Cosmology of a covariant Galileon field (1007.2700v2)

Abstract: We study the cosmology of a covariant scalar field respecting a Galilean symmetry in flat space-time. We show the existence of a tracker solution that finally approaches a de Sitter fixed point responsible for cosmic acceleration today. The viable region of model parameters is clarified by deriving conditions under which ghosts and Laplacian instabilities of scalar and tensor perturbations are absent. The field equation of state exhibits a peculiar phantom-like behavior along the tracker, which allows a possibility to observationally distinguish the Galileon gravity from the Lambda-CDM model.

• The paper presents a tracker solution evolving towards a de Sitter attractor that mimics effective dark energy.
• The paper demonstrates a phantom-like equation of state crossing w = -1, providing a testable prediction distinct from ΛCDM.
• The paper ensures ghost-free stability using the Faddeev-Jackiw method and maps viable parameter spaces through numerical simulations.

Cosmology of a Covariant Galileon Field

The paper investigates the cosmological implications of a scalar field respecting Galilean symmetry within a covariant framework in flat space-time. The key focus is to explore the conditions under which such a Galileon field can account for cosmic acceleration, which is typically attributed to dark energy. The scalar field exhibits non-linear self-interactions, leading to a cosmological behavior distinguishing it from the traditional $\Lambda$CDM model.

Key Contributions and Findings

The authors present a detailed analysis of a scalar field, referred to as the Galileon, characterized by its action's invariance under a Galilean transformation. They derive the field's Lagrangians, ensuring that the resulting equations of motion remain second-order in derivatives, thereby avoiding ghost instabilities that plagued previous theories like the DGP model.

1. Tracker Solution and de Sitter Attractor: The paper introduces a tracker solution that naturally evolves towards a de Sitter fixed point, driving cosmic acceleration. The existence of this stable attractor is significant as it allows the Galileon dynamics to mimic an effective dark energy era.
2. Equation of State Behavior: A notable feature of this work is the peculiar phantom-like behavior of the equation of state for the Galileon field. The authors show how it crosses the boundary of $w_{\rm DE} = -1$ without instability, offering a testable prediction that could differentiate this model from the $\Lambda$CDM theory.
3. Stability Analysis: By employing the Faddeev-Jackiw method, the paper derives comprehensive stability conditions against ghosts and Laplacian instabilities. This involves constraints on the choice of parameters denoted by $(\alpha, \beta)$. The analysis ensures that both scalar and tensor perturbations remain stable throughout the universe's evolution.
4. Parameter Space and Numerical Simulations: The paper provides a delineated parameter space where viable cosmological solutions exist. The authors confirm through numerical simulations that the Galileon can lead to a sequence of cosmological epochs—radiation, matter, and de Sitter—consistent with observations. The figures illustrate the trajectory of the effective equation of state and demonstrate the conditions under which the scalar and tensor perturbation propagation speeds remain sub-luminal.

Implications and Future Directions

The implications of this research are both practical and theoretical. Practically, the model's distinctive predictions, particularly the evolution of the equation of state, provide a framework for potential experimental validation with cosmological data. Theoretically, the covariant Galileon offers a robust alternative to GR modifications that suffer from instability issues.

Future research directions include:

• The exploration of cosmological perturbations and their observational signatures, potentially leading to constraints on model parameters based on the effective gravitational coupling's evolution.
• Analyzing the Vainshtein mechanism in varying gravitational settings, thereby shedding light on the transition from modified gravity scales to those consistent with solar system observations.
• Extending the Galileon framework by integrating more general functions of the scalar field, possibly unveiling connections with other scalar-tensor theories.

In summary, the cosmology of a covariant Galileon field presented in this paper offers a theoretically coherent and potentially observable modification of gravity. It adds to the current understanding of dark energy and cosmic acceleration, providing a fertile ground for further explorations in both cosmology and gravity theories.