Crunching, Bouncing, and Cyclical Cosmologies from Dark Sector Interactions

Abstract

We present new mechanisms that produce either a future Big Crunch turnaround or a past non-singular bounce in flat FLRW cosmologies within general relativity at the background level, driven solely by non-gravitational interactions between dark matter (DM) and dark energy (DE). We study phenomenological interacting dark energy (IDE) models based on linear kernels of the form $Q = 3H(δ_{\rm dm}ρ_{\rm dm} + δ_{\rm de}ρ_{\rm de})$, focusing on parameter regimes with strong energy transfer from dark energy to dark matter. In this strong interacting regime, the interaction does not vanish when one component crosses zero density, allowing one of the dark-sector densities to become negative. The resulting sign changes can violate the energy conditions required for cosmological turnarounds in a flat universe, thereby enabling either (i) a maximum scale factor followed by recollapse into a big crunch, or (ii) a minimum non-zero scale factor corresponding to a bounce. We derive analytic conditions for these turnarounds and obtain closed-form expressions for the associated maximum or minimum scale factor. We also show that, in a closed universe, a special case of the same IDE framework can be tuned to yield a cyclic scenario. Although these strong interaction scenarios are unlikely to describe the observed Universe, they provide a concrete demonstration that exotic cosmological behaviour can arise naturally in underexplored regions of the parameter space of familiar IDE models.

Figures (14)

