Testable solution of the cosmological constant and coincidence problems

Abstract

We present a new solution to the cosmological constant (CC) and coincidence problems in which the observed value of the CC, $\ensuremath{\Lambda}$, is linked to other observable properties of the Universe. This is achieved by promoting the CC from a parameter that must be specified, to a field that can take many possible values. The observed value of $\ensuremath{\Lambda}\ensuremath{\approx}(9.3\text{ }\text{ }\mathrm{Gyrs}{)}^{\ensuremath{-}2}$ [$\ensuremath{\approx}{10}^{\ensuremath{-}120}$ in Planck units] is determined by a new constraint equation which follows from the application of a causally restricted variation principle. When applied to our visible Universe, the model makes a testable prediction for the dimensionless spatial curvature of ${\ensuremath{\Omega}}_{\mathrm{k}0}=\ensuremath{-}0.0056({\ensuremath{\zeta}}_{\mathrm{b}}/0.5)$, where ${\ensuremath{\zeta}}_{\mathrm{b}}\ensuremath{\sim}1/2$ is a QCD parameter. Requiring that a classical history exist, our model determines the probability of observing a given $\ensuremath{\Lambda}$. The observed CC value, which we successfully predict, is typical within our model even before the effects of anthropic selection are included. When anthropic selection effects are accounted for, we find that the observed coincidence between ${t}_{\ensuremath{\Lambda}}={\ensuremath{\Lambda}}^{\ensuremath{-}1/2}$ and the age of the Universe, ${t}_{\mathrm{U}}$, is a typical occurrence in our model. In contrast to multiverse explanations of the CC problems, our solution is independent of the choice of a prior weighting of different $\ensuremath{\Lambda}$ values and does not rely on anthropic selection effects. Our model includes no unnatural small parameters and does not require the introduction of new dynamical scalar fields or modifications to general relativity, and it can be tested by astronomical observations in the near future.