Cosmological Filaments in the light of Excursion Set of Saddle Points
  The universe in large scales is structured as a network known as cosmic web.
Filaments are one of the structural components of this web, which can be
introduced as a novel probe to study the formation and evolution of structures
and as a probe to study the cosmological models and to address the missing
baryon problem. The aim of this work is to introduce an analytical framework to
study the statistics of filaments such as number density of them and also to
obtain the length-mass relation. For this objective, we model filaments as
collapsed objects which have an extension in one direction, accordingly we use
the ellipsoidal collapse to study the evolution of an over-dense region via
gravitational instability. %In this context, we consider the critical density
of filament formation, which will be a crucial parameter for number density
count. We find that the nonlinear density of filaments in the epoch of
formation is almost mass independent and is in order of $\sim 30$. By
introducing {\it{filament's extended condition}} we find a fitting function for
length-mass relation. For the statistics of filaments, we propose a novel
framework named excursion set of saddle points. In this approach, we count the
saddle points of the density field Hessian matrix, and relate it to the count
of filaments. In addition, we addressed the filament in filament problem with
up-crossing approximation.
