Dynamical dark energy: Current constraints and forecasts, (b) Dark energy models with equation of state parameterized. Rev. Theor. D. E. V. Linder, Exploring the expansion history of the universe, Phys. D. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. Copyright information regarding this work can be found at the following address. The root of this difficulty comes from the fact that a full theory of quantum gravity is absent. Rept. Phys. Phys. Using the fitting results, we make a comparison for these dark energy models and select the good ones among the models. (5 Mb) Phys. Mod. J. For the HDE model, we have ΔAIC=6.647 and ΔBIC=11.264. The αDE model with α=1 reduces to the DGP model and with α=0 reduces to the ΛCDM model. Moreover, actually, the cosmic acceleration can also be explained by the modified gravity (MG) theory, i.e., the theory in which the gravity rule deviates from the Einstein general relativity (GR) on the cosmological scales. We employ the AIC [57] and BIC [58] to do the model comparison, which are rather popular among the information criteria. We cannot make a fair comparison for different dark energy models by directly comparing their values of χ2, because they have different numbers of parameters. There also exist many other possible theoretical candidates for dark energy. V. We use the χ2 statistic to fit the cosmological models to observational data. 5, we see that the constraint results are consistent with GCG and wCDM within 1σ range, and consistent with ΛCDM on the edge of 1σ region. X. Zhang, In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. In addition to the latest Planck data, for our main analyses, we use background constraints from baryonic acoustic oscillations, type-Ia supernovae, and local measurements of the Hubble constant. [84, 85]). P. J. Steinhardt, L. M. Wang and I. Zlatev, [81, 82, 83]). XIV. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. Facing so many competing dark energy models, the most important mission is to find which one on earth is the right dark energy model. ... Cosmology: theory, Dark energy… From the analysis, we will know which model is the best one in fitting the current data and which models are excluded by the current data. (11), where zd is the redshift of the drag epoch, and its fitting formula is given by [65], We use four BAO data points: rs(zd)/DV(0.106)=0.336±0.015 from the 6dF Galaxy Survey [66], DV(0.15)=(664±25Mpc)(rd/rd,fid) from the SDSS-DR7 [67], DV(0.32)=(1264±25Mpc)(rd/rd,fid) and DV(0.57)=(2056±20Mpc)(rd/rd,fid) from the BOSS-DR11 [68]. J. F. Zhang, Y. H. Li and X. Zhang, Dark energy and modified gravity Planck Collaboration; Ade, P. A. R.; Aghanim, N. ... We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. A 4 per cent distance measure at. Phys. Phys. Since the smooth dark energy affects the growth of structure only through the expansion history of the universe, different smooth dark energy models yield almost the same growth history of structure. Since NADE and ΛCDM have the same number of parameters, the data-fitting capability can be directly compared through χ2min. The likelihood contours for the NADE model in the n–h plane is shown in Fig. Phys. Revisit of constraints on holographic dark energy: SNLS3 dataset with the effects of time-varying, J. F. Zhang, M. M. Zhao, Y. H. Li and X. Zhang, It however disappears when including CMB lensing. Dark Energy and the Accelerating Universe, 6. The equation of state of the NGCG fluid [52] is given by, where ~A(a) is a function of the scale factor a and β is a free parameter. Phys. B, J. Phys. The late ISW effect cannot be accurately measured currently, and so the only important information for constraining dark energy in the CMB data actually comes from the angular diameter distance to the last scattering surface, which is important because it provides a unique high-redshift (z≃1100) measurement in the multiple-redshift joint constraint. Phenomenological parameterization of quintessence, The HDE, NGCG, and CPL models are relatively not good from the perspective of fitting the current observational data in an economical way. WMAP constraints on low redshift evolution of dark energy, The JLA compilation is from a joint analysis of type Ia supernova observations in the redshift range of z∈[0.01,1.30]. The dark energy theory could be used to explain the late-time cosmic acceleration, a cosmological constant Λ with equation of state w Λ = − 1 is the simplest candidate of dark energy, which is favored by the cosmic microwave background observations from Planck 2015 [, , ], however it is plagued with the fine-tuning problem and coincidence problem [, , ]. We use the χ2 statistic to do the cosmological fits, but we cannot fairly compare different models by comparing their χ2min values because they have different numbers of parameters. From the Planck data the scientists were able to determine just how much dark energy existed in the past. Lett. Phys. We find that the constraint result of w is consistent with the cosmological constant at about the 1σ level. Not. 3. functions of time and scale. The CPL model has two more parameters than ΛCDM, so that it yields a lower χ2, but the difference Δχ2=−0.832 is rather small. 6, 461 (1978). We use the “Planck distance priors” from the Planck 2015 data [63]. Stat. G. A. G. Cohen, D. B. Kaplan and A. E. Nelson, Effective field theory, black holes, and the cosmological constant, Phys. More recently, Riess et al. Planck satellite measurements are able to constrain the dark energy equation … Journal Article, Planck intermediate results. But the cosmological constant has always been facing the severe theoretical challenges, such as the fine-tuning and coincidence problems. In this section, we describe the cosmological observations used in this paper. The model comparison needs to choose a well justified single model, so in our work, the same as Refs. "Surprisingly, the amount of early dark energy was … (49). The various observations described in this paper are consistent. D, Y. H. Li, J. F. Zhang and X. Zhang, New initial condition of the new agegraphic dark energy model, Chin. J. Considering this fact, a fair model comparison must take the factor of parameter number into account. α-attractors: Planck, LHC and dark energy. For the GCG model, we have ΔAIC=1.006 and ΔBIC=5.623. J. Mod. J. Mod. For this model, the form of w(z) is written as, where w0 and wa are free parameters. It should be noted that, for Gaussian errors, χ2min=−2lnLmax. