If the cosmological constant problem is solved in a way that Λ completely vanishes, we need to find alternative models of dark energy. As we already mentioned in the Introduction, there a re basically two approaches for the construction of dark energy models. The first approach is based on “modified matter models” in which the energy-momentum tensor Tμν on the r.h.s. of the Einstein equations contains an exotic matter source with a negative pressure. The second approach is based on “modified gravity models” in which the Einstein tensor Gμν on the l.h.s. of the Einstein equations is modified.

It is however important to realize t hat within General Relativity this division is mostly a practical way to classify the variety of dark energy models but does not carry a fundamental meaning. One can always write down Einstein's equations in the standard form Gμν = 8π GTμν by absorbing in Tμν all the gravity modifications that one conventionally puts on the l.h.s.. In other words, one can define a covariantly conserved energy-momentum tensor that equals the Einstein tensor. There is no way, within General Relativity, i.e. by using only gravitational interactions, to distinguish modified matter from modified gravity.