Consistent scalar and tensor perturbation power spectra in single fluid matter bounce with dark energy era

Abstract

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, where the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine tuned exception) must have one and only one dark energy phase, either occurring in the contracting era or in the expanding era. Hence, these bounce solutions are necessarily asymmetric. Naturally, the more convenient solution is the one where the dark energy phase happens in the expanding era, in order to be a possible explanation for the current accelerated expansion indicated by cosmological observations. In this case, one has the picture of a Universe undergoing a classical dust contraction from very large scales, the initial repeller of the model, moving to a classical stiff matter contraction near the singularity, which is avoided due to the quantum bounce. The Universe is then launched to a dark energy era, after passing through radiation and dust dominated phases, finally returning to the dust expanding phase, the final attractor of the model. We calculate the spectral indexes and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation or using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model where the presence of dark energy behavior in the Universe does not turn problematic the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine tunings, to yield the observed amplitude for scalar perturbations, and also for the ratio between tensor and scalar amplitudes, r = T /S 0.1. The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model where a single field induces not only an expanding background dark energy phase, but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order. * anna@cbpf.br † nelsonpn@cbpf.br ‡ sandro@isoftware.com.br observed today in the Cosmic Microwave Background radiation (CMB). Without inflation, these regions would be causally disconnected in a purely Big Bang model. This puzzle is the so called horizon problem, and it does not exist in bouncing models. Since the Universe had a very large period of contraction in the past, there is no limit to the particle horizon (if the fluids dominating the contracting phase satisfy the strong energy condition). Another puzzle of a purely Big Bang scenario is the ...

Bohmian Quantum Gravity and Cosmology

“…In the quantum case, Bohmian bounce solutions were found. Exact solutions were given in [34] and with some approximation in [35], yielding the same qualitative picture. With these solutions, the quantum effects become important near the singularity.…”

“…In this section, the question of big bang or big crunch singularities is considered in the simple case of a homogeneous and isotropic metric respectively coupled to a homogeneous scalar field (with zero matter potential [32,33] and with exponential matter potential [34,35]) and to a perfect fluid, modelled also by a scalar field [10,[36][37][38]. After considering the Wheeler-DeWitt quantization, we also consider the loop quantization of the former model [33].…”

“…The latter equation is the Friedmann equation. The acceleration equation, which corresponds to the second-order equation for α, follows from (34) and (35). There is a big bang or big crunch singularity when a = 0, i.e., α → −∞.…”

Bouncing and cyclic quantum primordial universes and the ordering problem

“…The quantum theory reviewed in this section was further developed in order to describe, for example, creation of particles [39], cosmological perturbations [40], and primordial gravitational waves [41]. We do not discuss here those results, limiting our analysis to the ordering ambiguity and its consequences for the above aspects of the theory.…”

Classical and quantum cosmology of Fab Four John theories

“…As mentioned in the introduction, there are some conceptual arguments in favor of Bohmian mechanics in quantum cosmology. In the references [29,[46][47][48][49], it is shown how to generalize the above Bohmian formalism to models of quantum gravity and quantum cosmology. Among other things, they show how that formalism exhibits quantum effects, but also describes scalar and tensor perturbations in spacetime.…”