Primordial non-Gaussianities

Quijote contains 4,000 N-body simulations with primordial non-Gaussianities: Quijote-PNG. All these simulations contain \(512^3\) dark matter particles in a periodic volume of \((1~h^{-1}{\rm Gpc})^3\) and share the same cosmology as the fiducial model: \(\Omega_{\rm m}=0.3175\), \(\Omega_{\rm b}=0.049\), \(h=0.6711\), \(n_s=0.9624\), \(\sigma_8=0.834\), \(w=-1\), \(M_\nu=0.0\) eV. These are standard N-body simulations run with initial conditions generated in a particular way.

The video below shows an example of two N-body simulations with Gaussian initial conditions (left) and local primordial non-Gaussianities initial conditions (right). As can be seen, differences are very small even for a value as large as \(f_{\rm NL}=200\) as the one we use.

The simulations in Quijote-PNG can be classified into four different sets: 1) local, 2) equilateral, 3) orthogonal CMB, and 4) orthogonal LSS (see Bispectrum shapes). Each set contains 1,000 simulations: 500 with \(f_{\rm NL}=+100\) and 500 with \(f_{\rm NL}=-100\). Quijote-PNG is thus organized into eight different folders, depending on the non-Gaussianity shape and the value of \(f_{\rm NL}\):

  • LC_p: contains data from 500 simulations with local type and \(f_{\rm NL}=+100\)

  • LC_m: contains data from 500 simulations with local type and \(f_{\rm NL}=-100\)

  • EQ_p: contains data from 500 simulations with equilateral type and \(f_{\rm NL}=+100\)

  • EQ_m: contains data from 500 simulations with equilateral type and \(f_{\rm NL}=-100\)

  • OR_CMB_p: contains data from 500 simulations with orthogonal CMB type and \(f_{\rm NL}=+100\)

  • OR_CMB_m: contains data from 500 simulations with orthogonal CMB type and \(f_{\rm NL}=-100\)

  • OR_LSS_p: contains data from 500 simulations with orthogonal LSS type and \(f_{\rm NL}=+100\)

  • OR_LSS_m: contains data from 500 simulations with orthogonal LSS type and \(f_{\rm NL}=-100\)

Each of the above folders contains 500 sub-folders, each of them hosting the result of a different simulation. For instance, the folder EQ_p/72/ contains the results of the 72th simulation run with \(f_{\rm NL}=+100\) for the equilateral shape. Depending on the location, these folder will contain the snapshots, halo catalogues, or other data products.

Bispectrum shapes

In Quijote-PNG we only consider models that have a primordial bispectrum, defined as

\[\langle \Phi(\mathbf{k}_1) \Phi(\mathbf{k}_2) \Phi(\mathbf{k}_3) \rangle = (2\pi)^3 \delta^{(3)}(\mathbf{k}_1+\mathbf{k}_2+\mathbf{k}_3)B_{\Phi}(k_1,k_2,k_3)~,\]

where \(\Phi(\mathbf{k})\) is the primordial potential. We consider four different shapes for the primordial bispectrum:

  1. Local. The local shape can be characterized by

\[B^{\mathrm{local}}_{\Phi}(k_1,k_2,k_3) = 2 f_{\mathrm{NL}}^{\mathrm{local}} P_\Phi(k_1)P_\Phi(k_2)+ \text{ 2 perm.}\]
  1. Equilateral. The equilaterial shape is described by

\[\begin{split} B^{\mathrm{equil.}}_{\Phi}(k_1,k_2,k_3) = 6 f_{\mathrm{NL}}^{\mathrm{equil.}}\Big[- P_\Phi(k_1)P_\Phi(k_2)+\text{ 2 perm.} \\ -2 \left( P_\Phi(k_1)P_\Phi(k_2)P_\Phi(k_3) \right)^{\frac{2}{3}} + P_\Phi(k_1)^{\frac{1}{3}}P_\Phi(k_2)^{\frac{2}{3}}P_\Phi(k_3) + \text{5 perm.}\Big]\end{split}\]
  1. Orthogonal CMB. The orthogonal CMB template is given by

