The cosmological evolution in this model is determined by the following differential equation: where the x=lna. Thus, E(z) is given by. Rev. The paper is organized as follows. Testing models of vacuum energy interacting with cold dark matter, The results of the model comparison using the information criteria are summarized in Table 2. Abstract. Phys. J.} Phys. Phys. The GCG, wCDM, and αDE models are worse than ΛCDM, but still are good models compared to others. Lett. Rev. WMAP constraints on low redshift evolution of dark energy, In this model, the energy density of RDE can be expressed as. Assistant Professor. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. (2016). 6. B, M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. Probing the dark energy: Methods and strategies, the 2015 data release from Planck 1 (Planck Collaboration I 2015 ) to perform a systematic analysis of a large set of dark energy and modiﬁed gravity theories. 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. We will find that, compared to the early study [59], in the post-Planck era we are now truly capable of discriminating different dark energy models. By Ade P., Aghanim N., Arnaud M., Ashdown M., ... 2016.We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. He, J. F. Zhang and X. Zhang, where ξobs is the experimentally measured value, ξth is the theoretically predicted value, and σξ is the standard deviation. 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. -Z. Ma, X. Zhang and Z. Zhang, From the joint observational constraints, we get the best-fit parameters and the corresponding χ2min: Based on the best-fit value of n, we can derive Ωm=0.336. J. C. R. G. Cai, B. Hu and Y. Zhang, Since the models have different numbers of parameters, in order to make a fair comparison, we employ the Akaike and Bayesian information criteria to assess the worth of the models. M. Li, X. D. Li, S. Wang and Y. Wang, For the HDE model, we have ΔAIC=6.647 and ΔBIC=11.264. Dark Energy and Fate of the Universe, The NADE and DGP models have the same number of parameters as ΛCDM. We use the JLA compilation of type Ia supernovae [62]. All results that include only background parameterizations (expansion of the equation of state, early DE, general potentials in minimally-coupled scalar fields or principal component analysis) are in agreement with ΛCDM. Phys. Phenomenological parameterization of quintessence, ; Rachen, J.P.; Zonca, A.; et al. Thus, the values of ΔAIC and ΔBIC are measured with respect to the ΛCDM model. For example, a spatially homogeneous, slowly rolling scalar field can also provide a negative pressure, driving the cosmic acceleration. The joint observational constraints give the best-fit parameters and the corresponding χ2min: The 1–2σ likelihood contours for the CPL model in the w0–wa and Ωm–h planes are shown in Fig. (2016) The χ2 function for CMB is. In this section, we briefly describe the dark energy models that we choose to analyze in this paper and discuss the basic characteristics of these models. J. Mod. A more realistic mission is to select which ones are better than others in explaining the various observational data. Phys. 4. The likelihood contours for the αDE model in the Ωm–α and Ωm–h planes are shown in Fig. XIV. JCAP, L. Feng and X. Zhang, The current astronomical observations have indicated that the universe is undergoing an accelerated expansion [1, 2, 3, 4, 5], for which a natural explanation is that the universe is currently dominated by dark energy (DE) that has negative pressure. Holographic dark energy in a Universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration, JHEP10(2015)147 Published for SISSA by Springer Received: July 9, 2015 Revised: October 3, 2015 Accepted: October 5, 2015 Published: October 22, 2015 α-attractors: Planck, LHC and dark energy John Joseph M. Carrasco,a Renata Kalloshb and Andrei Lindeb aInstitut de Physique Th´eorique, CEA/DSM/IPhT, CEA-Saclay, 91191 Gif-sur-Yvette, France The αDE model [54] is a phenomenological extension of the DGP model, in which the Friedmann equation is modified as, where α is a phenomenological parameter and rc=(1−Ωm−Ωr)1/(α−2)H−10. Mech. D, Y. H. Li, J. F. Zhang and X. Zhang, Of course, we will use the uniform data combination of various astronomical observations in the model comparison. A typical example of this type is the Dvali-Gabadadze-Porrati (DGP) model [53], which arises from a class of braneworld theories in which the gravity leaks out into the bulk at large distances, leading to the accelerated expansion of the universe. Rev. The new estimate of dark matter content in the universe is 26.8 percent, up from 24 percent, while dark energy falls to 68.3 percent, down from 71.4 percent. Lett. The χ2 function for JLA SN observation is written as. arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Specifically, we use the JLA SN data, the Planck CMB distance prior data, the BAO data, and the H0 measurement. Commun. PDF, Copyright Statement B, C. Dvorkin, M. Wyman, D. H. Rudd and W. Hu, B, X. Zhang and F. -Q. Wu, 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. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Once Eq. D, Y. H. Li, J. F. Zhang and X. Zhang, New initial condition of the new agegraphic dark energy model, Chin. In a spatially flat FRW universe (Ωk=0), the Friedmann equation can be written as, where Mpl≡1√8πG is the reduced Planck mass, ρm, ρr, and ρde(0) are the present-day densities of dust matter, radiation, and dark energy, respectively. 