Extended quintessence

We study quintessence cosmologies in the context of scalar-tensor theories of gravity, where a scalar field $\phi ,$ assumed to provide most of the cosmic energy density today, is nonminimally coupled to the Ricci curvature scalar R. Such “extended quintessence” cosmologies have the appealing feature that the same field causing the time (and space) variation of the cosmological constant is the source of a varying Newton constant in the manner of Jordan-Brans-Dicke. We investigate here two classes of models, where the gravitational sector of the Lagrangian is $F\left(\phi \right)R$ with $F\left(\phi \right)=\xi {\phi }^2$ [induced gravity (IG)] and $F\left(\phi \right)=1+\xi {\phi }^2$ [nonminimal coupling (NMC)]. As a first application of this idea we consider a specific model, where the quintessence field $\phi ,$ obeying the simplest inverse power potential, has ${\Omega }_{\phi }=0.6\mathrm{}$ today, in the context of the cold dark matter scenario for structure formation in the Universe, with scale-invariant adiabatic initial perturbations. We find that, if $\xi \lesssim 5\times {10}^{-4}$ for IG and $\xi \lesssim 5\times {10}^{-3}(\sqrt{G}{\phi }_0{)}^{-1}$ for NMC $({\phi }_0$ is the present quintessence value), our quintessence field satisfies the existing solar system experimental constraints. Using linear perturbation theory we then obtain the polarization and temperature anisotropy spectra of the cosmic microwave background (CMB) as well as the matter power spectrum. The perturbation behavior possesses distinctive features, that we name “QR effects:” the effective potential arising from the coupling with R adds to the true scalar field potential, altering the cosmic equation of state and enhancing the integrated Sachs-Wolfe effect. As a consequence, part of the CMB anisotropy level on COBE scales is due to the latter effect, and the cosmological perturbation amplitude on smaller scales, including the oscillating region of the CMB spectrum, has reduced power; this effect is evident on CMB polarization and temperature fluctuations, as well as on the matter power-spectrum today. Moreover, the acoustic peaks and the spectrum turnover are displaced to smaller scales, compared to ordinary quintessence models, because of the faster growth of the Hubble length, which, for a fixed value today, delays the horizon crossing of scales larger than the horizon wavelength at matter-radiation equality and slightly decreases the amplitude of the acoustic oscillations. These features could be detected in the upcoming observations on CMB and large-scale structure.