Hamiltonian formalism in Friedmann cosmology and its quantization

Journal Article · Wed Aug 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.043521· OSTI ID:21027586

Jie, Ren ^[1]; Xinhe, Meng ^[2]; Liu, Zhao ^[2]

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1. Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)
2. Department of Physics, Nankai University, Tianjin 300071 (China)

We propose a Hamiltonian formalism for a generalized Friedmann-Robertson-Walker cosmology model in the presence of both a variable equation of state parameter w(a) and a variable cosmological constant {lambda}(a), where a is the scale factor. This Hamiltonian system, containing 1 degree of freedom and without constraint, gives Friedmann equations as the equation of motion, which describes a mechanical system with a variable mass object moving in a potential field. After an appropriate transformation of the scale factor, this system can be further simplified to an object with constant mass moving in an effective potential field. In this framework, the {lambda} cold dark matter model as the current standard model of cosmology corresponds to a harmonic oscillator. We further generalize this formalism to take into account the bulk viscosity and other cases. The Hamiltonian can be quantized straightforwardly, but this is different from the approach of the Wheeler-DeWitt equation in quantum cosmology.

• OSTI ID: 21027586
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 76; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COSMOLOGICAL CONSTANT
COSMOLOGICAL MODELS
COSMOLOGY
DEGREES OF FREEDOM
EQUATIONS OF MOTION
EQUATIONS OF STATE
HAMILTONIANS
HARMONIC OSCILLATORS
NONLUMINOUS MATTER
POTENTIALS
QUANTIZATION
STANDARD MODEL
TRANSFORMATIONS
VISCOSITY