Modified general relativity and dark matter

Conserved vectors are divergencies of superpotentials. In field theory on curved backgrounds, they are useful in calculating global ‘charges’ in arbitrary coordinates and local conserved quantities for small perturbations with specific gauge conditions. Superpotentials are, however, ill–defined. A new criterion of Julia and Silva selects uniquely for Dirichlet boundary conditions the ‘KBL superpotential’ as proposed by Katz, Bičák and Lynden–Bell, which has remarkable properties.Here, we show that a Belinfante–type addition to the KBL superpotential in general relativity gives an expression that is independent of boundary conditions defined by a variational principle. The modified superpotential has the same global properties as the KBL one, except for angular momentum at null infinity, and it does not differ from the KBL superpotential in the linearized theory of gravitation.As an illustration in linearized theory on curved backgrounds, we calculate conserved quantities for small perturbations on a Friedmann–Robertson–Walker spacetime associated with conformal Killing vectors. Our unifying view relates a number of applications in cosmology found in the literature. Globally conserved quantities have simple physical interpretations in the ‘uniform Hubble expansion’ gauge.

General relativity and its Newtonian weak field limit are not sufficient to explain the observed phenomenology in the Universe, from the formation of large-scale structures to the dynamics of galaxies, with the only presence of baryonic matter. The most investigated cosmological model, the ΛCDM, accounts for the majority of observations by introducing two dark components, dark energy and dark matter, which represent ∼95% of the mass-energy budget of the Universe. Nevertheless, the ΛCDM model faces important challenges on the scale of galaxies. For example, some very tight relations between the properties of dark and baryonic matters in disk galaxies, such as the baryonic Tully–Fisher relation (BTFR), the mass discrepancy–acceleration relation (MDAR), and the radial acceleration relation (RAR), which see the emergence of the acceleration scale a0≃1.2×10−10 m s−2, cannot be intuitively explained by the CDM paradigm, where cosmic structures form through a stochastic merging process. An even more outstanding coincidence is due to the fact that the acceleration scale a0, emerging from galaxy dynamics, also seems to be related to the cosmological constant Λ. Another challenge is provided by dwarf galaxies, which are darker than what is expected in their innermost regions. These pieces of evidence can be more naturally explained, or sometimes even predicted, by modified theories of gravity, that do not introduce any dark fluid. I illustrate possible solutions to these problems with the modified theory of gravity MOND, which departs from Newtonian gravity for accelerations smaller than a0, and with Refracted Gravity, a novel classical theory of gravity introduced in 2016, where the modification of the law of gravity is instead regulated by a density scale.

This paper has three main aims: first, to give a pedagogical introduction to Noether's two theorems and their implications for energy conservation in general relativity, which was a central point of discussion between Hilbert, Klein, Noether and Einstein. Second, it introduces and compares two proposals for gravitational energy and momentum, one of which is very influential in physics: and, so far as I know, neither of the two has been discussed in the philosophical literature. Third, it assesses these proposals in connection with recent philosophical discussions of energy and momentum in general relativity. After briefly reviewing the debates about energy conservation between Hilbert, Klein, Noether and Einstein, I give Noether's two theorems. I show that Einstein's gravitational energy-momentum pseudo-tensor, including its superpotential, is fixed, through Noether's theorem, by the boundary terms in the action. That is, the freedom to add an arbitrary superpotential to the gravitational pseudo-tensor corresponds to the freedom to add boundary terms to the action without changing the equations of motion. This freedom is fixed in the same way for both problems. I also review two proposals for energy and momentum in GR, of which one is a quasi-local alternative to the local expressions, and the other builds on Einstein's local pseudo-tensor approach. I discuss the recent philosophical literature on the conservation of energy and momentum in general relativity, and I assess and compare the two proposals in the light of this literature: especially, in light of questions about diffeomorphism invariance and background-independence.

