Theory of Cosmological Perturbations with Cuscuton

Abstract

This paper presents the first derivation of the quadratic action for curvature perturbations, $\zeta$, within the framework of cuscuton gravity. We study the scalar cosmological perturbations sourced by a canonical single scalar field in the presence of cuscuton field. We identify $\zeta$ as comoving curvature with respect to the source field and we show that it retains its conservation characteristic on super horizon scales. The result provides an explicit proof that cuscuton modification of gravity around Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is ghost free. We also investigate the potential development of other instabilities in cuscuton models. We find that in a large class of these models, there is no generic instability problem. However, depending on the details of slow-roll parameters, specific models may display gradient instabilities.

11 pages, no figures

References in corpus (7)

• Quantum Gravity at a Lifshitz Point
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Cuscuton and low energy limit of Horava-Lifshitz gravity
• Caustics for Spherical Waves
• Horndeski meets McVittie: A scalar field theory for accretion onto cosmological black holes
• Magnon Inflation: Slow Roll with Steep Potentials

Cited by in corpus (18)

• Extended Cuscuton: Formulation
• Cuscuton Bounce
• First-order thermodynamics of Horndeski gravity
• Cuscuton gravity as a classically stable limiting curvature theory
• VCDM and Cuscuton
• Spectrum of Cuscuton Bounce
• Dressed Power-law Inflation with Cuscuton
• Cuscuton Inflation
• Accelerating Universe with a stable extra dimension in cuscuton gravity
• Peculiar thermal states in the first-order thermodynamics of gravity
• Theories with limited extrinsic curvature and a nonsingular anisotropic universe
• Generalized McVittie geometry in Horndeski gravity with matter
• Multi-field Cuscuton Cosmology
• Consistency of Tachyacoustic Cosmology with de Sitter Swampland Conjectures
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• How Much NEC Breaking Can the Universe Endure?
• Effects of Cuscuton dynamics on braneworld configurations in the scalar-tensor representation of $f\left(R,T\right)$ gravity
• Spatially covariant gravity with two degrees of freedom in the presence of an auxiliary scalar field: Hamiltonian analysis