Gauge-invariant perturbations in hybrid quantum cosmology

Journal Article · Mon Jun 01 00:00:00 EDT 2015 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2015/06/045· OSTI ID:22525750

Gomar, Laura Castelló; Marugán, Guillermo A. Mena ^[1]; Martín-Benito, Mercedes ^[2]

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1. Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain)
2. Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen, Heyendaalseweg 135, NL-6525 AJ Nijmegen (Netherlands)

We consider cosmological perturbations around homogeneous and isotropic spacetimes minimally coupled to a scalar field and present a formulation which is designed to preserve covariance. We truncate the action at quadratic perturbative order and particularize our analysis to flat compact spatial sections and a field potential given by a mass term, although the formalism can be extended to other topologies and potentials. The perturbations are described in terms of Mukhanov-Sasaki gauge invariants, linear perturbative constraints, and variables canonically conjugate to them. This set is completed into a canonical one for the entire system, including the homogeneous degrees of freedom. We find the global Hamiltonian constraint of the model, in which the contribution of the homogeneous sector is corrected with a term quadratic in the perturbations, that can be identified as the Mukhanov-Sasaki Hamiltonian in our formulation. We then adopt a hybrid approach to quantize the model, combining a quantum representation of the homogeneous sector with a more standard field quantization of the perturbations. Covariance is guaranteed in this approach inasmuch as no gauge fixing is adopted. Next, we adopt a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger-like equation for the quantum evolution of the perturbations. This evolution is governed by the Mukhanov-Sasaki Hamiltonian, with the dependence on the homogeneous geometry evaluated at quantum expectation values, and with a time parameter defined also in terms of suitable expectation values on that geometry. Finally, we derive effective equations for the dynamics of the Mukhanov-Sasaki gauge invariants, that include quantum contributions, but have the same ultraviolet limit as the classical equations. They provide the master equation to extract predictions about the power spectrum of primordial scalar perturbations.

• OSTI ID: 22525750
• Journal Information: Journal of Cosmology and Astroparticle Physics, Vol. 2015, Issue 06; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
BORN-OPPENHEIMER APPROXIMATION
DEGREES OF FREEDOM
DISTURBANCES
ENERGY SPECTRA
EXPECTATION VALUE
GAUGE INVARIANCE
HAMILTONIANS
LIMITING VALUES
MASS
POTENTIALS
QUANTIZATION
QUANTUM COSMOLOGY
SCALAR FIELDS
SCALARS
SCHROEDINGER EQUATION
SPACE-TIME
ULTRAVIOLET RADIATION