  We study the formation of galaxy clusters in the presence of thawing class of
scalar field dark energy. We consider cases where the scalar field has
canonical as well non canonical kinetic term in its action. We also consider
various form for the potential of the scalar field e.g, linear, quadratic,
inverse quadratic, exponential as well as Pseudo-Nambu-Goldstone Boson (PNGB)
type. Moreover we investigate situation where dark energy is homogeneous as
well as the situation where dark energy takes part in virialization process. We
use the Sheth-Tormen formalism while calculating the number density of galaxy
clusters. Our results show that cluster number density for different dark
energy models have significant deviation from the corresponding value for the
$\Lambda$CDM case. The deviation is more for higher redshifts. Moreover the
tachyon type scalar field with linear potential has the highest deviation from
the $\Lambda$CDM case. For the total cluster number counts, different dark
energy models can have substantial deviation from $\Lambda$CDM and this
deviation is most significant around $z \sim 0.5$ for all the models we
considered. We also constrain thawing class of models using the presently
available data for number counts of massive X-ray clusters. The results show
that current cluster data is not suitable enough for constraining potentials
for the thawing scalar fields as well as for other cosmological parameters like
$n_{s}$. But one can get significant constraint for the parameter $\sigma_{8}$
and a lower bound on $\Omega_{m0}$.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology