Résumé
The nature of the dark energy is still a mystery and several models have been proposed to explain it. Here we consider a phenomenological model for dark energy decay into photons and particles as proposed by Lima (Phys Rev D 54:2571, 1996). He studied the thermodynamic aspects of decaying dark energy models in particular in the case of a continuous photon creation and/or disruption. Following his approach, we derive a temperature redshift relation for the cosmic microwave background (CMB) which depends on the effective equation of state w (eff) and on the "adiabatic index" gamma. Comparing our relation with the data on the CMB temperature as a function of the redshift obtained from Sunyaev-Zel'dovich observations and at higher redshift from quasar absorption line spectra, we find w (eff) = -0.97 +/- 0.03, adopting for the adiabatic index gamma = 4/3, in good agreement with current estimates and still compatible with w (eff) = -1, implying that the dark energy content being constant in time.