## Inflation.jl

A Julia package for numerical evaluation of cosmic inflation models. Perturbations are solved for with the transport method. Supports an arbitrary number of fields, arbitrary field space metric, and arbitrary initial conditions.
Author rjrosati
Popularity
8 Stars
Updated Last
2 Years Ago
Started In
March 2020

# Inflation.jl

A Julia package for numerical evaluation of cosmic inflation models. Perturbations are evolved with the transport method. It supports symbolic calculation of the equations of motion, and remains efficient at a high number of fields, even with non-canonical kinetic terms.

`Inflation.jl`automatically applies the horizon-crossing approximation, if the potential is detected to be sum-separable. Support is planned for automatic application of other approximations when they are valid as well. ## Installation

For now, Inflation.jl is an unregistered Julia package. It can be installed with

```julia> import Pkg

## an example

```using Inflation
using SymPy

# this is a quadratic inflation model with 10 fields and randomly selected masses

# set the field space dimension
d = 10

# set the model parameters, and their values
params = [symbols("m\$i") for i in 1:d]
pvalues = rand(d)*1e-9

function G(Phi,p)
d = length(Phi)
g = Matrix{eltype(Phi)}(I,d,d)
return g
end

function V(Phi,p)
m = p
return sum([ m[i]*Phi[i]^2)/2 for i in 1:d])
end

# set the initial conditions
Pi0 = zeros(d) # zero initial velocity

# pick a position randomly over the sphere, with radius to give ~N0 e-folds
N0 = 100
Phi0 = randn(d)
Phi0 ./= norm(Phi0)
Phi0 .*= sqrt(4*N0)

# symbolically construct the equations of motion
# because this potential is sum-separable, the horizon-crossing approximation will automatically be calculated
funcs = inflation_setup(d,V,G,params)

# solve the background equations of motion
sol = background_evolve(Phi0,Pi0,pvalues,funcs,verbose=true)

# solve the 2-pt correlation function equations of motion
# by default, use 7 k-values centered at a pivot scale of 0.002 Mpc^-1
tsol = transport_perturbations(sol,pvalues,funcs,verbose=true)

println(tsol)```

see the `examples` directory for more complicated potentials and metrics, how to scan parameter space, evaluate several simulations in parallel, output and analyze data.

At the moment, `Inflation.jl` can only solve the 2-pt correlation function equations of motion. Solving for higher-point correlation functions is possible with PyTransport/CppTransport.