The statistics of primordial curvature fluctuations are our window into the
period of inflation, where these fluctuations were generated. To date, the
cosmic microwave background has been the dominant source of information about
these perturbations. Large scale structure is however from where drastic
improvements should originate. In this paper, we explain the theoretical
motivations for pursuing such measurements and the challenges that lie ahead.
In particular, we discuss and identify theoretical targets regarding the
measurement of primordial non-Gaussianity. We argue that when quantified in
terms of the local (equilateral) template amplitude $f_{
m NL}^{
m loc}$
($f_{
m NL}^{
m eq}$), natural target levels of sensitivity are $Delta
f_{
m NL}^{
m loc, eq.} simeq 1$. We highlight that such levels are within
reach of future surveys by measuring 2-, 3- and 4-point statistics of the
galaxy spatial distribution. This paper summarizes a workshop held at CITA
(University of Toronto) on October 23-24, 2014.
