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Solid Inflation

Solomon Endlich, Alberto Nicolis, Junpu Wang

TL;DR

Solid Inflation introduces a solid-like sector composed of three scalar fields whose internal symmetries drive inflation while keeping time translations unbroken. The framework yields a unique perturbation structure: scalar and tensor spectra with a blue-tilted tensor mode, and a highly non-Gaussian, squeezed bispectrum with a distinctive angular dependence and amplitude f_NL ~ 1/(ε c_L^2). The authors develop the EFT for solids, analyze cosmological perturbations, and compute the bispectrum, showing that standard adiabatic expectations do not apply during inflation, though ζ becomes adiabatic after reheating. They also provide a practical, factorizable template for data analyses and discuss reheating as a solid-to-fluid transition, along with potential generalizations to super-solids or crystalline variants. The work highlights novel observational signatures and broadens the space of inflationary scenarios beyond the conventional EFT of inflation.

Abstract

We develop a cosmological model where primordial inflation is driven by a 'solid', defined as a system of three derivatively coupled scalar fields obeying certain symmetries and spontaneously breaking a certain subgroup of these. The symmetry breaking pattern differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. Most notably, non-gaussianities in the curvature perturbations are unusually large, with f_NL ~ 1/(ε.c_s^2), and have a novel shape: peaked in the squeezed limit, with anisotropic dependence on how the limit is approached. Other unusual features include the absence of adiabatic fluctuation modes during inflation---which does not impair their presence and near scale-invariance after inflation---and a slightly blue tilt for the tensor modes.

Solid Inflation

TL;DR

Solid Inflation introduces a solid-like sector composed of three scalar fields whose internal symmetries drive inflation while keeping time translations unbroken. The framework yields a unique perturbation structure: scalar and tensor spectra with a blue-tilted tensor mode, and a highly non-Gaussian, squeezed bispectrum with a distinctive angular dependence and amplitude f_NL ~ 1/(ε c_L^2). The authors develop the EFT for solids, analyze cosmological perturbations, and compute the bispectrum, showing that standard adiabatic expectations do not apply during inflation, though ζ becomes adiabatic after reheating. They also provide a practical, factorizable template for data analyses and discuss reheating as a solid-to-fluid transition, along with potential generalizations to super-solids or crystalline variants. The work highlights novel observational signatures and broadens the space of inflationary scenarios beyond the conventional EFT of inflation.

Abstract

We develop a cosmological model where primordial inflation is driven by a 'solid', defined as a system of three derivatively coupled scalar fields obeying certain symmetries and spontaneously breaking a certain subgroup of these. The symmetry breaking pattern differs drastically from that of standard inflationary models: time translations are unbroken. This prevents our model from fitting into the standard effective field theory description of adiabatic perturbations, with crucial consequences for the dynamics of cosmological perturbations. Most notably, non-gaussianities in the curvature perturbations are unusually large, with f_NL ~ 1/(ε.c_s^2), and have a novel shape: peaked in the squeezed limit, with anisotropic dependence on how the limit is approached. Other unusual features include the absence of adiabatic fluctuation modes during inflation---which does not impair their presence and near scale-invariance after inflation---and a slightly blue tilt for the tensor modes.

Paper Structure

This paper contains 26 sections, 184 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Effective field theory for solids (and fluids)
  3. Inflation
  4. Physical 'clocks' and reheating
  5. Why not the EFT of inflation?
  6. Cosmological perturbations
  7. Two-point functions
  8. Tensor perturbations
  9. Scalar Perturbations
  10. The three-point function
  11. Analytic Calculation of Integral
  12. The size and shape of non-gaussianities
  13. A factorizable template
  14. Why Is $\zeta$ Not Conserved?
  15. Matching of correlation functions at reheating, and post-inflationary evolution
  16. ...and 11 more sections

Figures (2)

  • Figure 1: The shape of non-gaussianities for our model, according to the standard conventions and definitions of ref. BCZ.
  • Figure 2: Our factorizable approximation to the three-point function. The flat triangular surface is the difference with our exact three-point function. As clear from the picture, this is maximized for equilateral configurations ($x_2=x_3=1$), and is always quite small.