Negative cosmological constant in the dark sector?

We consider the possibility that the dark sector of our Universe contains a negative cosmological constant dubbed $\lambda$. For such models to be viable, the dark sector should contain an additional component responsible for the late-time accelerated expansion rate ($X$). We explore the departure of the expansion history of these models from the concordance$\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model. For a large class of our models, the accelerated expansion is transient with a nontrivial dependence on the model parameters. All models with $w_X>-1$ will eventually contract and we derive an analytical expression for the scale factor $a(t)$ in the neighborhood of its maximal value. We find also the scale factor for models ending in a Big Rip in the regime where dustlike matter density is negligible compared to $\lambda$. We address further the viability of such models, in particular when a high $H_0$ is taken into account. While we find no decisive evidence for a nonzero $\lambda$, the best models are obtained with a phantom behavior on redshifts $z\gtrsim 1$ with a higher evidence for nonzero $\lambda$. An observed value for $h$ substantially higher than 0.70 would be a decisive test of their viability.

Figure 1

Evolution of the maximum value of $\ddot{a}/a$ reached from matter era until today, as a function of $w_X$ for two different values of ${\mathrm{\Omega }}_{\lambda ,0}$ and ${\mathrm{\Omega }}_{\mathrm{m},0}=0.3$.

Figure 2

Evolution of the Universe in the space $(w_X,{\mathrm{\Omega }}_{\lambda ,0})$. In white, the Universe accelerates today, and in light gray, the Universe never accelerated until today. While in darker gray, we have a transient situation where the Universe accelerated in the past but does not accelerate today. These results do not rely on any observational constraints, only ${\mathrm{\Omega }}_{\mathrm{m},0}=0.3$ and $w_X$ constant are assumed. For comparison, we have added in red and purple lines the $({\mathrm{\Omega }}_{\lambda ,0},w_X)$ values which satisfy Eq. (26) for $h=0.74$ and $h=0.72$, respectively.

Figure 3

Parameters $(h,{\omega }_{\lambda },w_X)$ which satisfy the relation (26) for models with constant $w_X$. (a) In the upper panel, ${\omega }_{\lambda }$ is fixed and we see that an increasing $|{\omega }_{\lambda }|$ (from left to right) gives the same $h$ with less phantomness. We note the quasilinear relation, which follows from (43) for constant ${\omega }_{\lambda }$. (b) In the lower panel, all parameters are free. For the latter, we show the lines corresponding to a constant $h$ when (26) is satisfied: continuous line ($h=0.68$), long dashed line ($h=0.7$), and dashed line ($h=0.74$). They satisfy to good accuracy (43).

Figure 4

We show iso-$h$ curves for scenarios I (left), II (middle), and III with ${\mathrm{\Delta }}_1=-0.04$ (right-hand panel) in the $({\mathrm{\Delta }}_{1,2},{\omega }_{\lambda })$ parameter plane. The shaded areas correspond to the following $H_0$ values (in $\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ units): $73.30\pm 4$ (HST-Mira) [44]), $74.03\pm 1.42$ (SH0ES) [45], and $69.8\pm 1.9$ (TRGB) [46].

Figure 5

Marginalized posteriors for different models using SNIa, BAO, ${\theta }_{\mathrm{s}}$, and $H_0$ from HST Mira. The central value is the median, and the shared areas show the 68% credible intervals around it. Left: $\mathrm{\Lambda }\mathrm{CDM}$ (blue), III (orange), and $\lambda \mathrm{III}$ (green). Right: $\mathrm{\Lambda }\mathrm{CDM}$ (blue), $\lambda \mathrm{CPL}{w}_a$ (orange), $\lambda \mathrm{II}$ (green).