Classical and Quantum Solutions in Brans-Dicke Cosmology with a Perfect Fluid

Abstract

We consider the application of group invariant transformations in order to constrain a flat isotropic and homogeneous cosmological model, containing of a Brans-Dicke scalar field and a perfect fluid with a constant equation of state parameter $w$, where the latter is not interacting with the scalar field in the gravitational action integral. The requirement that the Wheeler-DeWitt equation be invariant under one-parameter point transformations provides us with two families of power-law potentials for the Brans-Dicke field, in which the powers are functions of the Brans-Dicke parameter ${\omega }_{BD}$ and the parameter $w$. The existence of the Lie symmetry in the Wheeler-DeWitt equation is equivalent to the existence of a conserved quantity in field equations and with oscillatory terms in the wavefunction of the universe. This enables us to solve the field equations. For a specific value of the conserved quantity, we find a closed-form solution for the Hubble factor, which is equivalent to a cosmological model in general relativity containing two perfect fluids. This provides us with different models for specific values of the parameters ${\omega }_{BD},$ and $w$. Finally, the results hold for the specific case where the Brans-Dicke parameter ${\omega }_{BD}$ is zero, that is, for the O'Hanlon massive dilaton theory, and consequently for $f\left(R\right)$ gravity in the metric formalism.

13 pages, 2 figures, discussion improved, accepted for publication by Phys. Rev. D

References in corpus (15)

• Dynamics of dark energy
• Modified teleparallel gravity: inflation without inflaton
• The 1% Concordance Hubble Constant
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Growing Matter
• Using the Noether symmetry approach to probe the nature of dark energy
• The dispersion of growth of matter perturbations in f(R) gravity
• Noether symmetry in $f(R)$ cosmology
• Decaying Gravity
• Gravity and Scalar Fields
• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Dynamical symmetries and observational constraints in scalar field cosmology
• Noether analysis of Scalar-Tensor Cosmology
• Introductory Lectures on Quantum Cosmology (1990)
• Noether symmetry approach in matter-dominated cosmology with variable G and Lambda

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