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 action was proposed as a self-tuning mechanism of the cosmological constant, preventing standard model vacuum energy from freely gravitating and enabling an estimation of the magnitude of its observed value. We explore here new aspects of this proposal. We first develop an equivalent Einstein-frame formalism to the current Jordan-frame formulation of the mechanism and use this to highlight similarities and differences of self-tuning to the sequestering mechanism. We then show how with an extension of the local self-tuning action by a coupled Gauss–Bonnet term and a companion four-form field strength, graviton loops can be prevented from incapacitating the degravitation of the standard model vacuum energy. For certain cases, we furthermore find that this extension can be recast as a 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 equations can alternatively be used to motivate a multiverse interpretation. In this context, we revisit the coincidence problem and provide an estimation for the probability of the emergence of intelligent life in our Universe as a function of cosmic age, inferred from star and terrestrial planet formation processes. We conclude that we live at a very typical epoch, where we should expect the energy densities of the cosmological constant and matter to be of comparable size. For a dimensionless quantity to compare the emergence of life throughout the cosmic history of different universes in an anthropic analysis of the multiverse, we choose the order of magnitude difference of the evolving horizon size of a Universe to the size of its proton as the basic building block of atoms, molecules, and eventually life. For our Universe we find this number to form peak at approximately 42. We leave the question of whether the same number is frequently assumed for the emergence of life across other universes or singles out a special case to future exploration.