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state w(a), as well as principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. M. Li, X. D. Li, S. Wang and Y. Wang, Subm. Astronomy and Astrophysics, 594, https://doi.org/10.1051/0004-6361/201525814, ATT00001.pdf 11, the values of ΔAIC and ΔBIC are given by taking ΛCDM as a reference. The AIC only considers the factor of parameter number but does not consider the factor of data point number. Since we do not include the WiggleZ data in the analysis, the inverse covariant matrix Cov−1CMB is a unit matrix in this case. The energy density of HDE is thus given by, where c is a dimensionless parameter which plays an important role in determining properties of the holographic dark energy and Rh is the future event horizon, defined as. In the models considered in this paper, only the HDE, NADE, RDE, and DGP models cannot reduce to ΛCDM, and among these models the HDE model is still the best one. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Roy. In Sect. Phys. All B, Q. G. Huang and Y. G. Gong, (2017) The Planck data also support the idea that the mysterious force known as dark energy is acting against gravity to push our universe apart at ever-increasing speeds. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. Astron. Compared to the previous study [59], the basic conclusion is not changed; the only subtle difference comes from the concrete orders of models in each group of the above three groups. The likelihood contours for the RDE model in the Ωm–γ and Ωm–h planes are shown in Fig. Planck Constraints on Holographic Dark Energy, The GCG, wCDM, and αDE models are still relatively good models in the sense of explaining observations. The cosmological model with Λ and CDM is called the ΛCDM model. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. D, Z. Chang, F. -Q. Wu and X. Zhang, Planck 2015 results. [71] by using the revised geometric maser distance to NGC 4258. Astrophys. A. Starobinsky, The case for a positive cosmological lambda term, Int. We constrain these models with the same observational data, and then we make a comparison for them. In addition, the Chaplygin gas model [50] is motivated by braneworld scenario, which is claimed to be a scheme for unifying dark energy and dark matter. Constraining dynamical dark energy with a divergence-free parametrization in the presence of spatial curvature and massive neutrinos, We use the JLA compilation of type Ia supernovae [62]. We present a theoretical study of an early dark energy (EDE) model. For example, the holographic dark energy (HDE) model has a quantum gravity origin, which is constructed by considering the holographic principle of quantum gravity theory in a quantum effective field theory [32, 33]. We take Tcmb=2.7255 K. z∗ is given by the fitting formula [64], Using the Planck TT+LowP data, the three quantities are obtained: R=1.7488±0.0074, ℓA=301.76±0.14, and Ωbh2=0.02228±0.00023. Thus, in this sense, the UV problem of the calculation of vacuum energy density is converted to an IR problem. [72] obtained a very accurate measurement of the Hubble constant (a 2.4% determination), H0=73.00±1.75 km s−1 Mpc−1. A global fit study on the new agegraphic dark energy model, The DGP model has the same number of parameters as ΛCDM. B.} These models can be viewed as interacting dark energy models with the interaction term Q∝ρdeρcρde+ρc, where ρde and ρc are the energy densities of dark energy and cold dark matter [77]. Rev. D, Y. H. Li and X. Zhang, In this paper, we consider three popular models in this setting: the HDE model [33], the NADE model [48], and the RDE model [49]. Detailed description can be found in Ref. Lett. When testing models that also change perturbations (even when the background is fixed to ΛCDM), some tensions appear in a few scenarios: the maximum one found is ~2σ for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to, at most, 3σ when external data sets are included. D, C. Wetterich, Request PDF | Planck 2015 results. We also show the 1–2σ posterior distribution contours in the Ωm–h plane for the ΛCDM model in Fig. Though with more parameters, the NGCG model only yields a little bit lower χ2min than the above sub-models, which is punished by the information criteria. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Lett. Thus, if we omit the issue of growth of structure, we may also consider such effective dark energy models. Eur. NASA's Planck Project Office is based at JPL. Constraints on holographic dark energy from x-ray gas mass fraction of galaxy clusters, Soc. Dark energy is a diffuse, very weakly interacting with matter and very low energy phenomenon. Mod. 10, we explicitly see that the DGP limit (α=1) is excluded by the current observations at high statistical significance, and the ΛCDM limit (α=0) is well consistent with the current data within the 1σ range. In this model, E(z) is given by the equation. (11), rs(z) is the comoving sound horizon at z. where ¯¯¯¯¯¯¯Rba=3ρb/(4ργ). Z. Ma, Y. Gong and X. Chen, When the gravity is considered, the number of degrees of freedom in a spatial region should be limited due to the fact that too many degrees of freedom would lead to the formation of a black hole [32], which leads to the holographic dark energy model with the density of dark energy given by. The CMB data alone cannot constrain dark energy well, because the main effects constraining dark energy in the CMB anisotropy spectrum come from a angular diameter distance to the decoupling epoch z≃1100 and the late integrated Sachs-Wolfe (ISW) effect. For example, the simplest parametrization model corresponds to the case of w=constant, and this cosmological model is sometimes called the wCDM model. Some dynamical dark energy models are built based on deep theoretical considerations. Z. Ma and X. Zhang, The holographic dark energy model, the new generalized Chaplygin gas model, and the Chevalliear–Polarski–Linder model can still fit the current observations well, but from an economically feasible perspective, they are not so good. 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