Parity violation in the Cosmic Microwave Background from a pseudoscalar inflaton

Abstract: If the inflaton is a pseudoscalar, then it naturally interacts with gauge fields via an axion-like coupling to $F_{\mu\nu} \tilde{F}^{\mu\nu}$. Through this coupling, the rolling inflaton produces quanta of the gauge field, that in their turn source the tensor components of the metric perturbations. Due to the parity-violating nature of the system, the right- and the left-handed tensor modes have different amplitudes. Such an asymmetry manifests itself in the form of non-vanishing TB and EB correlation functions in the Cosmic Microwave Background (CMB). We compute the amplitude of the parity-violating tensor modes and we discuss two scenarios, consistent with the current data, where parity-violating CMB correlation functions will be detectable in future experiments.

• The paper introduces a model where a pseudoscalar inflaton creates an imbalance between right- and left-handed tensor modes, resulting in detectable parity violation.
• It details how coupling with a U(1) gauge field amplifies vacuum fluctuations into chiral gravitational waves, quantified by the parameter Δχ linked to H and ξ.
• The study proposes using a curvaton field or multiple gauge fields to mitigate nongaussianities, thereby expanding the viable parameter space for observing CMB parity violation.

Parity Violation in the Cosmic Microwave Background from a Pseudoscalar Inflaton

The paper discusses a novel approach to imprinting parity violation on the Cosmic Microwave Background (CMB) via a pseudoscalar inflaton. The inflaton $\phi$, if a pseudoscalar, interacts with gauge fields through a characteristic coupling that triggers the production of right- and left-handed tensor modes with unequal amplitudes, thereby creating parity-violating signatures detectable in future CMB observations.

Theoretical Framework

The key mechanism involves a pseudoscalar inflaton, specifically a pseudo-Nambu-Goldstone boson (pNGb), which couples with a $U(1)$ gauge field. The rolling inflaton amplifies the vacuum fluctuations of the gauge field into classical states, resulting in the production of gravitational waves with different helicities. The chiral nature of gravitational waves is quantified by the parameter $\Delta\chi$, which exhibits a dependence on the Hubble parameter $H$ during inflation and a parameter $\xi = \dot{\phi} / (H f)$. The scenarios outlined can yield $\Delta\chi$ values assuming significant magnitudes under specific parameter values.

Implications and Observational Prospects

The presence of these parity-violating modes in the CMB is indicated by non-zero TB and EB correlation functions, signaling parity violation. The authors propose two scenarios consistent with current data: one involving a second field, a 'curvaton', to generate density perturbations, and another involving multiple gauge fields, both aimed at circumventing the issue of nongaussianities that arise in single-field models.

Constraints and Parameter Space

The main constraint on this model arises from nongaussianities, as the source of chiral tensor modes also induces scalar modes which are nongaussian in nature. The introduction of a curvaton field reduces the impact of these perturbations and allows for detectable parity violations while maintaining observables within bounds. In systems with multiple gauge fields, the constraints from nongaussianities can be mitigated, enabling a wider parameter space where detection of parity-violating effects is plausible.

Practical and Theoretical Developments

This work highlights the feasibility of detecting chirality in gravitational waves through future CMB experiments, and the potential for pseudoscalar inflaton models to yield parity-violating signals without modifications to the gravitational sector. The research paves the way for exploring more intricate models of inflation where such chiral imprints may be observed. Questions remain about the implementation in realistic models and the broader implications for inflationary cosmology.

Future Research

Investigating models beyond the single pseudoscalar inflaton, considering multifield inflationary scenarios, or integrating with string-theory motivated frameworks could enrich the understanding of parity violation in the early universe. Additionally, data from upcoming cosmic-variance-limited CMB surveys will be instrumental in either confirming or refuting the models presented. The exploration of parity-violating bispectra in the CMB provides an additional avenue for further inquiry.

In conclusion, the paper presents a compelling theoretical framework, offering predictions testable by forthcoming experiments, and underlining the potential significance of parity violation as a probe of early universe physics.