Tracking extended quintessence

Abstract

We investigate the cosmological role of a Tracking Field φ in Extended Quintessence scenarios, where the dynamical vacuum energy driving the acceleration of the universe today possesses an explicit coupling with the Ricci scalar, R, of the form F (φ)R/2, where F (φ) mimics General Relativity today, F (φ0) = 1/8πG. We analyse explicit non-minimally coupled (NMC) models where F (φ) = 1/8πG + ξ(φ 2 − φ 2 0 ), with ξ is the coupling constant and φ0 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 R-boost, caused by the effective potential generated by the Ricci scalar in the Klein-Gordon equation. During this phase the field 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 with the redshift z as (1 + z) 2 . When the R-boost ends, the field trajectory matches the tracker solution in minimally coupled theories. We compute perturbations in these Tracking Extended Quintessence models, by integrating the full set of equations for the evolution of linear fluctuations in scalar-tensor theories of gravity, and assuming Gaussian scale-invariant initial perturbations. The Integrated Sachs Wolfe (ISW) effect on the Cosmic Microwave Background (CMB) angular spectrum causes a change δC /C 2[1 − 8πGF (φ dec )] at < ∼ 10, where dec stands for decoupling. Similarly, the CMB acoustic peaks multipoles shift compared to ordinary tracking Quintessence models by roughly an amount δ / [8πGF (φ dec ) − 1]/8. The turnover wavenumber kturn in the matter power spectrum shifts by an amount δkturn/kturn [1 − 8πGF (φeq)]/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 ξ. We show that the above effects can be as large as 10 − 30% with respect to equivalent cosmological constant and ordinary tracking Quintessence models, respecting all the existing experimental constraints on scalartensor theories of gravity. These results demonstrate that the playground where the next decade data will have their impact includes the nature of the dark energy in the Universe, as well as the structure of the theory of gravity.

Quintessential perturbations during scaling regime

“…(44) and the solutions below this equation in [21], eqs. (23)(24)(25)(26)(27)(28)(29) in [30], and eqs. (49,50) in [26].…”

“…Although the scaling by itself cannot explain the acceleration in the present epoch, since the scaling works as an attractor we find many implementation of quintessence idea having such an attractor in the early evolution stage. The evolution of perturbation during the scaling regime as well as the following quintessential development has been actively studied in recent literature [3,5,[20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Boundary inflation and the WMAP data

“…On the other hand, since we are dealing with a multiscalar-tensor theory in the late-time cosmology, and especially today, the evolution of the conformal factor and its first and second gradients are constrained by various solar-system, astrophysical and cosmological measurements [52,53,54,55,56,57,59,60,61,62]. As discussed in Sect.…”

“…Scalar-tensor theories have been intensively studied as natural extensions of General Relativity and are strongly constrained in the solar system [50,51]. On the cosmological side, there are (weaker) constraints coming from the Big Bang Nucleosynthesis (BBN) and recent works have been focused on scalar-tensor effects in the Cosmic Microwave Background anisotropies (CMB) and in weak gravitational lensing [52,53,54,55,56,57,58,59,60,61,62,63]. In these works, scalar-tensor theories have been discussed in the context of the post-inflationary cosmology by quantifying the distortions the non-minimally scalar fields may induce compared to the pure General Relativity predictions.…”

Curvature Coupling and Accelerated Expansion of the Universe

“…One of the possible explanations is the existence of dark energy (see, e.g., the reviews [3,4]). There exists a number of dark energy candidates, the best known are a cosmological constant and different quintessence scenarios ( [5,6,7,8,9,10,11,12]). Negative pressure may also be the consequence of self-interactions in gas models of the Universe [13,14,15,16,17].…”