G-inflation: inflation driven by the Galileon field (1008.0603v3)

Abstract: We propose a new class of inflation model, G-inflation, which has a Galileon-like nonlinear derivative interaction of the form $G(\phi, (\nabla\phi)^2)\Box\phi$ in the Lagrangian with the resultant equations of motion being of second order. It is shown that (almost) scale-invariant curvature fluctuations can be generated even in the exactly de Sitter background and that the tensor-to-scalar ratio can take a significantly larger value than in the standard inflation models, violating the standard consistency relation. Furthermore, violation of the null energy condition can occur without any instabilities. As a result, the spectral index of tensor modes can be blue, which makes it easier to observe quantum gravitational waves from inflation by the planned gravitational-wave experiments such as LISA and DECIGO as well as by the upcoming CMB experiments such as Planck and CMBpol.

• The paper proposes the G-inflation model, which leverages Galileon interactions to sustain exact de Sitter expansion while producing scale-invariant scalar perturbations.
• It demonstrates that the unique Lagrangian structure avoids ghost instabilities and maintains positive sound speeds even with NEC violations.
• The model predicts a blue-tilted tensor spectrum with an elevated tensor-to-scalar ratio, offering new prospects for primordial gravitational wave detection.

Overview of "G-inflation: inflation driven by the Galileon field"

The paper introduces a novel class of inflation model termed "G-inflation," characterized by a Galileon-like nonlinear derivative interaction in the Lagrangian of the form $G(\phi, (\nabla\phi)^2)\Box\phi$. It represents a significant expansion in inflationary cosmology, traditionally driven by scalar fields known as inflatons. G-inflation's potential to generate (almost) scale-invariant curvature fluctuations even in an exact de Sitter background distinguishes it from traditional inflation models. Notably, the model suggests a tensor-to-scalar ratio substantially larger than standard predictions, challenging the conventional consistency relation.

Key Characteristics and Findings

The core feature of G-inflation is its ability to sustain an exactly de Sitter background while provoking scalar perturbations. This is facilitated by a unique Lagrangian structure, which limits derivatives to second order within the gravitational and scalar-field equations. Unlike potential-driven models of inflation, G-inflation can maintain scale-invariant fluctuations without explicit potential dependence. The paper asserts this is due to the distinctive dynamics ingrained in the Galileon structure, breaking symmetry in a curved spacetime context.

One remarkable result from this paper is the nil instability despite the model's allowance for null energy condition (NEC) violations. Typically, scenarios with NEC violations encounter stability issues, but G-inflation resolves these via positive sound speeds and avoidance of ghosts. This characteristic distinctly sets it apart from other advanced inflationary theories such as k-inflation and extends its utility beyond mere theoretical interest.

Stability and Spectrum Features

The paper explores stability analyses of its proposed G-inflation models. By employing unitary gauge calculations and examining perturbation equations, it demonstrates the model's robustness against instabilities. The consideration of various mass-dimension parameters elucidates conditions under which G-inflation reliably emulates a quasi-de Sitter inflationary phase.

From the spectral perspective, the model's capacity to yield a blue-tilted tensor spectrum without instability amplifies its attractiveness for experimental corroboration. The work highlights that gravitational wave signatures from G-inflation diverge from typical predictions, as NP aside, it proposes a blue spectral index. This feature, augmented by increased tensor amplitude, raises the prospects of detectable primordial gravitational waves by upcoming CMB and gravitational-wave observatories, namely LISA and DECIGO.

Implications and Future Prospects

The theoretical implications of G-inflation suggest broader pathways for advancing cosmological models accommodating enhanced tensor modes. Its nuanced handling of symmetry-breaking and derivative-order limitation instigates re-evaluation of inflationary dynamics and energy conditions. The potential for G-inflation to viably extend beyond dark energy applications points to further exploration, particularly concerning non-Gaussianity and model consistency across different cosmological scenarios.

Practically, the strengthened tensor-scalar dynamics enhance G-inflation's alignment with observational capabilities, potentially offering novel insights into the early universe's state from gravitational wave analyses. With a tensor-to-scalar ratio capable of exceeding chaotic inflation benchmarks, continued research could pivot around integrating G-inflation into broader inflationary paradigms, validating it via enhanced precision in cosmological measurements.

In summary, G-inflation introduces an innovative dimension to inflationary modeling, fostering constructive deviations from convention while maintaining physical viability. As experimental apparatus advance, the implications of this model pave the way for nuanced understandings of early universe phenomena and scalar-tensor interactions.