Testing the cosmic conservation of photon number with type Ia supernovae
  and ages of old objects
  In this paper, we obtain luminosity distances by using ages of 32 old passive
galaxies distributed over the redshift interval $0.11 < z < 1.84$ and test the
cosmic conservation of photon number by comparing them with 580 distance moduli
of type Ia supernovae (SNe Ia) from the so-called Union 2.1 compilation. Our
analyses are based on the fact that the method of obtaining ages of galaxies
relies on the detailed shape of galaxy spectra but not on galaxy luminosity.
Possible departures from cosmic conservation of photon number is parametrized
by $\tau(z) = 2 \epsilon z$ and $\tau(z) = \epsilon z/(1+z)$ (for $\epsilon =0$
the conservation of photon number is recovered). We find
$\epsilon=0.016^{+0.078}_{-0.075}$ from the first parametrization and
$\epsilon=-0.18^{+0.25}_{-0.24}$ from the second parametrization, both limits
at 95\% c.l. In this way, no significant departure from cosmic conservation of
photon number is verified. In addition, by considering the total age as
inferred from Planck (2015) analysis, we find the incubation time
$t_{inc}=1.66\pm0.29$ Gyr and $t_{inc}=1.23\pm0.27$ Gyr at 68\% c.l. for each
parametrization, respectively.}
