Constraints on growth index parameters from current and future
  observations
  We use current and future simulated data of the growth rate of large scale
structure in combination with data from supernova, BAO, and CMB surface
measurements, in order to put constraints on the growth index parameters. We
use a recently proposed parameterization of the growth index that interpolates
between a constant value at high redshifts and a form that accounts for
redshift dependencies at small redshifts. We also suggest here another
exponential parameterization with a similar behaviour. The redshift dependent
parametrizations provide a sub-percent precision level to the numerical growth
function, for the full redshift range. Using these redshift parameterizations
or a constant growth index, we find that current available data from galaxy
redshift distortions and Lyman-alpha forests is unable to put significant
constraints on any of the growth parameters. For example both $\Lambda$CDM and
flat DGP are allowed by current growth data. We use an MCMC analysis to study
constraints from future growth data, and simulate pessimistic and moderate
scenarios for the uncertainties. In both scenarios, the redshift
parameterizations discussed are able to provide significant constraints and
rule out models when incorrectly assumed in the analysis. The values taken by
the constant part of the parameterizations as well as the redshift slopes are
all found to significantly rule out an incorrect background. We also find that,
for our pessimistic scenario, an assumed constant growth index over the full
redshift range is unable to rule out incorrect models in all cases. This is due
to the fact that the slope acts as a second discriminator at smaller redshifts
and therefore provide a significant test to identify the underlying gravity
theory.
