Scaling behavior of observables as a model characteristic in multifield inflation

TL;DR

This paper investigates how observable behaviors in multifield inflation models exhibit scaling laws, proposing a method to characterize models through their scaling exponents, which vary with model parameters and energy scales.

Contribution

It introduces an iterative procedure to analyze scaling behavior of observables in multifield inflation, revealing simple scaling laws and parameter-dependent exponents.

Findings

Models exhibit characteristic scaling laws.

Scaling exponents depend on model parameters.

Exponents follow their own scaling laws with energy scales.

Abstract

One of the fundamental questions in inflation is how to characterize the structure of different types of models in the field theoretic landscape. Proposals in this direction include attempts to directly characterize the formal structure of the theory by considering complexity measures of the potentials. An alternative intrinsic approach is to focus on the behavior of the observables that result from different models and to ask whether their behavior differs among models. This type of analysis can be applied even to nontrivial multifield theories where a natural measure of the complexity of the model is not obvious and the analytical evaluation of the observables is often impossible. In such cases one may still compute these observables numerically and investigate their behavior. One interesting case is when observables show a scaling behavior, in which case theories can be characterized in terms of their scaling amplitudes and exponents. Generically, models have nontrivial parameter spaces, leading to exponents that are functions of these parameters. In such cases we consider an iterative procedure to determine whether the exponent functions in turn lead to a scaling behavior. We show that modular inflation models can be characterized by families of simple scaling laws and that the scaling exponents that arise in this way in turn show a scaling law in dependence of these varying energy scales.