Imprint of thawing scalar fields on large scale galaxy overdensity

We investigate the observed galaxy power spectrum for the thawing class of scalar field models taking into account various general relativistic corrections that occur on very large scales. We consider the full general relativistic perturbation equations for the matter as well as the dark energy fluid. We form a single autonomous system of equations containing both the background and perturbed equations of motion which we subsequently solve for different scalar field potentials. First we study the percentage deviation from $\Lambda$CDM model for different cosmological parameters as well as in the observed galaxy power spectra on different scales in scalar field models for various choices of scalar field potentials. Interestingly the difference in background expansion results enhancement of power from $\Lambda$CDM on small scales whereas the inclusion of GR corrections results the suppression of power from $\Lambda$CDM on large scales. This can be useful to distinguish scalar field models from $\Lambda$CDM with future optical/radio surveys. We also compare the observed galaxy power spectra for tracking and thawing types of scalar field using some particular choices for the scalar field potentials. We show that thawing and tracking models can have large differences in observed galaxy power spectra on large scales and for smaller redshifts due to different GR effects. But on smaller scales and for larger redshifts, the difference is small and is mainly due to difference in background expansion.