Constrain Cosmology

Simulate cosmological constraints from a sample of lensed SN.

All of these cosmology tools are based on Coe & Moustakas 2009. and Dan Coe’s Fisher matrix starter paper.

Run this notebook with Google Colab.

Creating a Survey

import sntd
import numpy as np

Start by defining your survey parameters. In this case we have a survey called “Test Survey” with 10 lenses with normally distributed lens and source redshifts, 5% lens model uncertainty and 2% time delay uncertainty.

np.random.seed(3)

my_survey=sntd.Survey(dTl=5,dTT=2,zl=np.random.normal(.5,.1,size=10),zs=np.random.normal(1.6,.2,size=10),name='Test Survey')

Gridded Parameter Search

This will make a smooth contour plot for 2 parameters.

my_survey.survey_grid(vparam_names=['h','Ode0'],
                      bounds={'h':[.65,.75],'Ode0':[0,1]},npoints=50)

my_survey.plot_survey_contour(['h','Ode0'],math_labels=[r'$h$',r'$\Omega_\lambda$'],confidence=[.68,.95],alphas=[.9,.4],show_legend=True)

Out:

No handles with labels found to put in legend.

<AxesSubplot:xlabel='$h$', ylabel='$\\Omega_\\lambda$'>

MCMC-Like Parameter Search

my_survey.survey_nestle(vparam_names=['h','Ode0'],
                      bounds={'h':[.65,.75],'Ode0':[0,1]},npoints=200)

my_survey.plot_survey_contour(['h','Ode0'],math_labels=[r'$h$',r'$\Omega_\lambda$'],filled=False)

Fisher Matrix Analysis

This will make a 5x5 fisher matrix with the given parameters

my_survey.survey_fisher(['h','Ode0','Om0','w0','wa'])

Add a prior that assumes perfect knowledge of all other parameters

my_survey.fisher_matrix.prior('Om0',0.0001)
my_survey.fisher_matrix.prior('Ode0',0.0001)
my_survey.fisher_matrix.prior('h',0.0001)
my_survey.fisher_matrix.plot('w0','wa',x_limits=[-1.7,-.3],y_limits=[-4,4])

Out:

<AxesSubplot:xlabel='w0', ylabel='wa'>