High-Scale Inflation and the Tensor Tilt

TL;DR

The paper investigates how higher-curvature corrections during slow-roll inflation, constrained by weakly broken conformal symmetry, modify the tensor sector. It shows that a field-dependent Weyl-squared coupling $f(\phi) W^2 / M^2$ introduces a nontrivial tensor sound speed and leads to a correction to the tensor tilt $n_t$ that can violate the standard single-field tensor consistency condition, with the leading effect scaling as $n_t \approx -2\varepsilon \pm 4 b \sqrt{2\varepsilon}\, H^2/M^2$. This result is corroborated both by a bulk analysis and by conformal perturbation theory, and it has a holographic interpretation via the wavefunction of the universe, where the relevant observables correspond to stress-tensor correlators in a dual CFT. The boundary analysis reproduces the bulk findings and identifies that the tensor tilt arises at $O(\varphi)$ in the CFT deformation, while the tensor-to-scalar ratio arises at $O(\varphi^2)$, providing a symmetry-protected route to probe high-scale physics and potentially observable signatures if the higher-curvature scale $M$ is near the Hubble scale $H$.

Abstract

In this paper, we explore a novel observational signature of gravitational corrections during slow-roll inflation. We study the coupling of the inflaton field to higher-curvature tensors in models with a minimal breaking of conformal symmetry. In that case, the most general correction to the tensor two-point function is captured by a coupling to the square of the Weyl tensor. We show that these scenarios lead to a correction to the tilt of the tensor power spectrum and hence a violation of the tensor consistency condition. We arrive at the same conclusion through an analysis in conformal perturbation theory.

Figures (1)

• Figure 1: The time-dependent inflaton vev, $\bar{\phi}(t)$, introduces a preferred time slicing of de Sitter space.