An example of plotting time on the bottom axis and redshift on the top.

plot_cosmo.py

from matplotlib import pyplot
from matplotlib.ticker import FuncFormatter
import numpy as np
from yt.utilities.cosmology import Cosmology

import matplotlib as mpl
mpl.rcParams['axes.unicode_minus'] = False

def _z_from_t(t, pos):
    global co
    return "%d" % np.round(co.z_from_t(co.quan(t, "Gyr")))

if __name__ == "__main__":
    co = Cosmology(omega_matter=0.266,
                   omega_lambda=0.734,
                   hubble_constant=0.71)

    my_fig, my_axes = pyplot.subplots(figsize=(10, 6))

    xlim = (14, 0)
    tx = my_axes.twiny()
    tx.xaxis.tick_top()
    # Set a list of redshifts to be included on the redshift axis
    z_ticks_in_t = co.t_from_z(np.array([8, 5, 4, 3, 2, 1, 0])).in_units("Gyr")
    tx.xaxis.set_ticks(z_ticks_in_t.d)
    tx.xaxis.set_major_formatter(FuncFormatter(_z_from_t))
    tx.set_xlim(xlim)
    tx.xaxis.set_label_text("z")

    my_axes.xaxis.set_ticks(np.arange(xlim[0], xlim[1]+1, 5), minor=True)
    my_axes.xaxis.set_label_text("t [Gyr]")
    my_axes.set_xlim(xlim[0], xlim[1])

    pyplot.savefig('cosmo.pdf')