Nonminimal coupling and the cosmological constant problem

Abstract

We consider a universe with a positive effective cosmological constant and a nonminimally coupled scalar field. When the coupling constant is negative, the scalar field exhibits linear growth at asymptotically late times, resulting in a decaying effective cosmological constant. The Hubble rate in the Jordan frame reaches a self-similar solution, $H=1/(\epsilon t)$, where the principal slow roll parameter $\epsilon$ depends on $\xi$, reaching maximally $\epsilon =2$ (radiation era scaling) in the limit when $\xi \to -\infty$. Similar results are found in the Einstein frame (E), with $H_E=1/({\epsilon }_{E}t)$, but now ${\epsilon }_E\to 4/3$ as $\xi \to -\infty$. Therefore in the presence of a nonminimally coupled scalar de Sitter is not any more an attractor, but instead (when $\xi <-1/2$) the Universe settles in a decelerating phase. Next we show that, when the scalar field $\varphi$ decays to matter with ${\epsilon }_m>4/3$ at a rate $\Gamma \gg H$, the scaling changes to that of matter, $\epsilon \to {\epsilon }_m$, and the energy density in the effective cosmological becomes a fixed fraction of the matter energy density, $M_{\mathrm{P}}^2{\Lambda }_{E\mathrm{eff}}/{\rho }_m=\mathrm{constant}$, exhibiting thus an attractor behavior. While this may solve the (old) cosmological constant problem, it does not explain dark energy. Provided one accepts tuning at the $1\%$ level, the vacuum energy of neutrinos can explain the observed dark energy.

22 pages, 7 figures

References in corpus (6)

• Dynamics of dark energy
• The Standard Model Higgs boson as the inflaton
• Measurement of the neutrino mass splitting and flavor mixing by MINOS
• Gauge invariant cosmological perturbations for the nonminimally coupled inflaton field
• Late-time backreaction from inflationary fluctuations of a non-minimally coupled massless scalar
• The Cosmological Constant and Lorentz Invariance of the Vacuum State