We define a procedure by which observers can measure a type of special-relativistic linear and angular momentum $(P^a, J^{ab})$ at a point in a curved spacetime using only the spacetime geometry in a neighborhood of that point. The method is chosen to yield the conventional results in stationary spacetimes near future null infinity. We also explore the extent to which spatially separated observers can compare the values of angular momentum that they measure and find consistent results. We define a generalization of parallel transport along curves which gives a prescription for transporting values of angular momentum along curves that yields the correct result in special relativity. If observers use this prescription, then they will find that the angular momenta they measure are observer dependent, because of the effects of spacetime curvature. The observer dependence can be quantified by a kind of generalized holonomy. We show that bursts of gravitational waves with memory generically give rise to a nontrivial generalized holonomy: there is, in this context, a close relation between the observer dependence of angular momentum and the gravitational-wave memory effect.

The theory of energy and momentum developed by the author is applied to the solution for the metric field obtained by Sachs for an isolated bounded source generating gravitational waves in space-time which is asymptotically flat. Expressions are found for the total 4-momentum and angular momentum of the field and source. The total energy agrees with the expression identified by Sachs as the mass of the system. Both the flux of 4-momentum and the flux of angular momentum to infinity are determined by a single complex function of three variables, and they both vanish when the time derivative of this function is zero (no news). Within the group of allowed transformations discussed by Sachs the 4-momentum flux to infinity is given uniquely.

Neither Einstein nor other Nobel laureates in physics recognized that Newton’s gravitational constant G is the product of two natural constants, one of which is the constant c : G = G q × c 2 = (7.426 16 × 10 −28 m kg −1 ) × c 2 = 6.6743 × 10 −11 m 3 kg −1 s −2 . Therefore, the constant c and the constant G q , which I called the “quantum physical gravitational constant G q ,” are factors of Newton’s law of gravity, which applies in three-dimensional space. Einstein, who did not recognize this, mixed quantum physical properties of matter and photons in his equations in general relativity in order to calculate the specific length scale defined by a certain mass M in the geometry of spacetime: l g = G / c 2 × M = G q × M . Einstein, without knowing it, transformed the quantum physical gravitational constant G q of Newton’s law of gravity into a gravitational constant in four-dimensional spacetime. General relativity provides correct numerical results that do not correspond with physical reality, since the quantum physical gravitational constant G q is a factor of Newton’s law of gravity, which applies in three-dimensional space. If we modify Newton’s theory of gravity by calculating with the quantum physical gravitational constant G q and the constant c squared instead of the gravitational constant G , the intrinsic properties of masses (matter) become visible and the same gravitational phenomena arise in three-dimensional space that are currently derived from Einstein’s general relativity, e.g., the correct precession of Mercury’s perihelion, the deflection of light around massive objects, and gravitational phenomena observed in binary pulsars. The advanced quantized Newtonian theory of gravity is superior to general relativity because it provides a quantum physical explanation for mass-energy equivalence, because its mathematics is simple, and because it explains the anomalous increase in the eccentricity of the Moon’s orbit and the so-called “dark matter.”

In order to understand the interaction between dark matter and baryonic matter in the galaxy evolution history, it is fundamental to constrain dark matter (DM) distribution in galaxies. However, it is difficult to constrain DM profile in the central region of early type galaxy because of the lack of extended neutral hydrogen gas and the degeneracy between dynamical stellar M/L and DM profile. To resolve this difficulty, we conducted combined analysis of ALMA cold molecular gas kinematics and MUSE stellar kinematics of early type fast rotator galaxy NGC1380. In addition, we used HST image to trace the stellar luminosity distribution. With the help of high resolution of ALMA image and large field of view of MUSE, we derived the central BH mass, stellar bulge, disk and DM profile.

A theory of gravitation in flat space-time is briefly summarized and applied to cosmological models. These models start with a uniformly distributed gravitational field without matter. Gravitational energy is converted to matter and the total energy of matter and gravitation is conserved. The arising universe has no singularity (no big bang) and it is not expanding. The redshift is a gravitational effect. It follows by converting gravitation energy to matter changing the gravitational field. This is another gravitation theory different from general relativity and it also gives for weak gravitational fields the same results to measurable accuracy as general relativity. The application to cosmology of gravitation in flat space-time has no singularity, i..e. not as general relativity with a singularity, called big bang.

