2. Decay by emission of matter or radiation

Bronstein (1933) introduced the idea that the dark energy density is decaying by the emission of matter or radiation. The continuing discussions of this and the associated idea of decaying dark matter (Sciama, 2001, and references therein) are testimony to the appeal. Considerations in the decay of dark energy include the effect on the formation of light elements at z ~ 10¹⁰, the contribution to the -ray or optical extragalactic background radiation, and the perturbation to the spectrum of the 3 K cosmic microwave background radiation. ⁽⁴⁷⁾

The effect on the 3 K cosmic microwave background was of particular interest a decade ago, as a possible explanation of indications of a significant departure from a Planck spectrum. Precision measurements now show the spectrum is very close to thermal. The measurements and their interpretation are discussed by Fixsen et al. (1996). They show that the allowed addition to the 3 K cosmic microwave background energy density _R is limited to just _R / _R 10^-4 since redshift z ~ 10⁵, when the interaction between matter and radiation was last strong enough for thermal relaxation. The bound on _R / _R is not inconsistent with what the galaxies are thought to produce, but it is well below an observationally interesting dark energy density.

Dark energy could decay by emission of dark matter, cold or hot, without disturbing the spectrum of the 3 K cosmic microwave background radiation. For example, let us suppose the dark energy equation of state is w_X = - 1, and hypothetical microphysics causes the dark energy density to decay as a^-n by the production of nonrelativistic dark matter. Then Bronstein's Eq. (36) says the dark matter density varies with time as

(46)

where A is a constant and 0 < n < 3. In the late time limit the dark matter density is a fixed fraction of the dark energy. But for the standard interpretation of the measured anisotropy of the 3 K background we would have to suppose the first term on the right hand side of Eq. (46) is not much smaller than the second, so the coincidences issue discussed in Sec. III.B.2 is not much relieved. It does help relieve the problem with the small present value of (to be discussed in connection with Eq. [47]).

We are not aware of any work on this decaying dark energy picture. Attention instead has turned to the idea that the dark energy density evolves without emission, as illustrated in Eq. (45) and the two classes of physical models to be discussed next.

⁴⁷ These considerations generally are phenomenological: the evolution of the dark energy density, and its related coupling to matter or radiation, is assigned rather than derived from an action principle. Recent discussions include Pollock (1980), Kazanas (1980), Freese et al. (1987), Gasperini (1987), Sato, Terasawa, and Yokoyama (1989), Bartlett and Silk (1990), Overduin, Wesson, and Bowyer (1993), Matyjasek (1995), and Birkel and Sarkar (1997). Back.