Virialization of matter overdensities within dark energy subsystems: special cases

The virialization of matter overdensities within dark energy subsystems is considered under the restrictive assumptions (i) spherical-symmetric density profiles, (ii) time-independent quintessence equation of state parameter, w, and (iii) nothing but gravitational interaction between dark energy scalar field and matter. In addition, the quintessence subsystem is conceived as made of ``particles'' whose mutual interaction has intensity equal to G(1+3w) and scales as the inverse square of their distance. Then the virial theorem is formulated for subsystems. In the special case of fully clustered quintessence, energy conservation is assumed with regard to either the whole system (global energy conservation), or to the matter subsystem within the tidal potential induced by the quintessence subsystem (partial energy conservation). Further investigation is devoted to a few special values, w=-1/3, -1/2, -2/3, -1. The special case of fully clustered (i.e. collapsing together with the matter) quintessence is studied in detail. The general case of partially clustered quintessence is considered in terms of a degree of quintessence de-clustering, \zeta, ranging from fully clustered (\zeta=0) to completely de-clustered (\zeta=1) quintessence, respectively. The special case of unclustered (i.e. remaining homogeneous) quintessence is also discussed. The trend exhibited by the fractional (virialization to turnaround) radius, \eta, as a function of other parameters, is found to be different from its counterparts reported in earlier attempts. The reasons of the above mentioned discrepancy are discussed.Comment: 44 pages, 8 figure

Dark Energy and the MSSM

We consider the coupling of quintessence to observable matter in supergravity and study the dynamics of both supersymmetry breaking and quintessence in this context. We investigate how the quintessence potential is modified by supersymmetry breaking and analyse the structure of the soft supersymmetry breaking terms. We pay attention to their dependence on the quintessence field and to the electroweak symmetry breaking, ie the pattern of fermion masses at low energy within the Minimal Supersymmetric Standard Model (MSSM) coupled to quintessence. In particular, we compute explicitly how the fermion masses generated through the Higgs mechanism depend on the quintessence field for a general model of quintessence. Fifth force and equivalence principle violations are potentially present as the vacuum expectation values of the Higgs bosons become quintessence field dependent. We emphasize that equivalence principle violations are a generic consequence of the fact that, in the MSSM, the fermions couple differently to the two Higgs doublets. Finally, we also discuss how the scaling of the cold dark and baryonic matter energy density is modified and comment on the possible variation of the gauge coupling constants, among which is the fine structure constant, and of the proton-electron mass ratioComment: 26 pages, minor corrections, typos correcte

Tracking Quintessence Would Require Two Cosmic Coincidences

Good tracking requires that the quintessence energy fraction slowly increase while the roll $\lambda\equiv -d\ln V/\varkappa d\phi$ slowly decreases, but is not yet truly slow-rolling. The supernova bound on the present quintessence equation of state requires either (1) a cosmological constant or other fine-tuned "crawling quintessence" or (2) "roll-over quintessence" that tracked until recently, but now became slow rolling, because of a sharp increase in potential curvature. Thus, fine-tuning is required by constant equation of state and inverse power potentials, but can be avoided by the SUGRA and Skordis-Albrecht potentials and other good trackers, provided quintessence energy domination and slow roll {\em both} began only recently. This makes the time in which we live special in {\em two} respects.Comment: 10 pages, including 2 figures, 3 table

The SUGRA Quintessence Model Coupled to the MSSM

We study the cosmological evolution of the universe when quintessence is modeled within supergravity, supersymmetry is broken in a hidden sector, and we also include observable matter in a third independent sector. We find that the presence of hidden sector supersymmetry breaking leads to modifications of the quintessence potential. We focus on the coupling of the SUGRA quintessence model to the MSSM and investigate two possibilities. First one can preserve the form of the SUGRA potential provided the hidden sector dynamics is tuned. The currently available limits on the violations of the equivalence principle imply a universal bound on the vacuum expectation value of the quintessence field now, \kappa ^{1/2}Q\ll 1. On the other hand, the hidden sector fields may be stabilised leading to a minimum of the quintessence potential where the quintessence field acquires a mass of the order of the gravitino mass, large enough to circumvent possible gravitational problems. However, the cosmological evolution of the quintessence field is affected by the presence of the minimum of the potential. The quintessence field settles down at the bottom of the potential very early in the history of the universe. Both at the background and the perturbation levels, the subsequent effect of the quintessence field is undistinguishable from a pure cosmological constantComment: 33 pages, 7 figure

WMAP Constraints on a Quintessence Model

We use the results from the Wilkinson Microwave Anisotropy Probe (WMAP) for the locations of peaks and troughs of the Cosmic Microwave Background (CMB) power spectrum, together with constraints from large-scale structure, to study a quintessence model in which the pure exponential potential is modified by a polynomial factor. Our analysis, in the $(\Omega_m, h, n_s)$ cosmological parameters space shows that this quintessence model is favoured compared to $\Lambda$CDM for $n_s\approx 1$ and relatively high values of early quintessence; for $n_s<1$, quintessence and $\Lambda$CDM give similar results, except for high values of early quintessence, in which case $\Lambda$CDM is favoured.Comment: 3 pages. Talk presented by N. M. C. Santos at the Tenth Marcel Grossmann Meeting on General Relativity, Rio de Janeiro, July 200