Multi-field galileons and higher co-dimension branes (1008.1305v2)

Abstract: In the decoupling limit, the DGP model reduces to the theory of a scalar field pi, with interactions including a specific cubic self-interaction - the galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a 5-dimensional bulk with Lovelock terms on the brane and in the bulk. We study multi-field generalizations of the galileon, and extend this probe brane view to higher co-dimensions. We derive an extremely restrictive theory of multiple galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher co-dimension bulk. We explore some properties of this theory, finding de Sitter like self accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general non-renormalization theorem: multi-field galileons are not renormalized quantum mechanically to any loop in perturbation theory.

• The paper establishes multi-field galileon actions via geometric brane extensions, identifying a unique quartic interaction in four-dimensional spacetime.
• It develops a non-renormalized framework that stabilizes modified gravity and cosmological models by avoiding quantum corrections.
• The study reveals that de Sitter-like solutions incur ghost instabilities if the underlying flat-space theory is ghost-free.

Overview of Multi-Field Galileon Theories in Higher Co-Dimension Branes

The paper "Multi-field galileons and higher co-dimension branes" by Kurt Hinterbichler, Mark Trodden, and Daniel Wesley focuses on exploring generalizations of galileon theories to configurations involving multiple fields and higher co-dimension branes. Galileon interactions play a significant role in the Dvali-Gabadadze-Porrati (DGP) model, reducing to scalar field dynamics in specific limits and offering potential applications in modified gravity and cosmology due to their interesting self-interaction properties and second-order equations of motion. The authors derive multi-field galileon actions by extending the geometric framework associated with brane constructions.

Numerical Results and Claims

The paper's results are rooted in abstract theoretical developments rather than presenting numerical computations typically seen in empirical studies. Strong claims relate to the dimensional continuation of Lovelock invariants as a means to define galileon actions, notably asserting a unique allowed quartic interaction among multi-field galileons in four-dimensional spacetime. Their investigation into de Sitter-like solutions results in the provocative insight that these solutions inevitably harbor ghost instabilities if the corresponding flat space theory is ghost-free.

Implications

Practical Implications

1. Cosmological Applications: The absence of renormalization of the galileon terms provides an opportunity to develop cosmological models free from the uncertainties of quantum corrections, stabilizing theoretical predictions in the regime of non-linear effects.
2. Modified Gravity: The second order, ghost-free nature of the multi-field galileon theories enables exploration of alternate gravity theories that could manifest differing behaviors compared to General Relativity at large scales.

Theoretical Implications

1. Simplicity and Constrained Dynamics: The theories derived, constrained by the combination of galilean and internal symmetries, emphasize simplicity with a single non-renormalized coupling constant, aligning with the elegance sought in fundamental theories.
2. Potential Verification of Higher-Dimensional Physics: The geometric underpinning of the model suggests a consistent way to extend our understanding of physics beyond four-dimensional spacetime, correlating lower-dimensional dynamics with higher-dimensional constructs.

Future Developments

The research opens pathways to explore more complex configurations in cosmological and gravitational setups. Future advancements may focus on refining the observational predictions of multi-field galileon cosmologies or testing the limits of ghost conditions under broader conditions, potentially seeking ways to circumvent the ghost issue without sacrificing self-acceleration. Further paper could involve the non-linear regimes allowed by this model's stability under perturbations and their implications for early universe dynamics or structuring modifications to gravity at cosmological distances.

In summary, this paper elucidates multi-field galileon theories with foundational geometric insights within the field of higher-dimensional branes, offering a promising tool for theoretical models grappling with gravity modification and intrinsic field interactions driven by a minimalistic yet rigorous mathematical framework.