Mass hierarchies and non-decoupling in multi-scalar field dynamics (1005.3848v2)

Abstract: In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these non-decoupled degrees of freedom and deduce its non-trivial contribution to the low energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory.

Overview of 'Mass Hierarchies and Non-Decoupling in Multi-Scalar Field Dynamics'

The paper authored by Ana Achúcarro et al. addresses the intricate dynamics of multi-scalar field theories with an inherent hierarchy of mass scales, exploring how heavy modes leave imprints on the effective dynamics of light modes. This investigation is rooted in contexts such as inflationary cosmology and low-energy string theory compactifications. The authors delve into scenarios where the vacuum manifold's geometry strays from the geodesic paths dictated by the field-space metric. Consequently, non-trivial interactions between light and heavy modes emerge, challenging traditional decoupling theorems.

Main Contributions

1. Field Space Curvature and Non-Decoupling Effects: The authors meticulously examine scenarios in which heavy modes, typically considered decoupled due to high mass, participate actively in the low-energy dynamics. This occurs notably when the trajectory of the scalar field undergoes sharp turns, inducing a mix of field perturbations along and orthogonal to the motion. The curvature of the trajectory becomes pivotal, as it defines how substantial the mixing is.
2. Effective Theory Formulation: Through detailed analysis, the paper derives an effective theory capturing the light modes' dynamics, incorporating contributions from the non-decoupled heavy modes. A key finding is that the effective dynamics of the light fields in a curved trajectory results in non-trivial corrections represented by the parameter $\beta$, with significant implications for the speed of sound of the perturbations.
3. Implications for Inflationary Models: In the context of inflation, such interactions could lead to observable effects on the primordial perturbation spectrum. Specifically, the correction factor $\beta$ could induce variations in the spectrum's scale dependence, notably affecting the inflationary particle production rates and predictions for non-Gaussianities in the cosmic microwave background.

Numerical Insights and Theoretical Implications

• The authors present a case paper where they assume a constant radius of curvature, which allows them to obtain exact analytical solutions. In these idealized settings, they find that the mix between light and heavy modes can significantly alter expected outcomes in scenarios like inflation.
• The parameter $e^\beta = 1 + 4 \zeta^2 / M^2$, where $\zeta$ measures the curvature-induced mixing and $M$ represents the heavy modes' mass scale, emerges as a crucial correction factor. This parameter may lead to reduced speed of sound scenarios, echoing DBI-like inflation models where particle excitations could lead to observable features.

Future Prospects and Applications

The research lays a foundation for a deeper understanding of scalar field dynamics in cosmological settings and more generally in high-energy physics models incorporating multi-field theories. The scenarios explored could offer new pathways in analyzing the coupling of light and heavy fields in supergravity models, influencing models' consistency and predictive power.

Future work could potentially extend this analysis to more complex bottlenecks where multi-field interactions due to geometric and dynamical effects might give rise to novel inflationary mechanisms or even new phases in the early Universe's evolution. Moreover, these insights may stimulate methodologies to reconcile effective field theories with string-theoretic landscapes, where compactifications naturally produce a plethora of scalar fields.

In conclusion, the work presents a significant advancement in understanding how curvature on field space and mass hierarchies influence scalar field theories' effective dynamics, with practical ramifications for cosmology and theoretical physics.