.. _mg:
================
Modified Gravity
================
Quijote contains N-body simulations with modified gravity: **Quijote-MG**. The movie below shows one of these simulations together wits :math:`\Lambda {\rm CDM}` counterpart:
.. raw:: html
If you are interested in using these simulations, please contact us at marco.baldi5@unibo.it or villaescusa.francisco@gmail.com.
General description
-------------------
Quijote-MG contains 4,048 N-body simulations run with `MG-Gadget `_ and using the `Hu & Sawicki f(R) model `_ as the modified gravity model. Each simulation follows the evolution of :math:`512^3` dark matter plus :math:`512^3` neutrinos in a periodic cosmological volume of :math:`(1000~{\rm Mpc}/h)^3`. The initial conditions have been generated using the Zel'dovich approximation at :math:`z=127` and the simulations have been run with the appropiate Hubble function :math:`H(z)`. We have saved 5 snapshots, at redshifts 0, 0.5, 1, 2, and 3. For each simulation we have saved FoF catalogs, Rockstar catalogs, and different power spectra (see below).
The simulations can be classified into two different groups:
- Simulations designed for Fisher matrix calculations
- Simulations designed for machine learning calculations
Simulations for Fisher matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For the first category we have 2,000 simulations. In this category there are four different types:
- 500 simulations run with :math:`f_{R_0}=-5\times10^{-7}`
- 500 simulations run with :math:`f_{R_0}=-5\times10^{-6}`
- 500 simulations run with :math:`f_{R_0}=-5\times10^{-5}`
- 500 simulations run with :math:`f_{R_0}=-5\times10^{-4}`
.. Note::
We refer the reader to :ref:`types` for details on the value of the cosmological parameters, the initial conditions...etc.
These simulations are designed for Fisher matrix calculations, and therefore, they have matching IDs between themselves and among other Quijote simulations. We note that to compute generic partial derivatives:
.. math::
\frac{\partial \vec{S}}{\partial f_R}
where :math:`\vec{S}` is a generic summary statistics and :math:`f_R` is the modified gravity parameter, we can use methods like this:
.. math::
\frac{\partial \vec{S}}{\partial f_R} &\simeq& \frac{\vec{S}(f_R+\delta f_R) - \vec{S}(f_R)}{\delta f_R}\\
\frac{\partial \vec{S}}{\partial f_R} &\simeq& \frac{-3\vec{S}(f_R) + 4\vec{S}(f_R+\delta f_R) - \vec{S}(f_R+2\delta f_R)}{2\delta f_R}\\
\frac{\partial \vec{S}}{\partial f_R} &\simeq& \frac{-21\vec{S}(f_R) + 32\vec{S}(f_R+\delta f_R) - 12\vec{S}(f_R+2\delta f_R) + \vec{S}(4\delta f_R)}{12\delta f_R}\\
\frac{\partial \vec{S}}{\partial f_R} &\simeq& \frac{-315\vec{S}(f_R) + 512\vec{S}(f_R+\delta f_R) - 224\vec{S}(f_R+2\delta f_R) + 28\vec{S}(4\delta f_R) - \vec{S}(8\delta f_R)}{168\delta f_R}
where the fiducial value of :math:`f_R` is set to zero.
.. Important::
Note that the chosen values of :math:`f_{R_0}` are not distributed equally in both linear and log considering that the fiducial value is :math:`f_{R_0}=0`. Thus, when performing Fisher matrix calculations, we recommend perform the following change of variables: :math:`Y=(f_{R_0})^{\log_{10}(2)}`. In that way, the values of :math:`f_{R_0}` equal to 0, :math:`-5\times10^{-7}`, :math:`-5\times10^{-6}`, :math:`-5\times10^{-5}`, :math:`-5\times10^{-4}`, map to :math:`Y` equal to 0, -0.0127, -0.0254, -0.0507, -0.101, and the above formulae can easily be used to evaluate :math:`\partial \vec{S}/\partial Y`.
Simulations for machine learning
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this category we have 2,048 simulations. Each simulation has a different value of the initial random seed and of the parameters :math:`\Omega_{\rm m}`, :math:`\Omega_{\rm b}`, :math:`h`, :math:`n_s`, :math:`\sigma_8`, :math:`M_\nu`, :math:`f_{R0}`. The value of those parameters in the simulations are organized in a Sobol sequence with boundaries:
.. math::
0.1 & \leq \Omega_{\rm m} \leq & 0.5\\
0.03 & \leq \Omega_{\rm b} \leq & 0.07\\
0.5 & \leq h \leq & 0.9\\
0.8 & \leq n_s \leq & 1.2\\
0.6 & \leq \sigma_8 (GR) \leq & 1.0\\
0.01 & \leq M_\nu[{\rm eV}] \leq & 1.0\\
-3\times10^{-4} & \leq f_{R0} \leq & 0
.. Note::
The actual value of these parameters for the different simulations can be found `here `__.
