Large-Scale Structure of the Universe and Cosmological ...

9 Summary & Conclusions
As illustrated throughout this work, PT provides a valuable tool to understand
and calculate predictions for the evolution of large scale structure in
the universe. The last decade has witnessed a substantial activity in this area,
with strong interplay with numerical simulations of structure formation and
observations of clustering of galaxies and, more recently, weak gravitational
lensing. As galaxy surveys become larger probing more volume in the weakly
non-linear regime, new applications of PT are likely to flourish to provide new
ways of learning about cosmology, the origin of primordial fluctuations, and
the relation between galaxies and dark matter.
The general framework of these calculations is well established and calculations
have been pursued for a number of observational situations, whether
it is for the statistical properties of the local density contrast, the velocity
divergence, for the projected density contrast, redshift measurements or for
more elaborate statistics such as joint density cumulants. All these results
provide robust frameworks for understanding the observations or for reliable
error computations. There are however a number of outstanding issues that
remain to be addressed in order to improve our understanding of gravitational
instability at large scales,
– Most of the calculations have been done assuming Gaussian initial conditions,
except for some specific cases such as χ 2 models. Although present
observations are consistent with Gaussian initial conditions, deriving quantitative
constraints on primordial non-Gaussianity requires some knowledge
or useful parametrization of non-Gaussian initial conditions and how they
evolve by gravity.
– Predictions of PT for velocity field statistics are still in a rudimentary state
compared to the case of the density field. Upcoming velocity surveys will
start probing scales where PT predictions can be used. In addition, robust
methods for calculating redshift distortions including the non-linear effects
due to the redshift-space mapping are needed to fully extract information
from the next generation of galaxy redshift surveys.
– Another observational context in which a PT approach can be very valuable
is the Lyman-α forest observed in quasar spectra. The statistical properties
of these systems should be accessible to perturbative methods since most of
the absorption lines correspond to modest density contrasts (from 1 to 10).
This is a very promising field for observational cosmology.
– Accurate constraints on cosmological parameters from galaxy surveys require
precise models of the joint likelihood of low and higher-order statistics
including their covariance matrices. To date this has only been investigated
in detail numerically, or analytically in some restricted cases.
In addition, as we probe the transition to the non-linear regime, there are a
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