Effective Field Theory for Inflation (0804.4291v2)

Abstract: The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the ${\cal R}$ correlation function are found to be purely of the $k$-inflation type. For tensor modes the leading corrections to the correlation function arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. These methods are also briefly applied to non-generic theories of inflation with an extra shift symmetry, as in so-called ghost inflation.

• The paper presents an effective field theory framework for inflation that systematically incorporates higher-derivative corrections in a single-field approach.
• It demonstrates that higher-derivative terms modify the sound speed of scalar perturbations while aligning with established k-inflation models.
• It uncovers parity-violating effects in tensor perturbations, highlighting potential observational impacts on gravitational waves and the cosmic microwave background.

Effective Field Theory for Inflation

This paper by Steven Weinberg presents an in-depth analysis applying effective field theory (EFT) methodologies to paper generic theories of inflation involving a single inflaton field. The core objective is to expand the foundational framework to incorporate scalar and tensor perturbations, while assessing the implications of higher-derivative corrections on cosmic inflation models.

Overview of Theoretical Foundation

The paper begins by situating the reader in the well-established theoretical landscape of inflationary models driven by a single, canonically normalized scalar field, typically represented by the Lagrangian form involving two spacetime derivatives. This fundamental form, pivotal in the description of cosmic perturbations, nevertheless warrants scrutiny beyond its immediate terms due to the substantial cosmic energy scales involved, approximately 14 orders of magnitude below the Planck scale. The author postulates the existence of additional terms, suppressed by powers of a large mass $M$, as part of a more comprehensive EFT framework. This approach does not commit to any underlying fundamental theory but rather utilizes dimensional analysis and perturbative expansions to enrich the current understanding.

Scalar and Tensor Perturbation Analysis

Weinberg meticulously progresses through the implications of enhanced EFT on scalar perturbations, engaging with the familiar gauge-invariant potential $R$. It is evident from his calculations that higher derivative terms predominantly influence the sound speed $c_s$ of these perturbations, a critical factor in estimating inflationary fluctuations. His analyses affirm that corrections primarily conform to the known "k-inflation" structure, without engendering new paradigms for scalar fluctuations beyond existing slow-roll or conventional calculations.

Conversely, tensor perturbations, confined to the spatial metric, expose a significant deviation through helicity-dependent propagation—attributed to parity-violating terms within the higher-derivative expansions. These terms, albeit not dictating energy-momentum conservation, challenge standard cosmological models by affecting cosmic microwave background tensor modes. Such results extend the structured analysis initially developed for scalar fields to tensor modes, encapsulating an essential aspect of gravitational wave dynamics in inflationary cosmology.

Case Study: Ghost Inflation

Weinberg closes with an exploration of non-generic models through the lens of ghost inflation, characterized by an additional shift symmetry in the inflaton field. This symmetry confines the Lagrangian to derivatives of the inflaton alone, thus permitting a substantially smaller mass scale $M$ than that required in generic models. Notably, while initially these models yield an unrealistic scalar spectral index, including derivative corrections cultivates a rich array of phenomena potentially aligning them closer with observational data.

Implications and Future Directions

The paper rigorously constructs a nuanced understanding of inflation through EFT, providing pivotal insights into the behavior of scalar and tensor fluctuations under various perturbative corrections. While these findings remain unassuming of groundbreaking new effects, their extensive implications offer an alternative perspective to conventional inflationary theories, one that embraces underlying high-energy corrections without direct reliance on fundamental theories.

Moreover, the analysis of parity violation in tensor modes merits continued exploration, particularly in observational astrophysics, where future gravitational wave data could empirically validate such theoretical predictions. As this theoretical framework matures, it may offer significant contributions to understanding the early universe, gravitational phenomena, and possibly, the integration of quantum theories with cosmic evolution.