Galactic Rotation Curves in Conformal Scalar-Tensor Gravity
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Galactic Rotation Curves in Conformal Scalar-Tensor Gravity Qiang Li1, 2* and Leonardo Modesto2** 1
2
Department of Physics, Harbin Institute of Technology, Harbin 150001, China Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China Received January 31, 2020; revised January 31, 2020; accepted February 12, 2020
Abstract—We show quantitatively that an exact solution of conformal scalar-tensor gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without the need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter space-time as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two fixed universal parameters. Using the Monte Carlo Markov Chain (MCMC) method, we make a fit of the observational rotation curves in order to get the mass-to-light ratio for each galaxy. Finally, we analytically compare our model with the modified Newtonian dynamics (MOND) and the metric skew tensor gravity (MSTG) showing that the three theories have a very different behavior at very large distances. DOI: 10.1134/S0202289320020085
1. INTRODUCTION
functional [1]: 2 ˆ + 6ˆ g φ R gμν ∂μ φ∂ν φ − 2f φ4 , S = d4 x −ˆ
One of the greatest mysteries in cosmology in our days is the “dark matter” or “dark gravity” puzzle. Indeed, in order to take into account all the observational evidences (the galactic rotation curves, structure formation in the universe, the CMB spectrum, the bullet cluster), we need to somehow modify the right or left side of the Einstein field equations. In this paper we do not pretend to provide a definitive answer to the long-standing question of what is dark matter, but we want to make known an extremely interesting result based on some previous work by Mannheim. Therefore, we here concentrate on only one of the above listed issues, namely, the galactic rotation curves.
(1) which is defined on a pseudo-Riemannian space-time manifold M equipped with a metric tensor field gˆμν , a scalar field φ (the dilaton), and it is also invariant under the following Weyl conformal transformation: = Ω2 gˆμν , gˆμν
*
(2)
where Ω(x) is a general local function. In (1) f is a dimensionless constant that has to be selected to be extremely small in order to have a cosmological constant compatible with the observed value. The Einstein-Hilbert gravity is recovered when the Weyl conformal invariance is broken spontaneously by exact analogy with the Higgs mechanism in the Standard Model of particle physics (for more details we refer the reader to [2, 3]). One possible vacuum of the theory (1) (an exact solution of the equations √ of motion) is φ = const = 1/ 16πG, together with √ Rμν ∝ gˆμν . Therefore, replacing φ = 1/ 16πG + ϕ in the action and using the conformal invariance to eliminate the gauge-dependent degree of freedom ϕ, we finally get the Einstein-Hilbert action in the presence of the cosmological constant, 1 ˆ − 2
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