Generalized G-inflation: Inflation with the most general second-order field equations (1105.5723v4)

Abstract: We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of G-inflation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner.

• The paper presents a unified scalar field model that broadens G-inflation to include diverse non-canonical and non-minimally coupled theories.
• The authors establish rigorous stability conditions and derive explicit formulations for both kinetically and potential-driven inflation scenarios.
• Numerical analysis reveals conditions for a blue tensor spectrum and opens pathways to explore non-standard inflationary effects.

Generalized G-Inflation: A Comprehensive Framework for Single-Field Inflation Models

The paper "Generalized G-inflation: Inflation with the most general second-order field equations" by Tsutomu Kobayashi, Masahide Yamaguchi, and Jun’ichi Yokoyama presents an extensive and meticulous exploration into generalized Galileon theories as a foundation for the most comprehensive single-field inflationary models. The authors offer a profound extension of the G-inflation paradigm, broadening the scope to encompass all forms of non-canonical and non-minimally coupled scalar field theories conducive to second-order field equations. This synthesis includes, but is not limited to, prior frameworks such as k-inflation, extended inflation, and various Higgs models.

Theoretical Contributions and Methodological Advancements

This paper embarks on an ambitious venture to generalize the covariant Galileon theory and integrate higher-order Lagrangians, ensuring that the resulting equations maintain second-order derivatives. Central to this endeavor is the notion of avoiding ghosts, a prevalent challenge in higher derivative theories, which is skillfully addressed through the covariantization strategy proposed by Deffayet et al. The authors proffer a new scalar field model named “Generalized G-inflation” or G$_G$-inflation that decisively steps beyond existing Galileon frameworks, albeit with a necessary break in Galilean symmetry to achieve phenomenologically viable inflation scenarios.

Analysis of Scalar Field Dynamics and Cosmological Implications

The paper explores two predominant inflationary mechanisms: kinetically driven G-inflation and potential-driven slow-roll inflation. By providing explicit formulations and background cosmological equations for both scenarios, the researchers elucidate the general behavior of inflationary backgrounds and primordial perturbations. Notably, for kinetically driven inflation, the shift symmetry $\phi \rightarrow \phi + c$ allows for de Sitter attractors, suggesting that inflation can be propelled by kinetic energy alone. The authors emphasize that although the symmetry must eventually be broken to facilitate inflation termination and reheating, the exact mechanism awaits further investigation.

For potential-driven inflation, the paper extends the standard slow-roll paradigm to incorporate additional Galileon terms, offering a theoretical landscape where scalar field dynamics deviate from conventional models. The authors put forth slow-roll equations while considering the perturbations within the framework, ultimately yielding stability criteria and evaluating power spectra for both tensor and scalar perturbations.

Deriving Numerical Stability and Power Spectra

In terms of numerical results, the authors derive stability conditions for scalar and tensor perturbations, articulated through positivity constraints on certain functions like $F_T$ and $G_T$. They also provide the primordial power spectra computations that reveal the dependence of spectral tilts on the model's parameters. A significant implication is that, under certain conditions, a blue spectrum (where tensor spectral tilt $n_T > 0$) can be realized, diverging from the canonical inflationary expectations. This paper offers ample scope for exploring inflationary scenarios where specific potential and Galileon terms could lead to observable differences.

Future Directions and Concluding Remarks

The research opens pathways for exploring higher-order effects, such as non-linear perturbations and potential non-Gaussianities, stemming from Generalized G-inflation. These aspects remain pertinent for aligning inflationary models with cosmological observations and understanding the intricate phenomenology of early Universe scenarios. The consideration of non-standard sound speeds and their impact on observational implications adds a layer of complexity that future works could further unravel.

In conclusion, the paper establishes a rigorous theoretical scaffold that broadens the horizon of possible single-field inflation models, reinforcing the existing literature while setting the stage for substantive future investigations within cosmology and theoretical physics. This pioneering work not only enhances our comprehension of inflationary processes but also fortifies the bridge between higher-order gravitational theories and fundamental cosmological phenomena.