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The non-minimal 3-form cosmology and the rise of the cuscuton

Antonio De Felice, Anamaria Hell

TL;DR

The paper analyzes a non-minimally coupled 3-form cosmology by exploiting its dual vector formulation to study degrees of freedom and stability. In a homogeneous and isotropic FLRW background with couplings to both the Ricci scalar and tensor, the theory propagates exactly three dof (one scalar and two tensor modes) and no extra vector dof, with explicit no-ghost and propagation-speed conditions. In an anisotropic Bianchi I background with the Ricci-tensor coupling set to zero, two background branches appear; one branch can be recast as a constrained scalar interacting with a cuscuton field, providing a systematically healthier description, while the other branch shows potential strong-coupling behavior along the anisotropic direction. The paper further diagonalizes the theory into an Einstein-frame representation featuring a cuscuton coupled to a constrained scalar, and demonstrates that perturbations in both FLRW and Bianchi I settings maintain unit propagation speeds for propagating modes and no ghost instabilities, highlighting the model’s viability and rich phenomenology for early and late-time cosmology.

Abstract

We consider the 3-form theory with non-minimal coupling to gravity in an expanding Universe. First, we assume that the background is homogeneous and isotropic, and that the three-form is coupled to both the Ricci scalar and the Ricci tensor. We show that in this case, it propagates three degrees of freedom: a scalar mode and two tensor ones. Then, we consider an anisotropic background that corresponds to a Bianchi Type I Universe, and set the coupling with the Ricci tensor to zero. We show that, similarly to the Proca theory with non-minimal coupling to gravity, this case leads to two branches for the background solutions - depending on the values of the 3-form. However, in contrast to the Proca case, we show that no extra modes appear. We explore the no-ghost conditions and speed of propagation for all three modes in both branches. Finally, we show that one of the branches can be written as a theory of a constrained scalar, coupled to a cuscuton field.

The non-minimal 3-form cosmology and the rise of the cuscuton

TL;DR

The paper analyzes a non-minimally coupled 3-form cosmology by exploiting its dual vector formulation to study degrees of freedom and stability. In a homogeneous and isotropic FLRW background with couplings to both the Ricci scalar and tensor, the theory propagates exactly three dof (one scalar and two tensor modes) and no extra vector dof, with explicit no-ghost and propagation-speed conditions. In an anisotropic Bianchi I background with the Ricci-tensor coupling set to zero, two background branches appear; one branch can be recast as a constrained scalar interacting with a cuscuton field, providing a systematically healthier description, while the other branch shows potential strong-coupling behavior along the anisotropic direction. The paper further diagonalizes the theory into an Einstein-frame representation featuring a cuscuton coupled to a constrained scalar, and demonstrates that perturbations in both FLRW and Bianchi I settings maintain unit propagation speeds for propagating modes and no ghost instabilities, highlighting the model’s viability and rich phenomenology for early and late-time cosmology.

Abstract

We consider the 3-form theory with non-minimal coupling to gravity in an expanding Universe. First, we assume that the background is homogeneous and isotropic, and that the three-form is coupled to both the Ricci scalar and the Ricci tensor. We show that in this case, it propagates three degrees of freedom: a scalar mode and two tensor ones. Then, we consider an anisotropic background that corresponds to a Bianchi Type I Universe, and set the coupling with the Ricci tensor to zero. We show that, similarly to the Proca theory with non-minimal coupling to gravity, this case leads to two branches for the background solutions - depending on the values of the 3-form. However, in contrast to the Proca case, we show that no extra modes appear. We explore the no-ghost conditions and speed of propagation for all three modes in both branches. Finally, we show that one of the branches can be written as a theory of a constrained scalar, coupled to a cuscuton field.

Paper Structure

This paper contains 23 sections, 124 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The 3-form field in a homogeneous and isotropic universe
  3. The background configuration and perturbations
  4. The scalar modes
  5. The vector modes
  6. The tensor modes
  7. The anisotropic universe
  8. The setup
  9. Case 1: The $A_1\neq0$ branch
  10. Even modes
  11. Odd modes
  12. Case 2: The $A_1=0$ branch
  13. The even modes
  14. The odd modes
  15. The interacting cuscuton
  16. ...and 8 more sections

Figures (1)

  • Figure 1: The summary of the main results.