Constraining thawing dark energy using galaxy cluster number counts

We study the formation of galaxy clusters in the presence of thawing class of scalar field dark energy (DE). We consider cases where the scalar field has canonical as well as non-canonical kinetic terms in its action. We also consider various forms 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 a situation where DE is homogeneous along with a situation where DE 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 DE models has a significant deviation from the corresponding value for the Lambda cold dark matter (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 DE models can have substantial deviation from Lambda CDM and this deviation is most significant around z similar to 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 are 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 (m0).