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Primordial gravitational waves in supersolid inflation

Angelo Ricciardone, Gianmassimo Tasinato

TL;DR

This work investigates a framework called supersolid inflation where four scalar fields break both time and space reparameterizations during inflation and couple non-minimally to gravity. The tensor sector acquires a nonzero mass and a reduced or altered sound speed, allowing a blue tensor spectrum and a squeezed-limit tensor bispectrum that can be parametrically larger than in standard single-field models. At leading order in a controlled expansion, the curvature perturbation spectrum is governed by space-reparameterization breaking, decoupling the tensor-to-scalar ratio $r$ from the time-breaking parameter and yielding $r \sim \frac{64}{\sqrt{3}} q_2^2 \lambda_0^4$. The results provide distinctive observational signatures and offer new insights for the EFT of inflation and the role of symmetry breaking patterns in the early universe.

Abstract

Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparameterization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate concrete realizations of such a scenario, including non-minimal couplings between gravity and the fields driving inflation. We focus in particular on the dynamics of primordial gravitational waves and discuss how their properties depend on the pattern of symmetry breaking that we consider. Tensor modes can have a blue spectrum, and for the first time we build models in which the squeezed limit of primordial tensor bispectra can be parametrically enhanced with respect to standard single-field scenarios. At leading order in a perturbative expansion, the tensor-to-scalar ratio depends only on the parameter controlling the breaking of space-reparameterization. It is independent from the quantities controlling the breaking of time-reparameterization, and this represents a difference with respect to standard single-field inflationary models.

Primordial gravitational waves in supersolid inflation

TL;DR

This work investigates a framework called supersolid inflation where four scalar fields break both time and space reparameterizations during inflation and couple non-minimally to gravity. The tensor sector acquires a nonzero mass and a reduced or altered sound speed, allowing a blue tensor spectrum and a squeezed-limit tensor bispectrum that can be parametrically larger than in standard single-field models. At leading order in a controlled expansion, the curvature perturbation spectrum is governed by space-reparameterization breaking, decoupling the tensor-to-scalar ratio from the time-breaking parameter and yielding . The results provide distinctive observational signatures and offer new insights for the EFT of inflation and the role of symmetry breaking patterns in the early universe.

Abstract

Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparameterization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate concrete realizations of such a scenario, including non-minimal couplings between gravity and the fields driving inflation. We focus in particular on the dynamics of primordial gravitational waves and discuss how their properties depend on the pattern of symmetry breaking that we consider. Tensor modes can have a blue spectrum, and for the first time we build models in which the squeezed limit of primordial tensor bispectra can be parametrically enhanced with respect to standard single-field scenarios. At leading order in a perturbative expansion, the tensor-to-scalar ratio depends only on the parameter controlling the breaking of space-reparameterization. It is independent from the quantities controlling the breaking of time-reparameterization, and this represents a difference with respect to standard single-field inflationary models.

Paper Structure

This paper contains 11 sections, 76 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System under consideration
  3. De Sitter background solution
  4. Power law background solution
  5. Dynamics of tensor fluctuations
  6. Quadratic tensor action: tensor mass and sound speed
  7. Cubic tensor action and tensor non-Gaussianity
  8. Dynamics of scalar fluctuations
  9. Consequences for the tensor-to-scalar ratio
  10. Conclusions
  11. Appendix A

Figures (3)

  • Figure 1: Evolution of $\gamma$, defined in Eq. \ref{['gadef1']} in the range of values allowed by Eq. \ref{['condqq2']}. As explained in the text, the parameter $\gamma$ controls the amplitude of the squeezed limit of tensor bispectrum in our model, and how much it differs from the same quantity calculated in standard inflationary scenarios.
  • Figure 2: ${\cal A}_{{\cal T}_{1}}^{+++}(1, k_2/k_1, k_3/k_1)(k_2/k_1)^{2}(k_3/k_1)^{2}$ as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to unity for equilateral configurations $k_2/k_1=k_3/k_1=1$. The contribution to the tensor bispectrum associated with operator ${\cal T}_1$ peaks in the squeezed limit.
  • Figure 3: ${\cal A}_{{\cal T}_{2}}^{+++}(1, k_2/k_1, k_3/k_1)(k_2/k_1)^{2}(k_3/k_1)^{2}$ as a function of $k_2/k_1$ and $k_3/k_1$. The plot is normalized to unity for equilateral configurations $k_2/k_1=k_3/k_1=1$.