Cotton gravity and 84 galaxy rotation curves

Recently, as a generalization of general relativity, a gravity theory has been proposed in which gravitational field equations are described by the Cotton tensor. That theory allows an additional contribution to the gravitational potential of a point mass that rises linearly with radius as $\Phi = -GM/r + \gamma r/2$, where $G$ is the Newton constant. The coefficients $M$ and $\gamma$ are the constants of integration and should be determined individually for each physical system. When applied to galaxies, the coefficient $\gamma$, which has the dimension of acceleration, should be determined for each galaxy. This is the same as having to determine the mass $M$ for each galaxy. If $\gamma$ is small enough, the linear potential term is negligible at short distances, but can become significant at large distances. In fact, it may contribute to the extragalactic systems. In this paper, we derive the effective field equation for Cotton gravity applicable to extragalactic systems. We then use the effective field equation to numerically compute the gravitational potential of a sample of 84 rotating galaxies. The 84 galaxies span a wide range, from stellar disk-dominated spirals to gas-dominated dwarf galaxies. We do not assume the radial density profile of the stellar disk, bulge, or gas; we use only the observed data. We find that the rotation curves of 84 galaxies can be explained by the observed distribution of baryons. This is due to the flexibility of Cotton gravity to allow the integration constant $\gamma$ for each galaxy. In the context of Cotton gravity, "dark matter" is in some sense automatically included as a curvature of spacetime. Consequently, even galaxies that have been assumed to be dominated by dark matter do not need dark matter.Comment: 22 pages, 7 figures, 1 table, accepted for publication in Phys. Rev. D, v2: published versio

Gravity at cosmological distances: Explaining the accelerating expansion without dark energy

Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations, rather than assuming it, and not necessarily considering conformally flat metrics as vacuum solutions. Existing theories, including general relativity, do not simultaneously fulfill all three criteria. To address this, a new gravitational field equation is proposed that satisfies these criteria. From this equation, a spherically symmetric exact solution is derived, which is a generalization of the Schwarzschild solution. It incorporates three terms: the Schwarzschild term, the de Sitter term, and a newly discovered term, which is proportional to $r^4$ in a radial coordinate, that becomes significant only at large distances. The equation is further applied to cosmology, deriving an equation for the scale factor. It then presents a solution that describes the transition from decelerating to accelerating expansion in a matter-dominated universe. This is achieved without the need for negative pressure as dark energy or the positive cosmological constant. This provides a novel explanation for the current accelerating expansion of the universe.Comment: 7 pages, 1 figure; accepted for publication in Phys.Rev.

Non-maximal \theta_{23}, large \theta_{13} and tri-bimaximal \theta_{12} via quark-lepton complementarity at next-to-leading order

We show that the next-to-leading order corrections in the quark-lepton complementarity are important to explain the observed pattern of neutrino mixing. In particular, the next-to-leading order corrections 1) lead to a deviation of \theta_{23} from maximal mixing, 2) reduce the predicted value of $\sin^2 2\theta_{13}$ by 9.8%, 3) provide the same value of $\sin^2 \theta_{12}$ as that of the tri-bimaximal mixing. This is shown by calculating $\sin^2 2\theta_{ij} (i,j=1,2,3)$ to ${\cal O}(\lambda^6)$ in the framework in which the product of the CKM and PMNS matrices is bimaximal.Comment: 14 pages, 3 figures, a version to appear in EP

Dark energy in conformal Killing gravity

The Friedmann equation, enriched by an additional term that effectively takes on the role of specific dark energy, is demonstrated to serve as an exact solution within the recently proposed gravitational theory named "conformal Killing gravity". This theory does not explicitly incorporate dark energy. This finding suggests that there's no necessity to postulate the existence of dark energy as an independent physical entity. The dark energy effectively arising from this theory is characterized by a specific equation of state parameter, denoted as $\omega$, which is uniquely determined to be $-5/3$, classifying it as phantom energy. If this effective dark energy is present in a moderate amount, typically around 5\% of the total energy density at the present time, and under the assumption of density parameters for matter and the cosmological constant, $\Omega_{\rm m}\sim 0.25$ and $\Omega_\Lambda \sim 0.7$, respectively, the expansion of the universe at low redshifts ($z < 1.5$) can exceed expectations, while the expansion at $z > 1.5$ remains unchanged. This holds the potential to address the Hubble tension problem.Comment: 6 pages, 2 figure