Dynamical analysis of quantum matter bounces with dark sector mimickers

TL;DR

The paper investigates matter-bounce cosmologies with a canonical scalar field having an exponential potential and additional barotropic fluids that mimic dark sector components. Using a phase-space approach, it derives fixed points and stability for one- and two-fluid configurations and then demonstrates a quantum bounce within Pilot-Wave cosmology, where the bounce is governed by the scalar field's kinetic energy and connects contracting to expanding branches. It then explores representative two-fluid models (dust, radiation, cosmological constant) for λ=√3 and λ=2, revealing sequences of stiff-matter, inflation-like, radiation-dominated, and dust-dominated phases with potential scalar-field dark matter/dark energy tracking. The results show how dark-sector mimickers can arise naturally in a quantum-corrected bouncing universe and suggest observationally relevant implications for perturbations and the Hubble tension, motivating further perturbative analyses and model refinements.

Abstract

We study the effects of the inclusion of fluids In bounce scenarios driven by an exponential potential scalar field. Most solutions exhibit well known tracking behavior between the fluids and the scalar field. This tracking behavior can model transitions between different phases of cosmic evolution. We will focus on an interesting bouncing model with a dust matter fluid, where the scalar field can drive an early dark energy expanding period with a radiation-like dominated phase just after it, and then tracks the dust matter fluid with energy density compatible with the dark matter energy density. The model is dust dominated in the far past of the contracting phase, and has stiff matter behavior when approaching the singularity, allowing well known quantum bounce transitions to the expanding era. Hence, it is a quantum matter bounce scenario with an inflationary phase together with a smooth transition through a radiation era to matter domination with a possible scalar field dark matter candidate.

Figures (11)

• Figure 1: Phase space trajectory of a contracting (dashed blue) and expanding (dotted red) universe with a standard scalar field with potential $V = \exp{-\sqrt{3}\kappa \phi}$ ($\lambda = \sqrt{3}$). At the points $B\pm$ the field behaves as dust $w_{\phi} = 0$. The quantum bounce connects $A+$ to $A-$, where the field behaves as stiff matter ($w_{\phi} = 1$). In the expansion phase when the trajectory goes through the point $y=1$ there is an accelerated expansion phase with $w_{\phi} = -1$.
• Figure 2: Evolution of the variables $x(\alpha)$ (dotted blue) corresponding to the kinetic term and $y(\alpha)$ (red dashed) corresponding to the potential term of Figure \ref{['fig:phasespace1']} (a) and the EoS parameter for the scalar field $w_{\phi}$ (b) with respect to $\alpha = \ln{a}$.
• Figure 3: Phase space trajectories for the system of equations \ref{['system-bounce']}, when $d = -1$ and $\sigma = 1$. The Figure depicts both bouncing and cyclic trajectories.
• Figure 4: Phase space trajectory for the case with $\lambda=\sqrt{3}$ and $w=-1$ (dark energy). Point C is the attractor (repeller) of the expanding (contracting) phase where the matter fluid dominates. In this case point B+ is an unstable attractor of the expanding phase. The contraction goes from $C$ to $A+$ (dashed blue line) and the expansion from $A-$ to $C$ passing through $B+$ (red dotted line).
• Figure 5: (a) Evolution of the dynamical system variables $x(\alpha)$ (dotted blue line), $y(\alpha)$ (dashed red line) and $z(\alpha)$ (solid green line). (b) EoS parameters for the matter fluid (in this case, $w=-1$, solid line) and the scalar field $w_{\phi}$ (dashed line).