Reconstruction of dark energy density by non-parametric approaches
  The evolution of dark energy density is a crucial quantity in understanding
the nature of dark energy. Often, the quantity is described by the so-called
equation of state, that is the ratio of dark energy pressure to its density. In
this scenario, the dark energy density is always positive throughout cosmic
history and a negative value is not allowed. Assuming a homogeneous and
isotropic universe, we reconstruct the dark energy density directly from
observational data and investigate its evolution through cosmic history. We
consider the latest SNIa, BAO and cosmic chronometer data and reconstruct the
dark energy density in both flat and non-flat universes up to redshift $z\sim
3$. The results are well in agreement with the $\Lambda$CDM up to redshift
$z\sim 1.5$, whereas all data and methods, in our analysis, provide a negative
dark energy density at high redshifts.
