# Inflationary Perturbations in No-Scale Theories

## TL;DR

This paper investigates inflationary perturbations within scale-invariant theories, demonstrating their viability and consistency with observations, and explores the role of Weyl-squared terms and specific no-scale models in inflationary dynamics.

## Contribution

It provides general formulas for perturbations in scale-invariant theories, analyzes the impact of Weyl-squared terms, and applies these to a concrete no-scale model with implications for observable inflationary parameters.

## Key findings

- Weyl-squared term does not cause negative energies with proper quantization.
- Pure planckion-inflation is compatible with observations if Weyl-squared coefficient is large.
- Weyl-squared term introduces an isocurvature mode within current bounds.

## Abstract

We study the inflationary perturbations in general (classically) scale-invariant theories. Such scenario is motivated by the hierarchy problem and provides natural inflationary potentials and dark matter candidates. We analyse in detail all sectors (the scalar, vector and tensor perturbations) giving general formulae for the potentially observable power spectra, as well as for the curvature spectral index $n_s$ and the tensor-to-scalar ratio $r$. We show that the conserved Hamiltonian for all perturbations does not feature negative energies even in the presence of the Weyl-squared term if the appropriate quantization is performed and argue that this term does not lead to phenomenological problems at least in some relevant setups. The general formulae are then applied to a concrete no-scale model, which includes the higgs and a scalar, "the planckion", whose vacuum expectation value generates the Planck mass. Inflation can be triggered by a combination of the planckion and the Starobinsky scalar and we show that no tension with observations is present even in the case of pure planckion-inflation, if the coefficient of the Weyl-squared term is large enough. In general, even quadratic inflation is allowed in this case. Moreover, the Weyl-squared term leads to an isocurvature mode, which currently satisfies the observational bounds, but may be detectable with future experiments.