On the possibility of blue tensor spectrum within single field inflation

TL;DR

This paper investigates the theoretical limits of single-field inflation models in producing a blue spectrum of primordial tensor perturbations, highlighting the constraints and possible avenues for such scenarios.

Contribution

It provides a detailed dynamical analysis showing the bounded phase space for blue tensor spectra in single-field inflation models and discusses alternative approaches.

Findings

Blue tensor spectrum in single-field inflation is highly constrained.

Achieving a blue tilt requires non-canonical models or beyond standard slow-roll scenarios.

The phase space for viable models is strongly limited.

Abstract

We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field.