The galileon as a local modification of gravity (0811.2197v2)

Abstract: In the DGP model, the self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar \pi, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internalgalilean'' invariance, under which \pi's gradient shifts by a constant. This symmetry constrains the structure of the \pi Lagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]

• The paper introduces a galileon field with derivative self-interactions that respect Galilean symmetry and avoid ghost instabilities.
• It demonstrates self-accelerating solutions with thorough stability analysis and effective implementation of the Vainshtein mechanism.
• The study addresses gravitational backreaction, superluminal propagation, and quantum consistency, offering insights for dark energy models.

Overview of "The Galileon as a Local Modification of Gravity"

The paper "The galileon as a local modification of gravity" by Alberto Nicolis, Riccardo Rattazzi, and Enrico Trincherini introduces a class of scalar-tensor theories aimed at modifying gravity on cosmological scales without introducing undesirable ghost-like instabilities. The framework is motivated by the quest to explain the late-time accelerated expansion of the universe, without resorting to a cosmological constant. The central construct is the "galileon" field, denoted by $\pi$, which possesses derivative self-interactions that are crucial for modifying gravity in the infrared (IR).

Key Contributions

1. Galilean Symmetry and Derivative Self-interactions: The galileon field $\pi$ is introduced with specific derivative self-interactions that respect an internal galilean symmetry, under which the gradient of $\pi$ shifts by a constant. This symmetry leads to a robust structure for the $\pi$ Lagrangian, limiting the possible interaction terms to a set of only five terms in four dimensions. This constrained form is essential to find modifications of gravity that produce self-accelerating solutions without ghost instabilities.
2. Self-accelerating Solutions and Stability Analysis: The authors demonstrate the existence of self-accelerating de Sitter solutions achievable without ghost-like instabilities, a major advancement over previous models like the Dvali-Gabadadze-Porrati (DGP) model. They provide a thorough analysis of the stability of these solutions against small perturbations, confirming the absence of ghosts. They further derive spherically symmetric, Vainshtein-like nonlinear perturbations and establish their stability, ensuring compliance with solar system tests.
3. The Vainshtein Mechanism: The Vainshtein mechanism, pivotal in decoupling the $\pi$ field from gravitational dynamics at sub-cosmological distances, is effectively implemented. This ensures that deviations from General Relativity (GR) are suppressed near massive sources, circumventing potential conflicts with observed solar system physics.

Implications and Challenges

• Gravitational Backreaction:

The introduction of the galileon affects spacetime geometry due to its coupling with the stress-energy tensor $T^{\mu}_{\mu}$. Ensuring that these modifications do not lead to excessive curvature is a critical requirement. The analysis shows bounds on the coupling parameters to maintain consistency with existing bounds on gravitational interactions.

• Superluminal Propagation:

Some configurations lead to superluminal propagation speeds for perturbations, a controversial phenomenon considering locality and causality principles in field theory. Although not necessarily leading to inconsistencies, these features demand careful interpretation regarding the broader properties of the theory.

• Quantum and Classical Consistency:

The quantum consistency of the galileon field is addressed, presenting challenges akin to those in the DGP model. Particularly, the strong coupling scale $\Lambda$ is affected near massive bodies, impacting the effective cutoff and suggesting potential conflicts with standard quantum field theory expectations.

Prospects for Future Research

The galileon framework offers a promising avenue for IR modifications of gravity, paving the way to experimentally viable models that might elucidate the nature of dark energy and cosmic acceleration. Future efforts can focus on connecting these local modifications to a consistent UV-complete theory and exploring their full cosmological implications. Additionally, addressing the superluminal propagation and further refining the theory to incorporate minimal coupling to gravity without violating phenomenological constraints remains a significant area of paper.

In conclusion, this paper contributes significantly to the discourse on modified gravity theories, presenting a well-structured approach to tackling cosmological conundrums while maintaining compatibility with established physics. However, the journey towards a full understanding and application of these concepts is still ongoing, with several theoretical and observational hurdles to overcome.