Constraints on a vacuum energy from both SNIa and CMB temperature
  observations
  We investigate the cosmic thermal evolution with a vacuum energy which decays
into photon at the low-redshift. We assume that the vacuum energy is a function
of the scale factor that increases toward the early universe. We put on the
constraints using recent observations of both type Ia supernovae (SNIa) by
Union-2 compilation and the cosmic microwave background (CMB) temperature at
the range of the redshift 0.01 < z < 3. From SNIa, we find that the effects of
a decaying vacuum energy on the cosmic expansion rate should be very small but
could be possible for z < 1.5. On the other hand, we obtain the severe
constraints for parameters from the CMB temperature observations. Although the
temperature can be still lower than the case of the standard cosmological
model, it should only affect the thermal evolution at the early epoch.
