Graduated dark energy: Observational hints of a spontaneous sign switch
  in the cosmological constant
  We study the cosmological constant ($\Lambda$) in the standard $\Lambda$CDM
model by introducing the \textit{graduated dark energy} (gDE) characterised by
a minimal dynamical deviation from the null inertial mass density of the
$\Lambda$ in the form $\rho_{\rm inert}\propto \rho^{\lambda}<0$ with
$\lambda<1$ being a ratio of two odd integers, for which its energy density
$\rho$ dynamically takes negative values in the finite past. For large negative
values of $\lambda$, it creates a phenomenological model described by a smooth
function that approximately describes the $\Lambda$ spontaneously switching
sign in the late universe to become positive today. We confront the model with
the latest combined observational data sets of PLK+BAO+SN+$H$. It is striking
that the data predict bimodal posterior probability distributions for the
parameters of the model along with large negative $\lambda$ values; the new
maximum significantly excludes the $\Lambda$, and the old maximum contains the
$\Lambda$. The improvement in the goodness of fit for the $\Lambda$ reaches
highly significant levels, $\Delta\chi_{\rm min}^2=6.4$ for the new maxima,
while it remains at insignificant levels, $\Delta\chi_{\rm min}^2\lesssim0.02$,
for the old maxima. We show that, in contrast to the old maxima, which do not
distinguish from the $\Lambda$, the new maxima agree with the model-independent
$H_0$ measurements, high-precision Ly-$\alpha$ data, and model-independent
$Omh^2$ diagnostic estimates. Our results provide strong hints of a spontaneous
sign switch in the cosmological constant and lead us to conjecture that the
universe has transitioned from AdS vacua to dS vacua, at a redshift $z\approx
2.32$ and triggered the late-time acceleration, and suggests looking for such
mechanisms in string theory constructions.