\[\begin{split}B^{\mathrm{ortho-CMB}}_\Phi(k_1,k_2,k_3) = 6 f_{\mathrm{NL}}^{\mathrm{ortho-CMB}}\Big[-3 P_\Phi(k_1)P_\Phi(k_2) \\ +\text{ 2 perm.} -8 \left( P_\Phi(k_1)P_\Phi(k_2)P_\Phi(k_3) \right)^{\frac{2}{3}} + 3P_\Phi(k_1)^{\frac{1}{3}}P_\Phi(k_2)^{\frac{2}{3}}P_\Phi(k_3) + \text{5 perm.}\Big]\end{split}\]
  1. Orthogonal LSS. The orthogonal LSS template is given by

\[\begin{split}B^{\mathrm{ortho-LSS}}_\Phi(k_1,k_2,k_3) = \\ 6 f_{\mathrm{NL}}^{\mathrm{ortho-CMB}} \left(P_\Phi(k_1)P_\Phi(k_2)P_\Phi(k_3)\right)^{\frac{2}{3}}\Bigg[ \\ -\left(1+\frac{9p}{27}\right) \frac{k_3^2}{k_1k_2} + \textrm{2 perms} +\left(1+\frac{15p}{27}\right) \frac{k_1}{k_3} \\ + \textrm{5 perms} -\left(2+\frac{60p}{27}\right) \\ +\frac{p}{27}\frac{k_1^4}{k_2^2k_3^2} + \textrm{2 perms} -\frac{20p}{27}\frac{k_1k_2}{k_3^2}+ \textrm{2 perms} \\ -\frac{6p}{27}\frac{k_1^3}{k_2k_3^2} + \textrm{5 perms}+\frac{15p}{27}\frac{k_1^2}{k_3^2} + \textrm{5 perms}\Big]\end{split}\]

Initial conditions

The initial conditions of the Quijote-PNG simulations have been generated using a modified version of the code described in Scoccimarro et al. 2012. Our modified version of the code is publicly available here.

The initial conditions of a given simulation can be found in a folder called ICs, that contains:

  • ics.X. These are the initial conditions that contain the particle positions, velocities, and IDs. These are Gadget format-II snapshots and can be read as described in Snapshots. X can go from 0 to 127.

  • 2LPT.params. This is the parameter file used to generate the initial conditions.

  • logIC. The output of the initial conditions generator code.

The value of initial random seed for the simulation \(i\) is \(10\times i+5\) (this can be found in the 2LPT.params file) independently of the shape and \(f_{\rm NL}\) value. For instance, the value of the initial random seed for OR_CMB_p/100 and OR_CMB_m/100 is 1005. This choice enables the calculation of partial derivatives, needed for Fisher matrix calculations.

For the details about the linear matter power spectrum used for these simulations see Linear power spectra.


We keep snapshots at redshifts 0, 0.5, 1, 2, and 3. The snapshots are saved as HDF5 files, and they can be read in the standard way (see Snapshots for details on this).

Halo catalogues

We store Friends-of-Friends (FoF) halo catalogues for each snapshot of each simulation in Quijote-PNG. We refer the user to Halo catalogs for details on how to read these files.

Density fields

To facilitate the post-processing of the data we also provide 3D grids containing the overdensity, \(\delta(x)=\rho(x)/\bar{\rho}-1\), for each redshift of all PNG simulations. We refer the user to Density fields for details on how to read these files.


Quijote-PNG was developed in 2022 by:

  • William Coulton (CCA, USA)

  • Gabriel Jung (Padova, Italy)

  • Francisco Villaescusa-Navarro (CCA/Princeton, USA)

  • Dionysios Karagiannis (Cape Town, South Africa)

  • Drew Jamieson (MPA, Germany)

  • Michele Liguori (Padova, Italy)

  • Marco Baldi (Bologna, Italy)

  • Licia Verde (Barcelona, Spain)

  • Benjamin Wandelt (IAP, France)