Implications of the Conformal Higgs Model

The postulate of universal local Weyl scaling (conformal) symmetry modifies both general relativity and the Higgs scalar field model. The conformal Higgs model (CHM) acquires a cosmological effect that fits the observed accelerating Hubble expansion for redshifts z≤1 (7.33 Gyr) accurately with only one free constant parameter. Conformal gravity (CG) has recently been fitted to anomalous rotation data for 138 galaxies. Conformal theory explains dark energy and does not require dark matter, providing a viable alternative to the standard ΛCDM paradigm. The theory precludes a massive Higgs particle but validates a composite gauge field W2 with mass 125 GeV.

Universal renormalization procedure for higher curvature gravities in D ≤ 5

We implement a universal method for renormalizing AdS gravity actions applicable to arbitrary higher curvature theories in up to five dimensions. The renormalization procedure considers the extrinsic counterterm for Einstein-AdS gravity given by the Kounterterms scheme, but with a theory-dependent coupling constant that is fixed by the requirement of renormalization for the vacuum solution. This method is shown to work for a generic higher curvature gravity with arbitrary couplings except for a zero measure subset, which includes well-known examples where the asymptotic behavior is modified and the AdS vacua are degenerate, such as Chern-Simons gravity in 5D, Conformal Gravity in 4D and New Massive Gravity in 3D. In order to show the universality of the scheme, we perform a decomposition of the equations of motion into their normal and tangential components with respect to the Poincare coordinate and study the Fefferman-Graham expansion of the metric. We verify the cancellation of divergences of the on-shell action and the well-posedness of the variational principle.

Stability of Schwarzschild (Anti)de Sitter black holes in conformal gravity

We study the thermodynamics of spherically symmetric, neutral and non-rotating black holes in conformal (Weyl) gravity. To this end, we apply different methods: (i) the evaluation of the specific heat; (ii) the study of the entropy concavity; (iii) the geometrical approach to thermodynamics known as thermodynamic geometry; (iv) the Poincaré method that relates equilibrium and out-of-equilibrium thermodynamics. We show that the thermodynamic geometry approach can be applied to conformal gravity too, because all the key thermodynamic variables are insensitive to Weyl scaling. The first two methods, (i) and (ii), indicate that the entropy of a de Sitter black hole is always in the interval $$2/3\le S\le 1$$ 2 / 3 ≤ S ≤ 1 , whereas thermodynamic geometry suggests that, at $$S=1$$ S = 1 , there is a second order phase transition to an Anti de Sitter black hole. On the other hand, we obtain from the Poincaré method (iv) that black holes whose entropy is $$S < 4/3$$ S < 4 / 3 are stable or in a saddle-point, whereas when $$S>4/3$$ S > 4 / 3 they are always unstable, hence there is no definite answer on whether such transition occurs. Since thermodynamics geometry takes the view that the entropy is an extensive quantity, while the Poincaré method does not require extensiveness, it is valuable to present here the analysis based on both approaches, and so we do.

Noether-Wald charges in six-dimensional Critical Gravity

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

Late cosmology in massive conformal gravity

In this paper, we find the cosmological solutions of the massive conformal gravity field equations in the presence of matter fields. In particular, we show that the solution of negative curvature is in good agreement with the late universe.