Model independent constraints on dark energy evolution from low-redshift
  observations
  Knowing the late time evolution of the Universe and finding out the causes
for this evolution are the important challenges of modern cosmology. In this
work, we adopt a model-independent cosmographic approach and approximate the
Hubble parameter considering the Pade approximation which works better than the
standard Taylor series approximation for $z>1$. With this, we constrain the
late time evolution of the Universe considering low-redshift observations
coming from SNIa, BAO, $H(z)$, $H_{0}$ , strong-lensing time-delay as well as
the Megamaser observations for angular diameter distances. We confirm the
tensions with $\Lambda$CDM model for low-redshifts observations. The present
value of the equation of state for the dark energy has to be phantom-like and
for other redshifts, it has to be either phantom or should have a phantom
crossing. For lower values of $\Omega_{m0}$, multiple phantom crossings are
expected. This poses serious challenges for single, non-interacting scalar
field models for dark energy. We derive constraints on the {\it statefinders}
$(r,s)$ and these constraints show that a single dark energy model cannot fit
data for the whole redshift range $0\leq z\leq 2$: in other words, we need
multiple dark energy behaviors for different redshift ranges. Moreover, the
constraint on sound speed for the total fluid of the Universe, and for the dark
energy fluid (assuming them being barotropic), rules out the possibility of a
barotropic fluid model for unified dark sector and barotropic fluid model for
dark energy, as fluctuations in these fluids are unstable as $c_{s}^2 < 0$ due
to constraints from low-redshift observations.
