Infrared-modified gravities and massive gravitons (0802.4379v1)

Abstract: We review some theoretical and phenomenological aspects of massive gravities in 4 dimensions. We start from the Fierz--Pauli theory with Lorentz-invariant mass terms and then proceed to Lorentz-violating masses. Unlike the former theory, some models with Lorentz-violation have no pathologies in the spectrum in flat and nearly flat backgrounds and lead to interesting phenomenology.

• The paper examines the limitations of Fierz-Pauli theory, highlighting ghost modes and the vDVZ discontinuity that challenge massive gravity models.
• It introduces Lorentz-violating frameworks that use residual gauge symmetries to bypass instabilities and achieve a smooth massless limit.
• The analysis explores cosmological implications, suggesting these modifications may account for late-time cosmic acceleration without exotic energy components.

Infrared-Modified Gravities and Massive Gravitons: A Summary of Key Concepts and Theoretical Analyses

The paper "Infrared-modified gravities and massive gravitons" authored by V.A. Rubakov and P.G. Tinyakov presents an in-depth exploration of 4-dimensional massive gravities. The focus is on both Lorentz-invariant and Lorentz-violating modifications of general relativity, particularly at large distances and long timescales. This analysis stems from fundamental questions regarding the behavior of gravity at these scales and is motivated by unsolved issues such as the cosmological constant problem and the accelerated expansion of the Universe.

Theoretical Foundations:

1. Fierz-Pauli Theory: The authors begin with a review of the Fierz-Pauli theory, which introduces a mass term to the graviton in a Lorentz-invariant way. However, several critical issues arise, such as the infamous van Dam-Veltman-Zakharov (vDVZ) discontinuity, which implies that predictions of light bending differ from those of general relativity regardless of how small the graviton mass becomes.
2. Self-Consistency Problems: The Fierz-Pauli model is shown to suffer from severe pathologies, like the emergence of ghost modes and strong coupling at a very low ultraviolet (UV) scale compared to general relativity. These lead to a quick loss of control over the theory.
3. Boulware-Deser Instability: When extended to curved spacetimes, the theory becomes susceptible to the Boulware-Deser instability, which introduces a new propagating ghost mode even when the background deviates slightly from Minkowski space.

Lorentz-Violating Alternatives:

1. Lorentz-Violating Massive Gravitons: To avoid some issues present in the Lorentz-invariant cases, the authors discuss models where Lorentz invariance is explicitly broken. This allows for the evasion of ghost instabilities in certain parameter spaces of the model.
2. The Role of Residual Symmetries: The paper highlights the advantage of leaving certain gauge symmetries unbroken, which can protect against the re-emergence of ghost modes when moving away from idealized background scenarios. This stability is crucial for constructing viable theories.
3. Scalar Field Framework: A reformulation in terms of scalar fields—where background fields acquire space-time dependent values—offers a fresh perspective where Lorentz-violating effects can be encapsulated within a spontaneous symmetry breaking framework.

Phenomenological Implications and Cosmology:

1. Exception to vDVZ and Black Hole Solutions: The paper explores how Lorentz-violating gravities circumvent the vDVZ discontinuity issue, allowing for a smooth transition in the massless limit akin to general relativity.
2. Massive Gravitons and Cosmology: The modified theories potentially provide new insights into cosmological dynamics, such as late-time cosmic acceleration without invoking exotic energy components.
3. Open Questions: The viability of these models rests on finding stable ultraviolet completions and ensuring observational compatibility, particularly regarding gravitational wave signatures and large-scale cosmic structures.

Conclusion and Future Directions:

The paper by Rubakov and Tinyakov articulates the difficulties intrinsic to formulating a consistent theory of massive gravity and suggests viable pathways through Lorentz-violation. This line of research holds promise for resolving longstanding issues in theoretical physics and cosmology, albeit interspersed with considerable challenges. Future progress hinges on further refinement of these models, both at the theoretical level and in context with observational data, to ensure consistency and predictive power in describing the Universe's gravitational phenomena.