Tracking extended quintessence - art. no. 123510

We investigate the cosmological role of a tracking field phi in extended qu intessence scenarios, where the dynamical vacuum energy driving the acceler ation of the universe today possesses an explicit coupling with the Ricci s calar R of the form F(phi )R/2, where F(phi) mimics general relativity toda y, F(phi (o)) = 1/8 piG. We analyze explicit nonminimally coupled (NMC) mod els where F(phi) = 1/8 piG+ xi(phi (2)-phi (2)(o)). with xi is the coupling constant and phi (o) is the Q value today. Tracker solutions for these NMC models, with inverse power-law potentials, possess an initial enhancement of the scalar field dynamics, named the R-boost, caused by the effective po tential generated by the Ricci scalar in the Klein-Gordon equation. During this phase the held performs a "gravitational'' slow rolling until the true potential becomes important. We give accurate analytic formulas describing the R-boost, showing that the quintessence energy in this phase scales wit h the redshift: as (1+z)(2). When the R-boost ends, the field trajectory ma tches the tracker solution in minimally coupled theories. We compute pertur bations in these tracking extended quintessence models, by integrating the full set of equations for the evolution of linear fluctuations in scalar-te nsor theories of gravity, and assuming Gaussian scale-invariant initial per turbations. The integrated Sachs-Wolfe (ISW) effect on the cosmic microwave background (CMB) angular spectrum causes a change deltaC(l)/C-l similar or equal to 6[1 - 8 pi GF(phi (dec))] at l less than or similar to 10, where "dec'' stands for decoupling. Similarly, the CMB acoustic peak multipoles s hift compared to ordinary tracking quintessence models by roughly an amount deltal/l similar or equal to [8 pi GF(phi (dec))- 1]/8. The turnover wave number k(turn) in the matter power spectrum shifts by an amount deltak(turn )/k(turn)similar or equal to [1-8 pi GF(phi (eq))]/2, where "eq" stands for matter-radiation equivalence. All these corrections may assume positive as well as negative values, depending on the sign of the NMC parameter xi. We show that the above effects can be as large as 10-30% with respect to equi valent cosmological constant and ordinary tracking quintessence models, res pecting all the existing experimental constraints on scalar-tensor theories of gravity. These results demonstrate that the playground where the data o f the next decade will have their impact includes the nature of the dark en ergy in the Universe, as well as the structure of the theory of gravity.