Distinct Acceleration Relations of Galaxies and Galaxy Clusters from Hyperconical Modified Gravity

Recently, the discovery of the radial acceleration relation (RAR) in galaxies has been regarded as an indirect support of alternative theories of gravity such as modified Newtonian dynamics (MOND) and modified gravity. This relation indicates a tight correlation between dynamical mass and baryonic mass in galaxies with different sizes and morphology. However, if the RAR relation is scale independent and could be explained by alternative theories of gravity, this relation should be universal and true for galaxy clusters as well. In this article, by using the X-ray data of a sample of galaxy clusters, we investigate if there exists any tight correlation between dynamical mass and baryonic mass in galaxy clusters, assuming hot gas mass distribution almost representing baryonic distribution and that the galaxy clusters are virialized. We show that the resulting RAR of 52 non-cool-core galaxy clusters scatters in a large parameter space, possibly due to our simplifying assumptions and unclear matter content in galaxy clusters. This might indicate that the RAR is unlikely to be universal and scale independent.

Recent observations of anomalous line-of-sight velocity dispersions of two ultra-diffuse galaxies (UDGs) provide a stringent test for modified gravity theories. While NGC 1052-DF2 exhibits an extremely low dispersion value ($\sigma \sim 7.8_{-2.2}^{+5.6}$ km/s), the reported dispersion value for NGC 1052-DF44 is quite high ($\sigma \sim 41.0 \pm 8$ km/s). For DF2, the dynamical mass is almost equal to the luminous mass suggesting the galaxy have little to no `dark matter' in $\Lambda$CDM whereas DF4 requires a dynamical mass-to-light ratio of $\sim 30$ making it to be almost entirely consists of dark matter. It has been claimed that both these galaxies, marking the extreme points in terms of the estimated dynamical mass-to-light ratio among known galaxies, would be difficult to explain in modified gravity scenarios. Extending the analysis presented in \cite{islam2019modified}, we explore the dynamics of DF2 and DF44 within the context of three popular alternative theories of gravity [Modified Newtonian Dynamics (MOND), Weyl Conformal gravity and Modified gravity (MOG)] and examine their viability against the dispersion data of DF2 and DF44. We further show that the galactic `Radial Acceleration Relation' (RAR) is consistent with DF44 dispersion data but not with DF2.

The dynamical mass of galaxies and the Newtonian acceleration generated from the baryons have been found to be strongly correlated. This correlation is known as 'Mass-Discrepancy Acceleration Relation' (MDAR). Further investigations have revealed a tighter relation - 'Radial Acceleration Relation' (RAR) - between the observed total acceleration and the (Newtonian) acceleration produced by the baryons. So far modified gravity theories have remained more successful than $\Lambda$CDM to explain these relations. However, a recent investigation has pointed out that, when RAR is expressed as a difference between the observed acceleration and the expected Newtonian acceleration due to baryons (which has been called the 'Halo acceleration relation or HAR'), it provides a stronger test for modified gravity theories and dark matter hypothesis. Extending our previous work \citep{kt2018}, we present a case study of modified gravity theories, in particular Weyl conformal gravity and Modified Newtonian Dynamics (MOND), using recent inferred acceleration data for the Milky Way. We investigate how well these theories of gravity and the RAR scaling law can explain the current observation.

The Aether-Scalar-Tensor (AeST) theory is an extension of General Relativity (GR) which can support Modified Newtonian Dynamics (MOND) behaviour in its staticweak-field limit, and cosmological evolution resembling ΛCDM.We consider static spherically symmetric weak-field solutions in this theory and show that the resulting equations can be reduced to a single equation for the gravitational potential.The reduced equation has apparent isolated singularities at the zeros of the derivative of the potential and we show how these are removedby evolving, instead, the canonical momentum of the corresponding Hamiltonian system that we find. We construct solutions in three cases: (i) in vacuum outside a bounded spherical object, (ii) within an extended prescribed source, and (iii) for an isothermal gas in hydrostatic equilibrium, serving as a simplified model for galaxy clusters.We show that the oscillatory regime that follows the Newtonian and MOND regimes, obtained in previous works in the vacuum case, also persists for isothermal spheres, and we show that the gas density profiles in AeST can become more compressed than their Newtonian or MOND counterparts.We construct the Radial Acceleration Relation (RAR) in AeST for isothermal spheres and find that it can display a peak, an enhancement with respect to the MOND RAR, at an acceleration range determined by the value of the AeST weak-field mass parameter, the mass of the system and the boundary value of the gravitational potential. For lower accelerations, the AeST RAR drops below the MOND expectation,as if there is a negative mass density. Similar observational features of the galaxy cluster RAR have been reported. This illustrates the potential of AeST to address the shortcomings of MOND in galaxy clusters, but a full quantitative comparison with observations will require going beyond the isothermal case.

