from constants import H0, omegaK, omegaM, omegaL, c, m , a0

from numpy import sqrt

def comobileTime(z):
   return -1/(H0*(1+z)*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def distPhoton(z):
   return -c/(H0*a0*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def distLepton(z,E):
   beta = sqrt(1-m**2*c**4/E**2)
   return -beta*c/(H0*a0*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))