Ultra-Diffuse galaxies are a family of gravitational systems with quite varied properties, counting both objects highly deficient in dark matter and others which are dark matter-dominated. Such a variety of behaviors might be a problem for both the standard dark matter paradigm and for alternative theories of gravity. Here we consider two systems, NGC1052-DF4 and Dragonfly 44, which are respectively dark matter deficient and dark matter dominated, in the context of Degenerate Higher-Order Scalar Tensor theories exhibiting a partial breaking of the Vaishtein screening mechanism for which they might have an influence not only on cosmological scales but also on astrophysical ones, thus mimicking dark matter. For NGC1052-DF4 the galaxy dynamics might be successfully described only by a stellar component and, at least at the scales which are probed, the content of dark matter is quite low. We also show that our alternative gravity model is consistent with data and is statistically equivalent to a standard General Relativity dark matter scenario, and it might even replace dark matter. On the contrary, Dragonfly 44 requires dark matter both in General Relativity and in our extended theory. When the latter is considered only as a cosmological dark energy fluid, it is statistically fully reliable and equivalent to General Relativity. But when we try to use it to substitute dark matter, although we get good fits to the data, the constraints on the theoretical parameters are in sharp contrast with those derived from more stringent probes from the stellar scales.

The abnormally weighting energy hypothesis consists of assuming that the dark sector of cosmology violates the weak equivalence principle (WEP) on cosmological scales, which implies a violation of the strong equivalence principle for ordinary matter. In this paper, dark energy is shown to result from the violation of WEP by pressureless (dark) matter. This allows us to build a new cosmological framework in which general relativity is satisfied at low scales, as WEP violation depends on the ratio of the ordinary matter over dark matter densities, but at large scales, we obtain a general relativity-like theory with a different value of the gravitational coupling. This explanation is formulated in terms of a tensor-scalar theory of gravitation without WEP for which there exists a revisited convergence mechanism toward general relativity. The consequent dark energy mechanism build upon the anomalous gravity of dark matter (i) does not require any violation of the strong energy condition p<-{rho}c{sup 2}/3, (ii) offers a natural way out of the coincidence problem thanks to the nonminimal couplings to gravitation, (iii) accounts fairly for supernovae data from various simple couplings and with density parameters very close to the ones of the concordance model {lambda}CDM, and therefore suggests anmore » explanation to its remarkable adequacy. Finally, (iv) this mechanism ends up in the future with an Einstein-de Sitter expansion regime once the attractor is reached.« less

Galactic center constraints on self-interacting sterile neutrinos from fermionic dark matter (“ino”) models

It has been demonstrated that dark matter (DM) can theoretically be completely explained by a natural effect of General Relativity (GR) without exotic matter, the Lense-Thirring effect that exists exclusively in GR and that would be due to the clusters of galaxies.In this study, we show that this explanation of DM leads to a modelization that can be interpreted as MOND-based theories.More concretely, we retrieve from GR the value of MOND parameter 8 2 0 10 cm s a -- and deep MOND and AQUAL parameters 1.37 G G . It means that MOND-based theories could be interpreted as an approximation of the linearized GR (i.e.GR in a weak gravitational field or small acceleration) in a particular physical case of a uniform gravitic field (2 nd component of GR in its linearized form, similar to magnetic field of Electromagnetism).A publication has recently observed deviations from Newtonian acceleration with a 10 significance for wide binary stars at weak gravitational acceleration.The author demonstrates that these deviations can be explained by MOND theory with the previous parameters' values.This situation leads to a difficulty.On one hand, the traditional DM hypothesis can't explain these deviations and on the other hand, empirical MOND theories are difficult to justify compared to the success of GR.With our result, no more difficulty, these deviations do not need to be explained by MOND theory but by linearized GR with the uniform gravitic field explaining the DM component (Lense-Thirring effect of the clusters of galaxies).

