[Paper Review] The Dark Side of Gravity

Frederic Henry-Couannier|arXiv (Cornell University)|Oct 16, 2006

Cosmology and Gravitation Theories7 references3 citations

TL;DR

This paper proposes Dark Gravity (DG), a non-geometrical theory of gravity on a flat Minkowski spacetime background, where gravity is described by two conjugate symmetric tensor fields—one corresponding to standard gravity, the other to a 'Dark Side' with antigravitational interactions. The theory resolves issues with negative energy states and tachyonic representations by treating both fields on equal footing via discrete symmetry invariance, yielding predictions consistent with general relativity at low orders but differing at Post-Post-Newtonian levels, avoiding black holes and offering a natural explanation for cosmic acceleration without dark energy.

ABSTRACT

Adopting a non geometrical point of view, we are led to an alternative theory of the order two and symetric gravitational tensor field of GR. The field is no more interpreted as the metric of our space-time. The true metric is globally Minkowskian and describes a flat manifold, a context which justifies a genuine rehabilitation of the global discrete space-time symetries involved in the structure of the Lorentz group along with their 'problematic' representations: the negative energy and tachyonic ones.

Motivation & Objective

• To resolve theoretical inconsistencies arising from negative energy states and tachyonic representations in relativistic quantum field theory by abandoning the geometric interpretation of gravity in general relativity.
• To rehabilitate global spacetime symmetries, including time reversal and Lorentz group representations, by formulating gravity on a fixed, non-dynamical Minkowski background.
• To construct a stable, unitary gravitational theory that treats positive and negative energy fields symmetrically through conjugate tensor fields, avoiding vacuum divergences and instability.
• To provide a classical framework that naturally accounts for cosmological phenomena like accelerated expansion and flat rotation curves without invoking dark matter or dark energy.
• To explore the phenomenological consequences of antigravitational matter and new gravitomagnetic effects, testable in experiments like Gravity Probe B.

Proposed method

• Adopt a non-geometrical formulation of gravity, treating the gravitational field as a symmetric, order-two tensor field on a fixed Minkowski spacetime background.
• Introduce two conjugate tensor fields related by discrete symmetry reversal (e.g., time reversal), both required to be included in the action to preserve invariance.
• Construct actions and field equations invariant under discrete symmetries, ensuring both positive and negative energy solutions are treated on equal footing.
• Use the conjugate field structure to define a 'Dark Side' of gravity where matter interacts only via antigravity with standard matter.
• Derive new solutions to the vacuum Einstein equations, including a modified Schwarzschild solution that avoids horizons and black holes.
• Analyze gravitational wave solutions and binary pulsar decay rates, comparing them to observations and GR predictions.

Experimental results

Research questions

• RQ1 Can a consistent classical theory of gravity be constructed on a flat spacetime background that incorporates negative energy and tachyonic states without instability?
• RQ2 How can time reversal symmetry be consistently implemented in a gravitational theory when it leads to negative energy states in a non-gravitational context?
• RQ3 What are the observable consequences of a gravitational field with two conjugate, symmetric tensor components, one corresponding to standard gravity and the other to antigravity?
• RQ4 Can the accelerated expansion of the universe be explained without a cosmological constant or dark energy in this framework?
• RQ5 Do new gravitomagnetic effects arise in this theory that could be detected in experiments like Gravity Probe B, differing from GR's frame-dragging prediction?

Key findings

• The new Schwarzschild solution in vacuum differs from General Relativity only at the Post-Post-Newtonian order, with no event horizon or black hole formation.
• The theory avoids the WEP violation and passes all current SEP tests except the Pioneer anomalous blue-shift, which is naturally explained as an SEP-violating effect.
• A spatially flat universe undergoes a naturally occurring accelerated expansion phase without requiring inflation or a cosmological constant.
• The Big-Bang singularity is avoided due to the absence of horizons and the structure of the field equations in the flat background.
• A helicity-zero gravitational wave solution is obtained, predicting the same orbital decay rate for binary pulsars as observed and predicted by General Relativity.
• New gravitomagnetic effects may be detectable in the Gravity Probe B experiment, differing from GR's predictions and potentially explaining the anomalous precession observed in the Pioneer anomaly.