Conformal classes of Brans-Dicke gravity

A classification of Brans-Dicke theories of gravitation, based on the behaviour of the dimensionless gravitational coupling constant, is given. It is noted that the discussion takes place in the current literature, about which of the two distinguished conformal frames in which scalar-tensor theories of gravity can be formulated: the Jordan frame and the Einstein frame, is the physical one, may, in most cases, be meaningless for both frames may belong to the same conformal class. It is also noted that the Jordan frame formulation of Brans-Dicke gravity with ordinary matter nonminimally coupled, that is shown to be just the Jordan frame formulation of general relativity, is scale-invariant, unlike the situation with the Jordan frame representation of Brans-Dicke gravity with matter minimally coupled (the original formulation of Brans-Dicke theory), where the presence of nonzero mass ordinary matter breaks the scale-invariance of the theory.Comment: 3 pages, LaTeX, a crucial error on violation of the WEP was corrected, minor changes adde

On the physical consequences of a Weyl invariant theory of gravity

In this paper we explore the physical consequences of assuming Weyl invariance of the laws of gravity from the classical standpoint exclusively. Actual Weyl invariance requires to replace the underlying Riemannian geometrical structure of the background spacetimes by Weyl integrable geometry (WIG). We show that gauge freedom, a distinctive feature of Weyl invariant theories of gravity, leads to very unusual consequences. For instance, within the cosmological setting in a WIG-based conformal invariant gravity theory, also known as conformal general relativity (CGR), a static universe is physically equivalent to a universe undergoing de Sitter expansion. It happens also that spherically symmetric black holes are physically equivalent to singularity-free wormholes. Another outstanding consequence of gauge freedom in the framework of CGR is that inflation is not required to explain the flatness, horizon and relict particle abundances, among other puzzles that arise in standard GR-based cosmology. Besides, the cosmological constant and the mass hierarchy problems do not arise neither in this setup.Comment: 31 pages, 2 figures. After a 6-years period draft rewritten to a large extent. Aims and scope slightly modified, title changed. Improved physical discussion including the physical implications of gauge freedom. Figures added for better understanding. arXiv admin note: text overlap with arXiv:1811.0245

Symmetry relating Gravity with Antigravity: A possible resolution of the Cosmological Constant Problem?

I discuss possible implications a symmetry relating gravity with antigravity might have for smoothing out of the cosmological constant puzzle. For this purpose, a very simple model with spontaneous symmetry breaking is explored, that is based on Einstein-Hilbert gravity with two self-interacting scalar fields. The second (exotic) scalar particle with negative energy density, could be interpreted, alternatively, as an antigravitating particle with positive energy.Comment: 3 pages, no figures, revte

Scale invariance and broken electroweak symmetry may coexist together

Here we show that local scale invariance -- invariance under Weyl rescalings -- may safely coexist with broken electroweak symmetry if assume the Weyl geometric theory to govern the affine structure of spacetime. We find that within the resulting scale invariant theory of gravity cosmological inflation is enough to explain the large hierarchy between the Higgs and Planck masses.Comment: 5 pages, no figures. Sustantial improvements: (i) the discussion on generation of mass hierarchy complemented with necessary statements about the measurable quantities in Weyl spaces, and (ii) unnecessary discussion on the coosmological constant, not relevant to the main focus of the paper remove

Spontaneous orbifold symmetry breaking and generation of mass hierarchy

A very simple mechanism is proposed that stabilizes the orbifold geometry within the context of the Randall-Sundrum proposal for solving the hierarchy problem. The electroweak TeV scale is generated from the Planck scale by spontaneous breaking of the orbifold symmetryComment: 10 pages, Revtex, no figure

Is the cosmological singularity really unavoidable in general relativity?

The initial singularity problem in standard general relativity is treated on the light of a viewpoint asserting that this formulation of Einstein's theory and its conformal formulations are physically equivalent. We show that flat Friedmann-Robertson-Walker universes and open dust-filled and radiation-filled universes are singularity free when described in terms of the formulation of general relativity conformal to the canonical one.Comment: this paper has been withdrawn by the author because it significantly overlaps with gr-qc/000207

Time-like vs Space-like Extra Dimensions

Higher-dimensional theories with time-like and space-like extra dimensions are compared both from the conceptual and from the phenomenological points of view. In this context causality and unitarity are discussed. It is shown that additional time-like dimensions allow to recover four-dimensional phenomenology without invoking neither Kaluza-Klein compactification procedure nor brane world construct. It is shown, also, that contrary to scenarios with space-like extra dimensions, in higher-dimensional space-times with additional time-like dimensions the cosmological constant problem can be safely solved.Comment: 5 pages, no figure

Scale invariance: fake appearances

In this paper we shall show that, unless the affine geometrical structure of the underlying spacetime manifold is specified, there is an ambiguity in the understanding of the scale invariance -- also Weyl invariance -- of the given theory of gravity. In this regard we cast doubts on several well-known theories which are claimed to be scale-invariant setups. We shall show that in a consistent scale invariant theory not only the action but also the geometrical laws which govern the affine structure of the underlying spacetimes are invariant under the Weyl gauge transformations.Comment: 12 pages, no figures. An important clarifying footnote and bibliographic references added. Discussion on the singularity issue improved. arXiv admin note: text overlap with arXiv:1401.264

Scale Invariant Kaluza-Klein Theory and the Fate of the Gravitational Collapse

Pushing forward the similitudes between the gravitational collapse and the expansion of the universe (in the reversed sense of time), it should be expected that, during the collapse, eventually, a spacetime domain would be reached where attained energy scales are very high. In consequence some of the compactified extra dimensions may be decompactified and some presently broken symmetries may be restored. A more fundamental theory (of which Einstein's theory is a symmetry broken phase) is then expected to take account of further description of the collapse. I propose a simple (classical) model for the description of the late stages of the gravitational collapse: A non-Riemannian, scale-invariant version of 5-dimensional Kaluza-Klein theory in which the standard Riemann structure of the higher-dimensional manifold is replaced by a Weyl-integrable one. A class of solutions, that generalize the "soliton" one by Gross and Perry and Davidson and Owen, is found. This class contains both naked singularities and wormhole solutions. On physical grounds it is argued that a wormhole is the most reasonable destiny of the gravitational collapse.Comment: 10 pages, latex, no figure

Causality and Unitarity Are Not Violated in Space-Times with an Additional Compact Time-like Dimension

The hypothesis that the causal properties of space-time, as well as other properties of physical systems like unitarity, charge conservation, etc., might be decided by the higher dimensional structure (in particular, higher-dimensional physical laws), rather than by the four-dimensional one, is explored in order to evade the most awkward problems of higher-dimensional theories with compact extra time-like dimensions: violation of causality and of unitarity.Comment: 5 pages, no figures. Argument on the phenomenology of the extra time-like dimension modified, references adde