Massive Gravity Theories and Cosmological Implications

Massive gravity theories extend Einstein’s general relativity by endowing the graviton with a finite mass, thereby modifying gravitational dynamics on large scales. Early linear constructions, such as the Fierz–Pauli framework, confronted the appearance of an unphysical ghost mode, but non-linear realisations have since resolved these inconsistencies. In particular, ghost-free models introduce carefully tuned interaction terms that eliminate pathological degrees of freedom while preserving diffeomorphism invariance in a decoupling limit. Extensions to bimetric formulations couple a second spin-2 field, enabling rich cosmological solutions that can mimic dark energy or self-accelerate without a cosmological constant. Screening mechanisms, notably the Vainshtein effect, recover standard gravity in high-density regions, ensuring compatibility with solar-system tests. On cosmological scales, these theories offer alternatives to ΛCDM by altering the growth rate of structure, affecting cosmic microwave background anisotropies and large-scale clustering. Moreover, massive spin-2 particles have been proposed as dark matter candidates, with production mechanisms during inflation or reheating leading to coherent oscillations that behave as non-relativistic matter. Black-hole solutions in massive gravity also exhibit novel horizon structures and thermodynamic behaviour, opening new avenues for observational tests via gravitational waves and high-energy astrophysics.

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Massive Gravity Theories and Cosmological Implications publication trend

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

Technical terms

Massive gravity: A modification of general relativity in which the graviton acquires a non-zero mass, altering long-range gravitational interactions.

Ghost-free interactions: Specially tuned non-linear terms in the action that remove unphysical scalar modes (Boulware–Deser ghosts).

Vainshtein mechanism: A non-linear screening effect that restores general relativity in regions of high matter density.

Higuchi bound: A lower limit on the mass of a spin-2 field in de Sitter or expanding universes, required to avoid negative-norm states.

BRST quantisation: A method for enforcing gauge invariance at the quantum level, utilising a graded symmetry to eliminate unphysical modes.

Cosmological gravitational particle production (CGPP): A process by which expanding spacetime generates particles that couple only to gravity, potentially sourcing dark matter.

References

1. Cosmological gravitational particle production of massive spin-2 particles. Journal of High Energy Physics (2023).
2. Massive gravity from a first-quantized perspective. European Physical Journal C (2024).
3. Dilatonic black holes in dRGT massive gravity. Physics Letters B (2024).
4. Massive Gravity. Living Reviews in Relativity (2014).
5. Oscillating spin-2 dark matter. Physical Review D (2018).