Quantum and Classical Cosmology in the Brans–Dicke Theory

Abstract

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

Radiation from a Classical Harmonic Oscillator

“…The first two are tensor polarizations similar to GR, and the third is scalar polarization. In recent years, there has been a decent amount of work either to test GR using the LIGO-Virgo-Kagra (LVK) data [6], [7] or to modify gravity to explain cosmological ambiguities like the nature of dark energy and Hubble tension [8], [9], [10]. There are many promising theories, but we choose BD for the following reason.…”

Constraining Brans-Dicke Parameter Using Gravitational Radiation

“…and the gravitational coupling depends through the relation G(1 − ζ), where G is the gravitational constant. Since the last hundred years, there have been many attempts to modify or test GR [6], [7], [8], [9], [10], [11] and it has successfully passed most of them. There are different regimes to test theories of gravity [12]: Quasi-stationary weak-field regime (G1), Quasi-stationary strong-field regime (G2), Highly-dynamical strong-field regime (G3) and Radiation regime (GW).…”

Testando o regime de altas energias do Universo: recentes avanços e próximos desafios

“…Portanto, espera-se que seja necessária uma descrição física além da Relatividade Geral (RG) para compreendermos a origem e evolução das flutuações. Cenários de gravitação que se propoem a implementar uma modificação da RG nestes regimes comumente produzem predições cosmológicas diferentes para a dinâmica do Universo no seu regime de altas energias, como é o caso por exemplo de certos modelos de bounce (ou ricochete) [4] [5][6] [7][8] [9] [10]. Devido à expansão do espaço-tempo, a cosmologia nos fornece uma janela de oportunidade para sondar a física próximo à escala de Planck, uma vez que a expansão acelerada do espaço-tempo traz essas escalas para o limite observável.…”