CosmoCoffee

The authors look at implications of a varying \Lambda(t) and G(t). I do have some comments that are not ment as criticism to this paper (which has a different spirit), but rather as general remarks on the topic:

In a general covariant theory, there is no quantity \Lambda(t): general covariance implies that it must be a function of space time, hence \Lambda(t) -> \phi(x) and we are back at a scalar field theory.

Secondly, a change of Newton's constant G(t) and hence the Planck mass can be absorbed by a Weyl scaling. Of course, it is a matter of taste and convenience which frame might be more suitable. In principle, however, one can get rid of G(t) and will introduce an additional scalar field plus some matter-field couplings.

I am not sure that a theory with variable G and Lambda is equivalent to a scalar coupling, modulo a Weyl rescaling. If G and Lambda are determined by some renormalization group trajectory, as in the quoted paper by Sola, it is not possible, in general, to describe their evolution of from an action principle. In other words, the equation of motion for the "scalar field" is not necessarely also a solution of the renormalization group equations. Possible solutions to this problem are presented in Phys.Rev.D69:104022,2004, and in Class.Quant.Grav.21:5005-5016,2004. On the other hand, one can imagine that a variable G and Lambda would act as a source term in the energy balance equation, and we are simply describing an exchange of energy between the dark sector and the matter sector.