A Cuscuton Representation of the Loop Quantum Cosmology Bounce
Abstract
Loop Quantum Cosmology (LQC) replaces the big bang singularity of the homogeneous universe by a bounce, usually described by the modified Friedmann equation H2=ρ(1−ρ/ρc)/(3Mp2). We show that this background dynamics follows from a local cuscuton effective theory, whose scalar equation is a constraint rather than a wave equation. One way to establish this is to write the cuscuton in terms of an angular coordinate θ, identified with the LQC polymerization angle 2λb. Its constraint gives H∝sinθ, while the Einstein constraint gives ρ=ρcsin2(θ/2), exactly reproducing the LQC bounce. To our knowledge, this is the first closed-form, local, generally covariant realization of the exact standard flat-FLRW LQC background dynamics for minimally coupled matter satisfying null energy condition, without introducing additional local dynamical degrees of freedom. A branchwise Legendre transformation establishes a canonical equivalence between the clock-gauge-fixed homogeneous mimetic system in the case of vanishing mimetic dust energy density and the cuscuton systems. It selects the constant-tension cuscuton coordinate Θ=sinθ−θ, while θ retains its interpretation as the LQC polymerization angle. This equivalence does not establish agreement of the inhomogeneous theories or their perturbations. The angular action also admits an explicit branched f(K) representation, where K is the mean extrinsic curvature of spatial hypersurfaces. The construction is therefore an effective covariant representation of the LQC holonomy correction, not a derivation from full loop quantum gravity.
Related
- On entropic cosmology, late-time acceleration and the quantum bounce
- Fractional power law inflationary potentials in loop quantum cosmology with inverse volume corrections in light of ACT observations
- Primordial Gravitational Waves in Loop Quantum Cosmology: Regularization Ambiguities and Initial State Dependence
- Toward Precision Kinetic Sunyaev-Zel'dovich Cosmology---1. The Matter - Momentum Bispectrum at One-Loop Order
- Cuscuton Fifth Force: Implications of Non-Dynamical Scalars for Structure Growth
BibTeX
@misc{afshordi2026cuscuton,
title = {{A Cuscuton Representation of the Loop Quantum Cosmology Bounce}},
author = {Niayesh Afshordi and Kristina Giesel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35222},
eprint = {2609.35222},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35222},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Cuscuton Representation of the Loop Quantum Cosmology Bounce
AU - Niayesh Afshordi
AU - Kristina Giesel
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35222
UR - https://arxiv.org/abs/2609.35222
AB - Loop Quantum Cosmology (LQC) replaces the big bang singularity of the homogeneous universe by a bounce, usually described by the modified Friedmann equation H^2=ρ(1−ρ/ρ_c)/(3M_p^2). We show that this background dynamics follows from a local cuscuton effective theory, whose scalar equation is a constraint rather than a wave equation. One way to establish this is to write the cuscuton in terms of an angular coordinate θ, identified with the LQC polymerization angle 2λb. Its constraint gives H∝sinθ, while the Einstein constraint gives ρ=ρ_csin^2(θ/2), exactly reproducing the LQC bounce. To our knowledge, this is the first closed-form, local, generally covariant realization of the exact standard flat-FLRW LQC background dynamics for minimally coupled matter satisfying null energy condition, without introducing additional local dynamical degrees of freedom. A branchwise Legendre transformation establishes a canonical equivalence between the clock-gauge-fixed homogeneous mimetic system in the case of vanishing mimetic dust energy density and the cuscuton systems. It selects the constant-tension cuscuton coordinate Θ=sinθ−θ, while θ retains its interpretation as the LQC polymerization angle. This equivalence does not establish agreement of the inhomogeneous theories or their perturbations. The angular action also admits an explicit branched f(K) representation, where K is the mean extrinsic curvature of spatial hypersurfaces. The construction is therefore an effective covariant representation of the LQC holonomy correction, not a derivation from full loop quantum gravity.
ER -