Wormhole solutions in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and it is well-known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in f (R) modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the rr–component of the metric tensor and employ Padè approximation to check whether a well–constrained shape function can be formulated in this manner. We then derive the field equations with a background of string cloud and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple f (R) gravity model, we use the background cloud of strings to estimate the wormhole shape function and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple f (R) gravity model considered. The results demonstrate that string cloud is a viable source for wormholes with NEC violations; however, the wormhole space-times in the simple f (R) gravity model considered in this study are unstable.

The tight radial acceleration relation (RAR) obeyed by rotationally supported disk galaxies is one of the most successful a priori predictions of the modified Newtonian dynamics (MOND) paradigm on galaxy scales. Another important consequence of MOND as a classical modification of gravity is that the strong equivalence principle (SEP) – which requires the dynamics of a small, free-falling, self-gravitating system not to depend on the external gravitational field in which it is embedded – should be broken. Multiple tentative detections of this so-called external field effect (EFE) of MOND have been made in the past, but the systems that should be most sensitive to it are galaxies with low internal gravitational accelerations residing in galaxy clusters within a strong external field. Here, we show that ultra-diffuse galaxies (UDGs) in the Coma cluster do lie on the RAR, and that their velocity dispersion profiles are in full agreement with isolated MOND predictions, especially when including some degree of radial anisotropy. However, including a breaking of the SEP via the EFE seriously deteriorates this agreement. We discuss various possibilities to explain this within the context of MOND, including a combination of tidal heating and higher baryonic masses. We also speculate that our results could mean that the EFE is screened in cluster UDGs. The fact that this would happen precisely within galaxy clusters, where classical MOND fails, could be especially relevant to the nature of the residual MOND missing mass in clusters of galaxies.

In four spacetime dimensions, there exists a special infinite-parameter family of chiral modified gravity theories. All these theories describe just two propagating polarisations of the graviton. General relativity (GR) with an arbitrary cosmological constant is the only parity-invariant member of this family. We review how these modified gravity theories arise within the framework of pure-connection formulation. We introduce a new convenient parametrisation of this family of theories by using a certain set of auxiliary fields. Modifications of GR can be arranged so as to become important in regions with large Weyl curvature, while the behaviour is indistinguishable from GR where Weyl curvature is small. We show how the Kasner singularity of GR is resolved in a particular class of modified gravity theories of this type, leading to solutions in which the fundamental connection field is regular all through the spacetime. There arises a new asymptotically De Sitter region ‘behind’ the would-be singularity, the complete solution thus being of a bounce type.

Recent observations of rotationally supported galaxies show a tight correlation between the observed radial acceleration at every radius and the Newtonian acceleration generated by the baryonic mass distribution, the so-called radial acceleration relation (RAR). The rotation curves (RCs) of the SPARC sample of disk galaxies with different morphologies, masses, sizes and gas fractions are investigated in the context of modified Newtonian dynamics (MOND). We include the effect of cold dark baryons by scaling the measured mass in the atomic form by a factor of $c$ in the mass budget of galaxies. In addition to the standard interpolating function, we also fit the RCs and the RAR with the empirical RAR-inspired interpolating function. Slightly better fits for about $47\%$ of galaxies in our sample are achieved in the presence of dark baryons ($c>1$) with the mean value of $c = 2.4\pm 1.3$. Although the MOND fits are not significantly improved by including dark baryons, it results in a decrease in the characteristic acceleration $g_\dag$ by $40\%$. We find no correlation between the MOND critical acceleration $a_0$ and the central surface brightness of the stellar disk, $\mu_{3.6}$. This supports $a_0$ being a universal constant for all galaxies.

Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However, the theory is incomplete, lacking a relativistic counterpart, and so makes no definite predictions about gravitational lensing. The most obvious form that MONDian lensing might take is that photons experience twice the deflection of massive particles moving at the speed of light, as in general relativity (GR). In such a theory there is no general thin-lens approximation (although one can be made for spherically symmetric deflectors), but the three-dimensional acceleration of photons is in the same direction as the relativistic acceleration would be. In regimes where the deflector can reasonably be approximated as a single point-mass (specifically low-optical depth microlensing and weak galaxy–galaxy lensing), this naive formulation is consistent with observations. Forthcoming galaxy–galaxy lensing data and the possibility of cosmological microlensing have the potential to distinguish unambiguously between GR and MOND. Some tests can also be performed with extended deflectors, for example by using surface brightness measurements of lens galaxies to model quasar lenses, although the breakdown of the thin-lens approximation allows an extra degree of freedom. None the less, it seems unlikely that simple ellipsoidal galaxies can satisfy both constraints. Furthermore, the low-density universe implied by MOND must be completely dominated by the cosmological constant (to fit microwave background observations), and such models are at odds with the low frequency of quasar lenses. These conflicts might be resolved by a fully consistent relativistic extension to MOND; the alternative is that MOND is not an accurate description of the Universe.

The phenomenological basis for Modified Newtonian Dynamics (MOND) is the radial-acceleration-relation (RAR) between the observed acceleration, $a=V^2_{rot}(r)/r$, and the acceleration accounted for by the observed baryons (stars and cold gas), $a_{bar}=V_{bar}^2(r)/r$. We show that the RAR arises naturally in the NIHAO sample of 89 high-resolution LCDM cosmological galaxy formation simulations. The overall scatter from NIHAO is just 0.079 dex, consistent with observational constraints. However, we show that the scatter depends on stellar mass. At high masses ($10^9 <M_{star} <10^{11}$ Msun) the simulated scatter is just $\simeq 0.04$ dex, increasing to $\simeq 0.11$ dex at low masses ($10^7 < M_{star} <10^{9}$Msun). Observations show a similar dependence for the intrinsic scatter. At high masses the intrinsic scatter is consistent with the zero scatter assumed by MOND, but at low masses the intrinsic scatter is non-zero, strongly disfavoring MOND. Applying MOND to our simulations yields remarkably good fits to most of the circular velocity profiles. In cases of mild disagreement the stellar mass-to-light ratio and/or "distance" can be tuned to yield acceptable fits, as is often done in observational mass models. In dwarf galaxies with $M_{star}\sim10^6$Msun MOND breaks down, predicting lower accelerations than observed and in our LCDM simulations. The assumptions that MOND is based on (e.g., asymptotically flat rotation curves, zero intrinsic scatter in the RAR), are approximately, but not exactly, true in LCDM. Thus if one wishes to go beyond Newtonian dynamics there is more freedom in the RAR than assumed by MOND.

We investigate the baryonic Faber–Jackson relation (BFJR), examining the correlation between baryonic mass and velocity dispersion in galaxy groups and clusters. Originally analysed in elliptical galaxies, the BFJR is derivable from the empirical radial acceleration relation (RAR) and MOdified Newtonian Dynamics (MOND), both showcasing a characteristic acceleration scale $\mathrm{g}_\mathrm{\dagger }=1.2\times 10^{-10}\, \mathrm{m}\, \mathrm{s}^{-2}$. Recent interpretations within MOND suggest that galaxy group dynamics can be explained solely by baryonic mass, hinting at a BFJR with g† in these systems. To explore this BFJR, we combined X-ray and optical measurements for 6 galaxy clusters and 13 groups, calculating baryonic masses by combining X-ray gas and stellar mass estimates. Simultaneously, we computed spatially resolved velocity dispersion profiles from membership data using the biweight scale in radial bins. Our results indicate that the BFJR in galaxy groups, using total velocity dispersion, aligns with MOND predictions. Conversely, galaxy clusters exhibit a parallel BFJR with a larger acceleration scale. Analysis using tail velocity dispersion in galaxy groups shows a leftward deviation from the BFJR. Additionally, stacked velocity dispersion profiles reveal two distinct types: declining and flat, based on two parallel BFJRs. The declining profile, if not due to the anisotropy parameters or the incomplete membership, suggests a deviation from standard dark matter (DM) density profiles. We further identify three galaxy groups with unusually low DM fractions.

