck 2018 result is moderately higher at about the 2.5/σ level. A new expression of the Hubble parameter in the late homogeneous universe is obtained. The growth of the field isotropically stretches geodesics. In homogeneous regions, this manifests as the Hubble acceleration of bodies and the redshifting of radiation attributed to dark energy. Geodesics may depend on gravitational energy density that retains its values at comoving locations. In inhomogeneous regions, such retentions lead to similar retentions of circular speeds and deflection angles - geodesic stretching - attributed to clustering dark matter. The baryonic Tully-Fisher relation is explained. Dependence of geodesics on gravitational energy explains tidal interactions as being inertial gravitational processes.

Square–torsion gravity, dark matter halos and the baryonic Tully–Fisher relation

Square–torsion gravity is applied to the long standing dark matter problem. In this context the theory reduces to General Relativity complemented by a dark stress–energy tensor due to the torsion of spacetime and is studied under the simplifying assumption of spherical symmetry. The dark stress–energy tensor satisfies an anisotropic structure equation. In vacuum this is equivalent to a wave equation with sources. A natural class of exact solutions is found which explicitly perturbs any seed spacetime metric by a conformal factor. This leads to the concept of dark coating. Static solutions are then used to construct structures that model dark matter halos surrounding baryonic bodies. In the Newtonian régime the baryonic mass $$m_b$$ m b and the flat rotation curve velocity $$v_f$$ v f are related by the baryonic Tully–Fisher relation$$m_b\propto v_f^4$$ m b ∝ v f 4 , a hitherto purely empirical result. The example of a dark halo on the Schwarzschild geometry is made as a toy model for a galaxy. Qualitative an quantitative features of galactic rotation curves are recovered. In this setting, a boundary of staticity is found, called torsion sphere, placed between the photon sphere and the event horizon. The phenomenon of dark radiation is briefly exposed.

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.

A black hole inside dark matter and the rotation curves of galaxies

In this paper, we find a four-dimensional metric for a large black hole immersed in dark matter. Specifically, we look for and find a static spherically symmetric black hole solution to the Einstein equations which gives, in the Newtonian limit, the rotation curves of galaxies, including the flat region and the baryonic Tully–Fisher relation, and which has a regular horizon. We obtain as well the energy–momentum tensor of the dark matter sourcing this spacetime and it turns, in special, to satisfy the four energy conditions (dominant, weak, null and strong) everywhere outside the horizon. This black-hole-dark-matter system represents a successful simplified model for galaxies, opens a new area for exploring the relativistic regime of dark matter, and shows that the theory of General Relativity together with dark matter can account for the rotation curves of galaxies.