Generalized holographic dark energy and the IR cutoff problem

Abstract

We consider a holographic dark energy model, in which both the cosmological-constant (CC) energy density ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ and the Newton constant ${G}_{N}$ are varying quantities, to study the problem of setting an effective field-theory IR cutoff. Assuming that ordinary matter scales canonically, we show that the continuity equation univocally fixes the IR cutoff, provided a law of variation for either ${\ensuremath{\rho}}_{\ensuremath{\Lambda}}$ or ${G}_{N}$ is known. Previous considerations on holographic dark energy disfavor the Hubble parameter as a candidate for the IR cutoff (for spatially flat universes), since in this case the ratio of dark energy to dark matter is not allowed to vary, thus hindering a deceleration era of the universe for the redshifts $z\ensuremath{\gtrsim}0.5$. On the other hand, the future event horizon as a choice for the IR cutoff is being favored in the literature, although the ``coincidence problem'' usually cannot be addressed in that case. We extend considerations to spatially curved universes, and show that with the Hubble parameter as a choice for the IR cutoff one always obtains a universe that never accelerates or a universe that accelerates all the time, thus making the transition from deceleration to acceleration impossible. Next, we apply the IR cutoff consistency procedure to a renormalization-group (RG) running CC model, in which the low-energy variation of the CC is due to quantum effects of particle fields having masses near the Planck scale. We show that bringing such a model (having the most general cosmology for running CC universes) in full accordance with holography amounts to having such an IR cutoff which scales as a square root of the Hubble parameter. We find that such a setup, in which the only undetermined input represents the true ground state of the vacuum, can give early deceleration as well as late-time acceleration. The possibility of further improvement of the model is also briefly indicated.