The existence of traversable wormhole (TW) in the Einstein’s general theory of relativity is explored with density profile obtained from modified Newtonian dynamics (MOND) with or without a scalar field. The shape functions for wormholes and the null energy conditions (NEC) of matter in the wormhole are determined with a constant redshift function. Wormholes are found to exist with MOND density profile in the presence of exotic matter and determine the mass of a asymptotic flat wormhole geometry. The addition of an extra massless scalar field with MOND density profile permits wormholes even when NEC is obeyed at the throat depending on the initial value of the scalar field. Considering a non-linear equation of state (EoS) , (where A, B and ρ c are constants) in Einstein gravity we obtain TW. In this case new classes of TW solutions are determined which depends on the EoS parameters A and B. TW exists with normal matter when ρ(r 0) ⩾ ρ c and with exotic matter when ρ(r 0) < ρ c at the throat where .

The radial acceleration relation (RAR) connects the total gravitational acceleration of a galaxy at a given radius, atot(r), with that accounted for by baryons at the same radius, abar(r). The shape and tightness of the RAR for rotationally-supported galaxies have characteristics in line with MOdified Newtonian Dynamics (MOND) and can also arise within the cosmological constant + cold dark matter (ΛCDM) paradigm. We use zoom simulations of 20 galaxies with stellar masses of M⋆ ≃ 107–11 M⊙ to study the RAR in the FIRE-2 simulations. We highlight the existence of simulated galaxies with non-monotonic RAR tracks that ‘hook’ down from the average relation. These hooks are challenging to explain in Modified Inertia theories of MOND, but naturally arise in all of our ΛCDM-simulated galaxies that are dark-matter dominated at small radii and have feedback-induced cores in their dark matter haloes. We show, analytically and numerically, that downward hooks are expected in such cored haloes because they have non-monotonic acceleration profiles. We also extend the relation to accelerations below those traced by disc galaxy rotation curves. In this regime, our simulations exhibit ‘bends’ off of the MOND-inspired extrapolation of the RAR, which, at large radii, approach atot ≈ abar/fb, where fb is the cosmic baryon fraction. Future efforts to search for these hooks and bends in real galaxies will provide interesting tests for MOND and ΛCDM.

We demonstrate a very general mathematical and physical expression of the rotation speed at the end of the galaxy (far from the vast majority of the galaxy’s baryonic mass) obtained from General Relativity without non-baryonic matter. We show the excellent agreement with measurements obtained for the Milky Way published in a recent article which confirms a significantly faster decline in the circular velocity curve at outer galactic radii up to 30 kpc compared to the inner parts. This relation comes from Linearized General Relativity (GRL). Some papers argue that the GRL solution cannot explain dark matter (DM). We demonstrate that this conclusion is too premature because they only consider mass currents of the galaxies which is not the most general theoretical solution. And because this GRL explanation suffers from the same defects as exotic matter, only direct measurement of the Lense-Thirring effect can objectively reject this solution. Current experiments are not yet precise enough to test this solution. But meanwhile, if the relevance of this expression were confirmed for most galaxies, this would strongly challenge exotic matter to explain DM and could drastically change the point of view on the DM component. Two known physical fields (contrary to an exotic matter) which are until now neglected or rather underestimated would then explain DM. The DM mystery would then consist for theory in understanding how the values of these fields can be larger than expected and for observation in being able to measure these two fields with sufficient precision. In addition, these fields allow obtaining the TULLY-FISHER relation and the MOND theory.

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.