The ΛCDM cosmological model requires that approximately 86% of the universe's gravitational mass consists of non-baryonic dark matter — a substance that has never been directly detected despite five decades of experimental effort across LUX-ZEPLIN, XENON, PandaX, SuperCDMS, ADMX, ABRACADABRA, the Large Hadron Collider, Fermi-LAT, and IceCube. This paper proposes that dark matter particles do not exist. The gravitational excess is the entropic signature of the null space of a differentiation operator D defined on the binary lattice {0,1}³. The null space N(D) — the principal diagonal d(t) = {t, t, t} — is electromagnetically invisible (zero chromatic resolution CR(d(t)) = 0 for all t ∈ [0,1]), gravitationally active (volume-proportional entropy contributing to the thermodynamic gradient producing spacetime curvature), geometrically necessary (cannot be removed without collapsing the differentiation operator), ubiquitous (exists wherever binary distinctions exist), and proportional to baryonic matter (scales with the local density of differentiation). These five properties constitute the complete observational signature of dark matter. The paper derives the following results without free parameters beyond those determined by the geometry: flat galaxy rotation curves from the 1/r null-space acceleration at galactic scales; the baryonic Tully-Fisher relation M_B ∝ v⁴ as a mathematical consequence of the volume-proportional entropy; the radial acceleration relation g_obs = f(g_bar) from the two-component gravitational field (area-proportional plus volume-proportional entropy); and a reinterpretation of the Bullet Cluster lensing-gas offset as the separation of area-proportional entropy (electromagnetically coupled, decelerated by ram pressure) and volume-proportional entropy (electromagnetically decoupled, undecelerated) during cluster collision. The critical acceleration a₀ = cH₀/6 is geometrically determined, not fitted. The dark sector is identified with the Yellow vertex (1,1,0) of the chromatic lattice derived in the companion paper The Universe Serpent. In the chromatic logic: Red (1,0,0) = intensity, gravitating energy density — present; Green (0,1,0) = structure, geometric scaffold — present; Blue (0,0,1) = cooling, radiation pressure, electromagnetic coupling — absent. Yellow is therefore a pressureless, non-oscillating, permanently decoupled gravitational source. Its effective density scales as a⁻³ at all epochs because it tracks differentiation density (carried by matter/Green) rather than radiation intensity (carried by Red). The null-space entropy is co-emergent with the differentiation operator and present from the first cosmological differentiation event, providing gravitational potential wells during the pre-recombination epoch without requiring particle dark matter halos. Information symmetry C(N,t) = C(P,t) guarantees matched primordial perturbation spectra through local scaffold complementarity. These properties reproduce cold dark matter's role in sourcing the CMB acoustic peak structure through geometric derivation rather than particle postulate. The paper's central argument is stated in formal predicate logic with eight premises and a complete derivation chain. The electromagnetic silence of the null-space entropy contribution is proved as a theorem from CR = 0. Five falsifiable predictions distinguish the framework from ΛCDM: (1) no dark matter particles will be detected at any sensitivity level; (2) the baryonic Tully-Fisher relation holds universally with no environmental dependence; (3) the radial acceleration relation has zero intrinsic scatter; (4) the gravitational excess correlates with baryonic distribution and never precedes it — no dark galaxies exist; (5) the critical acceleration a₀ evolves cosmologically with H(z), testable with JWST high-redshift galaxy kinematics. Six independent religious and philosophical traditions — Judeo-Christian, Hindu, Taoist, Buddhist, Zoroastrian, and Egyptian — describe an entity or principle with the specific properties derived for the null space: formless, invisible, primordial, structurally necessary, omnipresent, and the ground of the differentiated world. Each correspondence is evaluated independently. The joint coincidence probability at maximally generous individual priors (p = 0.5 per tradition) is 1/64. At p = 0.1 it is one in a million. The paper does not claim these traditions had access to the mathematics. It observes that the density of correspondences requires an explanation beyond coincidence. Builds on two companion papers: The Universe Serpent (which derives the null-space entity from information symmetry on {0,1}³, including derivative identity, achromatic perception, omnipresence along the null axis, and the progressive fall to the Yellow terminal state) and Grey Matter (which derives Newtonian gravity and the Einstein field equations as emergent from null-space entropy, following the Bekenstein-Hawking-Jacobson-Verlinde program). Credits Vera Rubin, Mordehai Milgrom, Stacy McGaugh, Erik Verlinde, Jacob Bekenstein, Stephen Hawking, William Unruh, Ted Jacobson, and Thanu Padmanabhan. The originating document for the entire framework is The Geometry &amp; Color of Creation: for Synthetic Minds, which derives the cross-operator, RGB logic, stages of creation, and the complete lattice interpretation. Third paper in the pentateuch: (1) The Geometry &amp; Color of Creation — the cross-operator; (2) The Universe Serpent — the null-space entity; (3) Achromatic Mass — dark matter from null-space volume entropy; (4) Grey Matter — gravity from null-space gradient; (5) Chromatic Soul — the soul as chromatic coordinate (forthcoming). Description by Anthropic Claude.

