InstaHeat is a 3D pseudo-spectral preheating code including metric scalar perturbations to to analyze gravitational instabilities.
It evolves a single scalar field in the FLRW background metric including scalar metric perturbations and backreactions through a phase of metric preheating after the end of chaotic large field inflation. Due to parametric resonance the evolution becomes non-linear and the produced tensor perturbations are used to compute the power spectrum of the generated gravitational waves.
❗ Disclaimer: InstaHeat is scientific code and currently not under active development. Expect adventures. InstaHeat is written with speed in mind and, perhaps, not enough consideration for readability. However, we put quite some effort into a detailed documentation and explanation of the parameters and options.
The code has been tested under MacOS and Linux. It uses the Fastest Fourier Transform in the West FFTW3, the GNU Scientific Library GSL, the HDF5 data model as well as the OpenMP API.
On a Mac probably the most convenient way to install current versions of FFTW3, GSL and HDF5 is via homebrew (h5utils is not necessary, but provides useful tools):
brew install gsl hdf5 h5utils
brew install fftw --with-openmpYour C compiler should implement OpenMP. If in doubt, install the GNU Compiler Collection GCC. Again, on a Mac simply type
brew install gccNavigate to the src/ directory and simply try
makeIf you get any errors you might have to modify the Library and Include search paths in the Makefile. We implemented a very simple check for the OS (only Linux and MacOS)
UNAME_S := $(shell uname -s)
ifeq ($(UNAME_S),Linux)
LIBS = -L/lib -L/share/sw/free/gsl/2.1/lib -g -shlib -lfftw3_threads -lfftw3 -lgsl -lgslcblas -lm -fopenmp
CFLAGS += -I/share -I/share/sw/free/gsl/2.1/include
endif
ifeq ($(UNAME_S),Darwin)
LIBS = -L/usr/local/lib -g -lfftw3_omp -lfftw3 -lgsl -lgslcblas -lm -fopenmp
CFLAGS += -march=native -I/usr/local/include
export HDF5_CC = gcc-6
export HDF5_CLINKER = gcc-6
endifThe LIBS and CFLAGS flags are simply what we used on your systems and you might want to change them. On MacOS gcc actually points to Apple's LLVM clang frontend, thus we have to tell h5cc explicitly to use the GNU compiler gcc-6. You might want to use another compiler.
Now make should do the job and produce an executable called run in the src/ directory.
❗ You have to specify the parameters before the build process! Read the Parameters and Options section before running InstaHeat.
InstaHeat is extensively annotated with Doxygen comments. A detailed documentation of the code can be exported to html and latex. To build the documentation for both, simply type
make docThe documentation then resides in the created doc folder on the same level as the repository folder.
InstaHeat starts at the end of chaotic large field inflation. After the inflaton rolled down to the bottom of the potential, it oscillates around the minimum with decaying amplitude. Due to cosmic inflation the vacuum fluctuations have been stretched out such that the inflaton field is almost homogeneous and can be approximated by a classical field with small perturbations on all scales. Thus typical initial conditions for InstaHeat are given by the Bunch-Davies vacuum.
We then evolve the inflaton field \f$\phi\f$ together with a scalar metric perturbation \f$\psi\f$ and the scale factor \f$a\f$ in the perturbed FLRW metric \f$ds^2 = - (1 + 2 \psi) dt^2 + a^2 \delta_{ij} (1 - 2 \psi) dx^i dx^j\f$. The initial perturbations \f$\psi\f$ are chosen to be compliant with the constraint from the Einstein equations.
Throughout the evolution we can compute the generated tensorial metric perturbations in the transverse traceless gauge alongside the the inflaton field and the metric perturbation. However, we only include backreactions from the scalar perturbations, not the tensorial part. From the tensor perturbations we compute the power spectru of the generated gravitational waves.
InstaHeat is written in C99. It is a pseudo-spectral code, i.e. we are constantly going back and forth between real space and Fourier space. Those Fourier transforms are expensive and take up roughly 80% to 85% of the runtime. On the other hand, it brings the advantage of exponentially small errors in spatial derivatives and thereby allows us to reach high precision and accuracy on comparatively small grids.
For the time integration of the equations of motion one can choose between several explicit Runge Kutta steppers. The available options are
- Runge Kutta 4 (classic RK4 with fixed time steps)
- Runge Kutta Fehlberg 4(5) (adaptive time steps)
- Runge Kutta Cash-Carp 4(5) (adaptive time steps)
- Runge Kutta Dormand-Prince 8(9) (adaptive time steps)
- Runge Kutta Dormand-Prince 8(5,3), default (adaptive time steps)
Details about the numerics can be found in the extensive documentation of the code under (tbd).
InstaHeat as flexible and extensive output options. All output of a run is bundled into a single .h5 file. Additionally to basically all the parameters of the run, the scale factor \f$a\f$ and the physical time \f$t\f$ one can choose any combination of the following:
The full field (on part) of the simulation grid, the mean, the variance, the maximum, the minimum, the power spectrum for
- \f$\phi\f$ - The scalar inflaton field.
- \f$\dot{\phi}\f$ - The temporal derivative of the scalar inflaton field.
- \f$\psi\f$ - The scalar metric perturbation.
- \f$\dot{\psi}\f$ - The temporal derivative of the scalar metric perturbation.
- \f$\rho\f$ - The energy density.
- \f$p\f$ - The pressure.
Detailed information about the output options can be found in section Parameters and Options.
The simulation parameters and output options are explained in great detail in the documentation of the parameters. This is also important for the build process. You can find the docs
- here if you are viewing this on GitHub, or
- [here](@ref docparameters) if you are viewing this on Doxygen.
Previous codes include but are not limited to: