Sanggyu Biern - September 11, 2015

Nonlinear effects of the relativity and the dark energy in the large scale structure
formation of the universe

In this seminar, we will discuss the nonlinear effects on the large scale structure
formation of the universe in the Newtonian and the relativistic cosmology.

By studying nonlinearities, we can obtain more accurate results. Many studies of the
nonlinear effects have been conducted in the Newtonian context, which works fine only
in the subhorizon scale. To investigate the horizon scale, the study of the
relativistic cosmology is essential, and the relativistic effects mostly occur at the
nonlinear order. The dark energy effect also becomes important at the nonlinear order.

This seminar is mainly divided into two parts : Part.1 the structure formation in the
physical spacetime and Part 2. the observables in the observation spacetime.

In the Part.1, the dark matter clustering in the Newtonian and relativistic cosmology
will be discussed. I will introduce how to derive the nonlinear solutions and show the
results of the power and bi- spectra in the Newtonian cosmology.

In case of the relativistic cosmology is more complicated. By contrast to the
Newtonian cosmology, the relativistic cosmology has a lot of gauge choices but only
some particular gauges contain the Newtonian cosmology. This gauge issue will be
investigated, and the results of the proper gauge will be shown.

In the Part.2, we will discuss the (theoretical) observations. Since the observation
is undertaken in the redshift space, we will study how to map the solutions in the
physical spactime to the observational spacetime. The relativistic and dark energy
effects are much more significant in the observation spacetime compared to those of
the physical spacetime.

In addition, we will study a non-Gaussianity effect from the relativistic approach.
It mimics the effect of the primordial non-Gaussianity. As a result, the existence of
the primordial non-Gaussianity can be misunderstood by the observation, even if it
does not exist. This misunderstanding effect can be parameterised as the effective
f_nl, and it depends significantly on the property of the dark energy. We will study
this issue at the end.