Conformal Gravity Theories and Cosmic Phenomena

Conformal gravity theories rest on the principle of local Weyl invariance, extending general relativity by requiring invariance under pointwise rescaling of the metric. By augmenting the Einstein–Hilbert action with terms quadratic in the Weyl tensor or by introducing a conformally coupled scalar field, these theories naturally include higher-order derivatives while preserving a symmetry that can address both cosmic acceleration and galactic dynamics without invoking new forms of unseen matter. In the early universe, conformal invariance influences the thermal history and primordial element production, potentially accommodating sterile neutrino species within a unified framework. On galactic scales, modified gravitational potentials featuring linear and quadratic terms reproduce the systematics of rotation curves across diverse galaxy types, offering a single-parameter description that obviates the need for particle dark matter. Black hole and gravitational wave solutions have been constructed within conformal and conformal-Killing gravity, revealing novel regular black holes and distinctive wave modes. Moreover, by integrating a conformal Higgs mechanism, the late-time cosmic expansion can be modelled without a separate cosmological constant, and subtle corrections arise in gravitational lensing that may be testable with forthcoming surveys. Overall, conformal gravity frameworks propose a coherent and symmetry-driven alternative to the standard ΛCDM paradigm, with global significance for our understanding of dark matter, dark energy and the geometric governance of cosmic evolution.

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Conformal Gravity Theories and Cosmic Phenomena publication trend

The graph below shows the total number of articles in conformal gravity theories and cosmic phenomena across all publications each year (not limited to Nature Index journals).

Technical terms

Conformal symmetry: Invariance under local rescaling of the metric tensor at each spacetime point, preserving angles but not absolute distances.

Weyl tensor: The traceless component of the Riemann curvature tensor that encapsulates the conformal curvature of spacetime.

Cotton tensor: A three-index tensor in three dimensions that vanishes for conformally flat geometries and appears in some conformal gravity field equations.

Conformal Killing vector: A vector field generating a conformal transformation that preserves the angle structure of the metric up to a scale factor.

Nucleosynthesis: The process in the early universe by which light atomic nuclei such as hydrogen, helium and lithium were formed.

Regular black hole: A solution of gravitational field equations that avoids a curvature singularity at the core, often through modified matter or geometric terms.

References

1. Early universe nucleosynthesis in massive conformal gravity. European Physical Journal C (2023).
2. Cotton gravity is not predictive. Physics Letters B (2024).
3. (Regular) Black holes in conformal Killing gravity coupled to nonlinear electrodynamics and scalar fields. Classical and Quantum Gravity (2024).
4. Galactic rotation curves in conformal gravity. Journal of Physics Conference Series (2013).
5. Conformal Gravity: Dark Matter and Dark Energy. Entropy (2013).