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 non-minimally 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 ’ s constant à la Jordan-Brans-Dicke .
We investigate here two classes of models , where the gravitational sector of the Lagrangian is F ( \phi ) R with F ( \phi ) = \xi \phi ^ { 2 } ( Induced Gravity , IG ) and F ( \phi ) = 1 + \xi \phi ^ { 2 } ( Non-Minimal 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 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 .