Cosmological perturbation theory with matter time
arXiv:2007.06609 · doi:10.1103/PhysRevD.102.124062
Abstract
We study cosmological perturbation theory with scalar field and pressureless dust in the Hamiltonian formulation, with the dust field chosen as a matter-time gauge. The corresponding canonical action describes the dynamics of the scalar field and metric degrees of freedom with a non-vanishing physical Hamiltonian and spatial diffeomorphism constraint. We construct a momentum space Hamiltonian that describes linear perturbations, and show that the constraints to this order form a first class system. We then write the Hamiltonian as a function of certain gauge invariant canonical variables and show that it takes the form of an oscillator with time dependent mass and frequency coupled to an ultralocal field. We compare our analysis with other Hamiltonian approaches to cosmological perturbation theory that do not use dust time.
arXiv comment22 pages
References in corpus (18)
- The Dynamics of General Relativity
- Dust as a Standard of Space and Time in Canonical Quantum Gravity
- Einstein-Aether Waves
- Mimetic Dark Matter
- Cosmology with Mimetic Matter
- Dust of Dark Energy
- Time and a physical Hamiltonian for quantum gravity
- On the recently proposed Mimetic Dark Matter
- Scalar Material Reference Systems and Loop Quantum Gravity
- Relational Observables in Gravity: a Review
- Resolving Cosmological Singularities
- Dust reference frame in quantum cosmology
- Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
- Time evolution in deparametrized models of loop quantum gravity
- Variations on an aethereal theme
- On the properties of the irrotational dust model
- Linearized gravity with matter time
- Dynamics of Dirac observables in canonical cosmological perturbation theory