• Figure 1: Visualization of how negative dark energy $\rho_{\rm de}<0$ may arise in the future for the interaction model $Q= 3 H \delta \rho_{\text{dm}}$, given the case where there is a strong coupling, $\delta\gg 0$, that causes energy transfer from dark energy to dark matter, here named the Strong interacting Dark Energy Dark Matter (SiDEDM) regime. For this specific coupling, the SiDEDM corresponds to the upper limit $\delta>-\dfrac{w}{1+r_0}$ that causes negative energies, which has been previously derived from both dynamical system analysis considerations vanderWesthuizen:2025I (illustrated here in Figure \ref{['fig:2D_Q_general_Phase_portrait_boundaries']}) and from the analytical solutions for the evolution of dark energy vanderWesthuizen:2023hcl. We consider a volume element of space as we move from the present into the future, the universe expands $H>0$. The strong energy transfer causes dark energy to dilute and dark matter to increase, but we see that $Q\neq0$ when $\rho_{\rm de}=0$, thus energy transfer continues which causes negative dark energy to emerge. This feature may lead to future big crunch, as discussed in Section \ref{['sec:crunch']}.
• Figure 2: Visualization of how negative dark matter $\rho_{\rm dm}<0$ may arise in the past for the interaction model $Q= 3 H \delta \rho_{\text{de}}$, given the case where there is a strong coupling, $\delta\gg 0$, that causes energy transfer from dark energy to dark matter (SiDEDM regime). For this specific interaction, the SiDEDM corresponds to the upper limit $\delta>-\dfrac{w}{1+1/r_0}$ which causes negative dark matter densities, which has been previously derived from both dynamical system analysis considerations vanderWesthuizen:2025I (illustrated here in Figure \ref{['fig:2D_Q_general_Phase_portrait_boundaries']}) and from the analytical solutions for the evolution of dark matter vanderWesthuizen:2023hcl. We consider a volume element of space as we move back in time from the present into the past such that the universe contracts $H<0$ and the energy transfer is from dark matter to dark energy. Dark energy increases and dark matter dilutes away, but since $Q\neq0$ when $\rho_{\rm dm}=0$, the energy transfer is not stopped when no dark matter remains, causing negative dark matter to emerge. This feature may lead to past non-singular bounce, as discussed in Section \ref{['sec:bounce']}.
• Figure 3: Evolution of scale factor $a$ vs time for interacting dark energy model $Q= 3 H \delta \rho_{\text{dm}}$. For both cases we have set $\Omega_{\rm{(bm,0)}}=0.05$, $\Omega_{\rm{(dm,0)}}=0.26$, $\Omega_{\rm{(de,0)}}=0.69$, $w=-1$. From these parameters, the upper positive energy limit is $\delta = -\frac{w }{1+r_0}=0.726$. If the interaction strength is below this limit ($\delta =0.724< -\frac{w }{1+r_0}$) the universe expands forever, while if above the limit ($\delta=0.728 > -\frac{w }{1+r_0}$), negative dark energy emerges and the universe eventually re-collapses in the future. A wide range of initial conditions that allow for negative dark energy can cause a big crunch turnaround, as seen in the phase portraits in Figure \ref{['fig:DSA_H_Qdm']}. The negative energy densities emerge from the mechanisms illustrated in Figure \ref{['fig:neg_de_visual']} and \ref{['fig:2D_Q_general_Phase_portrait_boundaries']}.
• Figure 4: Evolution of the scale factor $a(t)$, dimensionless energy densities $\rho_i/\rho_{c0}$, Hubble parameter $H(t)$, dimensionless interaction term $Q/(\rho_{c0}H_0)$, and the strong and null energy conditions (SEC and NEC) for interacting dark energy model $Q= 3 H \delta \rho_{\text{dm}}$. As illustrated in Figure \ref{['fig:neg_de_visual']}, as energy is transferred from DE to DM, at some point DE becomes negative since $Q>0$ when $\rho_{\rm{de}}=0$, and the universe starts to decelerate $w^{\rm{eff}}_{\rm{tot}}<-\frac{1}{3}$. After some time we find $\rho_{\rm{dm}}=-\rho_{\rm{de}}$, corresponding to $\rho_{\rm{tot}}=0$, $H=0$ (as well as $Q=0$), where the universe experiences a turnaround from expansion $H>0$ to contraction $H<0$. During contraction, the negative $H$ causes $Q<0$ and energy now transfers back from DM to DE, causing DE to become positive at some point and even causing acceleration again $w^{\rm{eff}}_{\rm{tot}}<-\frac{1}{3}$. The matter components dominate again as $a$ becomes small causing deceleration and faster contraction, and a future big crunch occurs where $a\rightarrow 0$ and $\rho_{\rm{tot}}\rightarrow \infty$. See Figure \ref{['fig:DSA_H_Qdm']} for phase portraits showing similar behaviour for a larger selection of initial conditions.
• Figure 5: Phase portraits of the dynamical system \ref{['DSA.Qde_w']} for interaction kernel $Q= 3 H \delta \rho_{\text{dm}}$, with a large energy transfer from dark energy to dark matter ($\delta\gg0$), which allow for future big crunch-capable turnarounds. The left panel and right panels show dimensionless dark matter $x_{\rm dm}=\rho_{\rm{dm}}/\rho_{(c,0)}$ and dark energy $x_{\rm de}=\rho_{\rm{de}}/\rho_{(c,0)}$ evolution respectively, both relative to the Hubble parameter. The trajectories within the yellow background allow for future big crunch capable turnarounds where $H=0$ and $\dot h<0$, which in the right panel necessitate a crossing into the negative dark energy region ($x_{\rm de}<0$), as required by \ref{['BCdH.5']}, and which corresponds to the SiDEDM regime in the left panel of Figure \ref{['fig:2D_Q_general_Phase_portrait_boundaries']}. Trajectories in the green region do not experience turnarounds and are regions in the iDEDM regime. The bounce-capable turnarounds in the red regions are unphysical, as they correspond to regions where dark matter is negative ($x_{\rm dm}<0$) at present and at all other times, as there exists an invariant submanifold at $x_{\rm dm}=0$ preventing sign-switching for dark matter. The purple dot shows initial conditions in a two fluid model close to those found in Figure \ref{['fig:crunch_limit']}, \ref{['fig:crunch_5']} and \ref{['fig:2D_Q_general_Phase_portrait_boundaries']}. The purple dotted lines show the past expansion, where densities increase approaching the Big Bang. The solid and dashed lines show the future expanding and contracting regions, respectively, indicating dark energy crossing into negative values at the turnaround (here $\rho_{\rm dm}=-\rho_{\rm de}$), before becoming positive again in the contracting phase prior to a crunch. This agrees with Figure \ref{['fig:crunch_5']} and Table \ref{['tab:crunch_phases_ide']}.