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

1 Introduction and Notation
Understanding the large scale structure of the Universe is one of the main
goals of cosmology. In the last two decades it has become widely accepted
that gravitational instability plays a central role in giving rise to the remarkable
structures seen in galaxy surveys. Extracting the wealth of information
contained in galaxy clustering to learn about cosmology thus requires a quantitative
understanding of the dynamics of gravitational instability and application
of sophisticated statistical tools that can best be used to test theoretical
models against observations.
In this work we review the use of non-linear cosmological perturbation theory
(hereafter PT) to accomplish this goal. The usefulness of PT in interpreting
results from galaxy surveys is based on the fact that in the gravitational instability
scenario density fluctuations become small enough at large scales (the
so-called “weakly non-linear regime”) that a perturbative approach suffices
to understand their evolution. Since early developments in the 80’s, PT has
gone through a period of rapid evolution in the last decade which gave rise to
numerous useful results. Given the imminent completion of next-generation
large-scale galaxy surveys ideal for applications of PT, it seems timely to provide
a comprehensive review of the subject.
The purpose of this review is twofold:
1) To summarize the most important theoretical results, which are sometimes
rather technical and appeared somewhat scattered in the literature with often
fluctuating notation, in a clear, consistent and unified fashion. We tried in
particular to unveil approximations that might have been overlooked in the
original papers, and to highlight the outstanding theoretical issues that remain
to be addressed.
2) To present the state of the art observational knowledge of galaxy clustering
with particular emphasis in constraints derived from higher-order statistics on
galaxy biasing and primordial non-Gaussianity, and give a rigorous basis for
the confrontation of theoretical results with observational data from upcoming
galaxy catalogues.
We assume throughout this review that the universe satisfies the standard
homogeneous and isotropic big bang model. The framework of gravitational
instability, in which PT is based, assumes that gravity is the only agent at
large scales responsible for the formation of structures in a universe with
density fluctuations dominated by dark matter. This assumption is in very
good agreement with observations of galaxy clustering, in particular, as we
discuss in detail here, from higher-order statistics which are sensitive to the
detailed structure of the dynamics responsible for large-scale structures 1 . The
non-gravitational effects associated with galaxy formation may alter the dis-
1 As opposed to just properties of the linearized equations of motion, which can be
mimicked by nongravitational theories of structure formation in some cases [10].
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