Exploring the self-tuning of the cosmological constant from Planck mass variation

Recently, the variation of the Planck mass in the General Relativistic Einstein-Hilbert actionwas proposed as a self-tuning mechanism of the cosmologicalconstant, preventing Standard Modelvacuum energy from freely gravitating and enabling an estimation of the magnitude of its observedvalue. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frameformalism to the current Jordan-frame formulation of the mechanism and use this to highlightsimilarities and differences of self-tuning to the sequestering mechanism. We then show how with anextension of the local self-tuning action by a coupled Gauss-Bonnet term and a companion four-formfield strength, graviton loops can be prevented from incapacitating the degravitation of the StandardModel vacuum energy. For certain cases, we furthermore find that this extension can be recast asa Horndeski scalar-tensor theory and be embedded in the conventional local self-tuning formalism.We then explore the possibility of a unification of inflation with self-tuning. The resulting equationscan alternatively be used to motivate a multiverse interpretation. In this context, we revisit thecoincidence problem and provide an estimation for the probability of the emergence of intelligentlife in our Universe as a function of cosmic age, inferred from star and terrestrial planet formationprocesses. We conclude that we live at a very typical epoch, where we should expect the energydensities of the cosmological constant and matter to be of comparable size. For a dimensionlessquantity to meaningfully compare the emergence of life throughout the cosmic history of differentuniverses in an anthropic analysis of the multiverse, we introduce the order of magnitude differenceof the evolving horizon size of a universe to the size of its proton as the basic building blockof atoms, molecules, and eventually life. For our Universe we find this number to form peak atapproximately 42. We leave the question of whether the same number must be assumed for theemergence of life across other universes to future exploration.