.. Important::
The above link will bring you to the file with the value of the parameters. We note that for :math:`\sigma_8` there are two values quoted: 1) s8(LCDM) which represents the :math:`\sigma_8` values of the GR underlying cosmology, and 2) s8(MG) which represents the :math:`\sigma_8` value of the full modified gravity model. We recommend using s8(MG) rather than s8(LCDM). However, the sobol sequence was created with a uniform prior in s8(GR). For that reason, we think the best option is to use the value of :math:`A_s` rather than :math:`\sigma_8` when working with these QuijoteMG simulations.
Organization
------------
The data is split into different folders:
- ``Snapshots``. This folder contains 2,048 subfolders, one for each simulation. Inside these subfolders, the user can find the initial conditions, snapshots, simulation parameters, and additional files produced by MG-Gadget.
- ``Halos``. This folder contains 2 folders: ``FoF`` and ``Rockstar``. Each of those folders contains 2,048 folders, inside which the halo catalogs at different redshifts are located.
- ``Pk``. This folder contains 2,048 subfolders, one for each simulation. Inside these subfolders, the user can find the different power spectra.
Snapshots
---------
Every simulation contains 5 snapshots. Each snapshot is stored in a folder called ``snapdir_00X``, where ``X=0`` is :math:`z=3`, ``X=1`` is :math:`z=2`, ``X=2`` is :math:`z=1`, ``X=3`` is :math:`z=0.5`, ``X=4`` is :math:`z=0`. The snapshots are stored in hdf5 format, and can be read using Pylians (see details in :ref:`snapshots`). Note that the snapshots have been compressed to save space, so please take a look at :ref:`faq` if you encounter problems reading them.
.. Note::
The initial conditions are located inside a folder called ``ICs``. The initial conditions are also stored as hdf5 files, and can be read in the same way as the simulation snapshots.
The MG-Gadget snapshots contains more blocks than traditional Gadget N-body simulations. The fields stored in the snapshots are:
::
/CompressionInfo
/Header
/PartType1
/PartType1/Acceleration
/PartType1/Coordinates
/PartType1/ModifiedGravityAcceleration Dataset
/PartType1/ModifiedGravityGradPhi Dataset
/PartType1/ModifiedGravityPhi Dataset
/PartType1/ParticleIDs
/PartType1/Velocities
/PartType2
/PartType2/Acceleration
/PartType2/Coordinates
/PartType2/ModifiedGravityAcceleration Dataset
/PartType2/ModifiedGravityGradPhi Dataset
/PartType2/ModifiedGravityPhi Dataset
/PartType2/ParticleIDs
/PartType2/Velocities
where ``PartType1`` represent cold dark matter and ``PartType2`` correspond to neutrinos.
Halo catalogs
-------------
Quijote-MG contains both FoF and Rockstar halo catalogs for every snapshot of each simulation. You can find details about how to read these files in :ref:`halo_catalogues`.
Power spectra
-------------
For every snapshot of each Quijote-MG simulation we have computed the following power spectra:
- cold dark matter auto-Pk in real-space: ``Pk_CDM_z=X.XXX.dat``
- cold dark matter auto-Pk in redshift-space: ``Pk_CDM_RS_axis=Y_z=X.XXX.dat``
- neutrino auto-Pk in real-space: ``Pk_NU_z=X.XXX.dat``
- neutrino auto-Pk in redshift-space: ``Pk_NU_RS_axis=Y_z=X.XXX.dat``
- total matter auto-Pk in real-space: ``Pk_CDM+NU_z=X.XXX.dat``
- total matter auto-Pk in redshift-space: ``Pk_CDM+NU_RS_axis=Y_z=X.XXX.dat``
- CDM-neutrino cross-Pk in real-space: ``Pk_CDMNU_z=X.XXX.dat``
- CDM-neutrino cross-Pk in redshift-space: ``Pk_CDMNU_RS_axis=Y_z=X.XXX.dat``
Where ``X.XXX`` is the redshift and ``Y`` (0, 1, or 2) is the axis along which the redshift-space distortions have been placed.
Bispectra
---------
For every snapshot of each Quijote-MG simulation we have computed the full matter bispectrum. We use a grid with :math:`384^3` voxels and we measure the bispectrum in more than 7,000 different triangle configurations. The name of the files is ``Bk_m_z=X.X.txt``, where ``X.X`` represents the redshift.