NSC++

Non-Standard Cosmologies in C++ z Get the stable (recommended) version by running

    git clone -b stable https://github.com/dkaramit/NSCpp

The most recent (assumed under development) version by running

    git clone https://github.com/dkaramit/NSCpp.git
	cd NSCpp
	git submodule init
	git submodule update --remote

Once everything is downloaded, run bash configure.sh in the root directory of NSC++. This creates a few things that NSC++ may need.

Relativistic degrees of freedom of the plasma

NSC++ comes with tabulated RDOF as calculated in 2005.03544 (in NSCpp/src/data/eos_2020.dat). However, this one can use another file when calling the Cosmo class costructor (see below). Ideally, the RDOF we choose should be changed by assigning a path to another file to the cosmo_PATH variable in the file NSCpp/Paths.mk before running bash configure.sh. The main reason is that this script makes sure that the data file complies with the requirements of NSC++; that is, the file must be in format:

$T$ (in GeV)	$h_{\rm eff}(T)$	$g_{\rm eff}(T)$

with increasing $T$.

Using NSC++

NSC++ is a header-only library with no external dependencies appart from a c++ compiler that supports the c++17 standard. That is, NSC++ only needs to be included in a c++ source file. Then, at compilation one only needs to specify the path to the NSC++ root directory using the -I flag.

NSC++ can also be used directly from python scripts. To do this, one needs to run

    make lib

in the root directory of NSC++. Then, the NSC++ modules can be used in a script as:

    from sys import path as sysPath
    sysPath.append('path_to_src')
    from interfacePy.Evolution import Evolution 
    from interfacePy.Cosmo import Cosmo 

with 'path_to_src' the path to NSCpp/src relative to the tocation of the script.

Examples

In arXiv:2301.08253 you can find description the classes and function in detail. However, it is worth showing an example in c++ and python here.

C++

#include<iostream>
#include<iomanip>

//Include everything you need from NSC++
#include"NSCpp.hpp"
    
int main(){
    //Use cosmo_PATH to interpolate heff and geff from T=0 to T=mP.
    nsc::Cosmo<long double> plasma(cosmo_PATH, 0, nsc::Cosmo<long double>::mP);
    
    //Declare Evolution instance using the Rosenbrock method RODASPR2
    nsc::Evolution<long double,1,RODASPR2<long double>> BE;
    
    //Declare parameters
    long double TEND=1e-2, c=3, Ti=1e7, ratio=1e-2, TSTOP=1e-4, umax=200;
    
    bool check=BE.solveNSC(TEND, c, Ti, ratio, TSTOP, umax, &plasma,
                {
                    .initial_step_size=1e-2, .minimum_step_size=1e-8, .maximum_step_size=1e-2, 
                    .absolute_tolerance=1e-11, .relative_tolerance=1e-11, .beta=0.9, 
                    .fac_max=1.2, .fac_min=0.8, .maximum_No_steps=10000000
                });
    
    if(check){
        // If the solver returns true, the solver probably worked.
        std::cout<<std::setprecision(5);
        std::cout<<BE.TE1<<"\t"<<BE.TE2<<"\t"<<BE.TD1<<"\t"<<BE.TD2<<"\n";
        
        //print the results and the errors
        for(size_t i=0; i<BE.pointSize; ++i ){
            std::cout<<std::left<<std::setw(15)<<BE.u[i]<<std::setw(15);
            std::cout<<std::left<<BE.T[i]<<std::setw(15)<<BE.dT[i]<<std::setw(15);
            std::cout<<std::left<<BE.rhoPhi[i]<<std::setw(15)<<BE.drhoPhi[i]<<"\n";
        }
    }else{
        // If the solver returns false, you may need a larger umax.
        std::cerr<<"Something went wrong. Try using larger value for umax\n";
        exit(1);
    }
    
    return 0;
}

Assuming that this code is in NSCpp/UserSpace and has a name example.cpp, it can be simply compiled by

g++ -I../ -O3 -std=c++17 example.cpp -o example

It can also be compiled using clang as

clang -lstdc++ -lm -I../ -O3 -std=c++17 example.cpp -o example

Python

# append the path to the src directory 
from sys import path as sysPath
sysPath.append('../src')

#load the NSC module
from interfacePy.Evolution import Evolution 

# load Cosmo and the Planck mass
from interfacePy.Cosmo import Cosmo,mP 

#This gives you access to the path of the rdof file.
from misc_dir.path import cosmo_PATH

#Instance of the Cosmo class. Interpolate from T=0 to T=mP
plasma=Cosmo(cosmo_PATH,0,mP)

# Evolution instance
BE=Evolution()

# solve the system
check,time=BE.solveNSC(TEND=1e-2, c=3, Ti=1e7, ratio=1e-2, umax=500, TSTOP=1e-4, plasma=plasma,
    initial_step_size=1e-2, minimum_step_size=1e-8, maximum_step_size=1e-2, 
    absolute_tolerance=1e-11, relative_tolerance=1e-11, beta=0.9, fac_max=1.2, 
    fac_min=0.8,maximum_No_steps=10000000)

if check:
    # get points 
    BE.getPoints()
    # get errors
    BE.getErrors()

    print(BE.TE1,BE.TE2,BE.TD1,BE.TD2)

    for i,u in enumerate(BE.u):
        print(u,BE.T[i],BE.dT[i],BE.rhoPhi[i],BE.drhoPhi[i])
else:
    print("Something went wrong. Try using larger value for umax")
    exit(1)

#run the destructors
del BE
del plasma

This script can be ran after make lib has finished. Here we assume that the path of this script is NSCpp/UserSpace. If it is located in another directory, we only need to change sysPath.append('../src') to sysPath.append('path_to_src') as described before.

If you have trouble using the library I would be happy to help.

Contact e-mail: dkaramit@yahoo.com, dimitrios.karamitros@manchester.ac.uk.

Citation

If you use NSC++ please cite it as

@article{Karamitros:2023uak,
    author = "Karamitros, Dimitrios",
    title = "{NSC++: Non-Standard Cosmologies in C++}",
    eprint = "2301.08253",
    archivePrefix = "arXiv",
    primaryClass = "astro-ph.CO",
    month = "1",
    year = "2023"
}

Accepted for publication in Computer Physics Communications!

Enjoy,
Dimitris

Note:

You can use NSC++ to produce the non-standard cosmological input that MiMeS needs. MiMeS is an axion/ALP simulator. The stable version of MiMeS can be found: github.com/dkaramit/MiMeS/tree/stable.