Degrees of freedom of quadratic scalar-nonmetricity theory

TL;DR

This paper investigates the degrees of freedom in quadratic scalar-nonmetricity theory, revealing cases with 5, 6, or 10 propagating modes, and highlights the presence of strongly coupled modes in some scenarios.

Contribution

It provides a detailed Hamiltonian and perturbative analysis of the degrees of freedom in QSN theory, identifying conditions for viable models and revealing strongly coupled modes.

Findings

Case II propagates 10 degrees of freedom.

Cases V and VI have 8 degrees of freedom Hamiltonian count, but fewer in perturbations.

Additional modes are strongly coupled in some models.

Abstract

We study the number of degrees of freedom (DOFs) in quadratic scalar-nonmetricity (QSN) theory, whose Lagrangian is the linear combination of five quadratic nonmetricity invariants with coefficients depending on a dynamical scalar field. Working in the coincident gauge, we perform the Arnowitt-Deser-Misner decomposition and classify QSN models into distinct cases according to the numbers of their primary constraints. For cases that are physically viable in the sense that both a consistent cosmological background and tensor gravitational waves exist, we count the number of degrees of freedom based on two approaches. First we investigate the linear cosmological perturbations around an FLRW background. Then we perform a Dirac-Bergmann Hamiltonian constraint analysis to count the number of DOFs at the nonperturbative level. We focus on three representative cases. In case II, both the perturbative and nonperturbative approaches yield the same result, which indicates that the theory propagates 10 degrees of freedom. In contrast, in cases V and VI, the Hamiltonian analysis yields 8 degrees of freedom, while only 6 and 5 modes are visible at linear order in perturbations, respectively. This indicates that additional modes are strongly coupled on cosmological backgrounds.