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.
