Abstract
Detecting primordial non-Gaussianity on mildly non-linear scales requires
precise modelling of late-time structure formation. Accurately predicting the
impact of non-linear gravitational collapse, non-linear tracer bias and
baryonic physics on the variance and higher order moments of the cosmic density
field is challenging, as they strongly depend on the tails of the probability
distribution function (PDF) of density fluctuations. A way around this problem
is to directly analyse the bulk of the PDF instead. For this purpose we devise
a new method to predict the impact of general non-Gaussian initial conditions
on the late-time density PDF. With this formalism we show that - even when
marginalizing over potential ignorance of the amplitude and slope of the
non-linear power spectrum - an analysis of the PDF at mildly non-linear
densities can measure the amplitude of different primordial bispectrum shapes
to an accuracy of $\Delta f_NL^loc = 3.1\ ,\ \Delta
f_NL^equi = 10.0\ ,\ \Delta
f_NL^ortho = 17.0\ $. This assumes a joint analysis
of the PDF on smoothing scales of $15$Mpc/$h$ and $30$Mpc/$h$ in a survey
volume of $V=100(Gpc/h)^3$ at $z=1$, analysing only densities of
$\delta(15Mpc/h) -0.4, 0.5$ ($87\%$ of probability) and
$\delta(30Mpc/h) -0.3, 0.4$ ($95\%$ of probability).
Note that a formalism closely related to ours was already successfully applied
to observational data Gruen2018, Friedrich2018, demonstrating that the
methodology developed here can indeed be carried over to real data analysis.
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