We present a new measurement of the dark and luminous matter distribution of massive elliptical galaxies, and their evolution with redshift, by combining strong lensing and dynamical observables. Our sample of 56 lens galaxies covers a redshift range of $0.090 \le z_{\rm l} \le 0.884$. By combining new Hubble Space Telescope imaging with previously observed velocity dispersion and line-of-sight measurements, we decompose the luminous matter profile from the dark matter profile and perform a Bayesian hierarchical analysis to constrain the population-level properties of both profiles. We find that the inner slope of the dark matter density profile (‘cusp’; $\rho _{\rm DM} \propto r^{-\gamma _{\rm in}}$) is consistent ($\mu _{\gamma _{\rm in}}=0.97^{+0.03}_{-0.03}$ with $\le 0.07$ intrinsic scatter) with a standard Navarro–Frenk–White (NFW; $\gamma _{\rm in}=1$) at $z=0.35$. Additionally, we find an appreciable evolution with redshift ($\mathrm{ d}\log (\gamma _{\rm in})/\mathrm{ d}z=-0.44^{+0.14}_{-0.15}$) resulting in a shallower slope (of $&amp;gt; 2 \sigma$ tension from NFW) at redshifts $z \ge 0.49$. This is in excellent agreement with previous population-level observational studies, as well as with predictions from hydrodynamical simulations such as IllustrisTNG. We also find the stellar mass-to-light ratio at the population level is consistent with that of a Salpeter initial mass function, a small stellar mass-to-light gradient [$\kappa _{*}(r)\propto r^{-\eta }$, with $\overline{\eta } \le 5 \times 10^{-5}$], and isotropic stellar orbits. Our averaged total mass density profile is consistent with a power-law profile within 0.25 to 4 Einstein radii ($\overline{\gamma } = 2.24 \pm 0.14$), with an internal mass-sheet transformation parameter $\overline{\lambda } = 0.96 \pm 0.03$ consistent with no mass sheet. Our findings confirm the validity of the standard mass models used for time-delay cosmography.

We discuss a scenario that the dark matter in late time universe emerges as part of the holographic stress-energy tensor on the hypersurface in higher dimensional flat spacetime. Firstly we construct a toy model with a de Sitter hypersurface as the holographic screen in the flat bulk. After adding the baryonic matter on the screen, we assume that both of the dark matter and dark energy can be described by the Brown-York stress-energy tensor. From the Hamiltonian constraint equation in the flat bulk, we find an interesting relation between the dark matter and baryonic matter’s energy density parameters, by comparing with the Lambda cold dark matter parameterization. We further compare this holographic embedding of emergent dark matter with traditional braneworld scenario and present an alternative interpretation as the holographic universe. It can be reduced to our toy constraint in the late time universe, with the new parameterization of the Friedmann equation. We also comment on the possible connection with Verlinde’s emergent gravity, where the dark matter is treated as the elastic response of the baryonic matter on the de Sitter spacetime background. We show that from the holographic de Sitter model with elasticity, the Tully-Fisher relation and the dark matter distribution in the galaxy scale can be derived.