No Arabic abstract
We present a systematic study of modified gravity (MG) models containing a single scalar field non-minimally coupled to the metric. Despite a large parameter space, exploiting the effective field theory of dark energy (EFT of DE) formulation and imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions about the large scale structures.
In this paper we revisit the dynamical dark energy model building based on single scalar field involving higher derivative terms. By imposing a degenerate condition on the higher derivatives in curved spacetime, one can select the models which are free from the ghost mode and the equation of state is able to cross the cosmological constant boundary smoothly, dynamically violate the null energy condition. Generally the Lagrangian of this type of dark energy models depends on the second derivatives linearly. It behaves like an imperfect fluid, thus its cosmological perturbation theory needs to be generalized. We also study such a model with explicit form of degenerate Lagrangian and show that its equation of state may cross -1 without any instability.
We focus on three scalar-field dark energy models (i.e., $phi$CDM models), which behave like cosmological trackers with potentials $V(phi)propto phi^{-alpha}$ (inverse power-law (IPL) model), $V(phi)propto coth^{alpha}{phi}$ (L-model) and $V(phi)propto cosh(alphaphi)$ (Oscillatory tracker model). The three $phi$CDM models, which reduce to the $Lambda$CDM model with the parameter $alpha to 0$, are investigated and compared with the recent observations of type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO) and cosmic microwave background radiation (CMB). The observational constraints from the combining sample (SNe Ia + BAO + CMB) indicate that none of the three $phi$CDM models exclude the $Lambda$CDM model at $68.3%$ confidence level, and a closed universe is strongly supported in the scenarios of the three $phi$CDM models (at 68.3% confidence level). Furthermore, we apply the Bayesian evidence to compare the $phi$CDM models and the $Lambda$CDM model with the analysis of the combining sample. The concordance $Lambda$CDM model is still the most supported one. In addition, among the three $phi$CDM models, the IPL model is the most competitive one, while the L-model/Oscillatory tacker model is moderately/strongly disfavored.
We present a systematic exploration of dark energy and modified gravity models containing a single scalar field non-minimally coupled to the metric. Even though the parameter space is large, by exploiting an effective field theory (EFT) formulation and by imposing simple physical constraints such as stability conditions and (sub-)luminal propagation of perturbations, we arrive at a number of generic predictions. (1) The linear growth rate of matter density fluctuations is generally suppressed compared to $Lambda$CDM at intermediate redshifts ($0.5 lesssim z lesssim 1$), despite the introduction of an attractive long-range scalar force. This is due to the fact that, in self-accelerating models, the background gravitational coupling weakens at intermediate redshifts, over-compensating the effect of the attractive scalar force. (2) At higher redshifts, the opposite happens; we identify a period of super-growth when the linear growth rate is larger than that predicted by $Lambda$CDM. (3) The gravitational slip parameter $eta$ - the ratio of the space part of the metric perturbation to the time part - is bounded from above. For Brans-Dicke-type theories $eta$ is at most unity. For more general theories, $eta$ can exceed unity at intermediate redshifts, but not more than about $1.5$ if, at the same time, the linear growth rate is to be compatible with current observational constraints. We caution against phenomenological parametrization of data that do not correspond to predictions from viable physical theories. We advocate the EFT approach as a way to constrain new physics from future large-scale-structure data.
We constrain the parameters of dynamical dark energy in the form of a classical or tachyonic scalar field with barotropic equation of state jointly with other cosmological ones using the combined datasets which include the CMB power spectra from WMAP7, the baryon acoustic oscillations in the space distribution of galaxies from SDSS DR7, the power spectrum of luminous red galaxies from SDSS DR7 and the light curves of SN Ia from 2 different compilations: Union2 (SALT2 light curve fitting) and SDSS (SALT2 and MLCS2k2 light curve fittings). It has been found that the initial value of dark energy equation of state parameter is constrained very weakly by most of the data while the rest of main cosmological parameters are well constrained: their likelihoods and posteriors are similar, have the forms close to Gaussian (or half-Gaussian) and their confidential ranges are narrow. The most reliable determinations of the best fitting value and $1sigma$ confidence range for the initial value of dark energy equation of state parameter were obtained from the combined datasets including SN Ia data from the full SDSS compilation with MLCS2k2 fitting of light curves. In all such cases the best fitting value of this parameter is lower than the value of corresponding parameter for current epoch. Such dark energy loses its repulsive properties and in future the expansion of the Universe will change into contraction. We also perform an error forecast for the Planck mock data and show that they narrow essentially the confidential ranges of cosmological parameters values, moreover, their combination with SN SDSS compilation with MLCS2k2 light curve fitting may exclude the fields with initial equation of state parameter $>-0.1$ at 2$sigma$ confidential level.
In the present paper, we investigate three scalar fields, qu field, phantom field and tachyon field, to explore the source of dark energy, using the Gaussian processes method from the background data and perturbation growth rate data. The corresponding reconstructions all suggest that the dark energy should be dynamical. Moreover, the quintom field, a combination between qu field and phantom field, is powerfully favored by the data within 68% confidence level. Using the mean values of scalar field $phi$ and potential $V$, we fit the function $V(phi)$ in different fields. The fitted results imply that potential $V(phi)$ in each scalar field may be a double exponential function or Gaussian function. The Gaussian processes reconstructions also indicate that the tachyon scalar field cannot be convincingly favored by the data and is at a disadvantage to describe the dark energy.