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. where N is the number of data points used in the fit. From Eq. D. P. Zhang, M. Liguori, R. Bean and S. Dodelson, Probing gravity at cosmological scales by measurements which test the relationship between gravitational lensing and matter overdensity,” So the total χ2 is written as. Neutrinos help reconcile Planck measurements with both the early and local Universe, Such a light scalar field is usually called “quintessence” [15, 16, 17, 18], which provides a possible mechanism for dynamical dark energy. In this paper, we choose ten typical, popular dark energy models to analyze. Phys. Detailed description can be found in Ref. Astron. G. Efstathiou, H0 revisited, Mon. Lett. We can use the BAO measurements to get the ratio of the effective distance measure DV(z) and the comoving sound horizon size rs(zd). Dynamical dark energy: Current constraints and forecasts, Some dynamical dark energy models are built based on deep theoretical considerations. D, Y. H. Li and X. Zhang, The BIC [58], also known as the Schwarz information criterion, is given by. The DGP model has the same number of parameters as ΛCDM. D. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. Rev. 5, where the parameter η is defined as η=1+β in [52]. Planck 2015 results: XIV. J. F. Zhang, Y. H. Li and X. Zhang, Commun. The cosmological model with Λ and CDM is called the ΛCDM model. A, E. V. Linder, In this model, the evolution of Ωde(z) is governed by the following differential equation: The NADE model has the same number of parameters as ΛCDM. A. Sen, Generalized chaplygin gas, accelerated expansion and dark energy matter unification, Phys. T o get from the supergravity model (4.2) to the Planck, LHC, dark energy potential (4.11) requires stabilization of the ﬁeld ϑ at ϑ = 0. The HDE, NGCG, and CPL models are relatively not good from the perspective of fitting the current observational data in an economical way. In this class, we consider two models: the constant w parametrization (wCDM) model and the Chevallier-Polarski-Linder (CPL) parametrization model. 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. [20]. Also, its theoretical variant, the αDE model [54], can fit the observational data much better. The original Chaplygin gas model has been excluded by observations [54], thus here we only consider the generalized Chaplygin gas (GCG) model [51] and the new generalized Chaplygin gas (NGCG) model [52]. The distance priors contain the shift parameter R, the “acoustic scale” ℓA, and the baryon density ωb≡Ωbh2, where Ωm is the present-day fractional energy density of matter, DA(z∗) is the proper angular diameter distance at the redshift of the decoupling epoch of photons z∗. To make a fair comparison for these models, we employ AIC and BIC as model-comparison tools. Work done in 2013 based on the Planck spacecraft observations of the CMB gave a more accurate estimate of 68.3% dark energy, 26.8% dark matter, and 4.9% ordinary matter. B. H. K. Jassal, J. S. Bagla and T. Padmanabhan, Planck 2015 results. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. The JLA compilation is from a joint analysis of type Ia supernova observations in the redshift range of z∈[0.01,1.30]. A 4 per cent distance measure at. Phys. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. For the DGP model, we have ΔAIC=ΔBIC=86.951. 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. A more physical and realistic situation is that w is time variable, which is often probed by the so-called Chevalliear-Polarski-Linder (CPL) parametrization [19, 20], w(a)=w0+wa(1−a). (49) is solved, one can then use Ωm=1−Ωde(0)−Ωr to get the value of Ωm (for detailed discussions, we refer the reader to Refs. Phys. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Eur. V. We use the χ2 statistic to fit the cosmological models to observational data. Person Planck satellite measurements are able to constrain the dark energy equation of state significantly. Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints, Dark energy and modiﬁed gravity. B, J. F. Zhang, Y. H. Li and X. Zhang, R. Bean, S. M. Carroll and M. Trodden, Insights into dark energy: interplay between theory and observation, astro-ph/0510059. Constraints on the dark energy from holography, We present a theoretical study of an early dark energy (EDE) model. For the αDE model, we have ΔAIC=1.199 and ΔBIC=5.816. JCAP, M. Li, X. D. Li, S. Wang, Y. Wang and X. Zhang, P. J. Steinhardt, L. M. Wang and I. Zlatev, To fit the observational data in a better way, its theoretical variants, the generalized Chaplygin gas (GCG) model [51] and the new generalized Chaplygin gas (NGCG) model [52], have also been put forward. More recently, Riess et al. Since NADE and ΛCDM have the same number of parameters, the data-fitting capability can be directly compared through χ2min. Rev. A difference in ΔBIC of 2 is considerable positive evidence against the model with higher BIC, while a ΔBIC of 6 is considered to be strong evidence. XIV. XIV. Not. [63]. Subm. Astronomy and Astrophysics, 594, https://doi.org/10.1051/0004-6361/201525814, ATT00001.pdf Lett. (2016) According to the observational point of view, we can get the distance modulus of a SN Ia from its light curve through the empirical linear relation [62], where m∗B is the observed peak magnitude in the rest frame B band, MB is the absolute magnitude which depends on the host galaxy properties complexly, X1 is the time stretching of the light curve, and C is the supernova color at maximum brightness. The order of these models in Table 2 and Fig. Statefinder diagnostic for coupled quintessence, Within the framework of quantum field theory, the evaluated vacuum energy density will diverge; even though a reasonable ultraviolet (UV) cutoff is taken, the theoretical value of the vacuum energy density will still be larger than its observational value by several tens orders of magnitude. From the Planck data the scientists were able to determine just how much dark energy existed in the past. 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 evolution of the HDE is governed by the following differential equations. This parametrization has some advantages such as high accuracy in reconstructing scalar field equation of state and has simple physical interpretation. ... Cosmology: theory, Dark energy… But this measurement is in tension with the Planck data. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. G. Schwarz, Estimating the dimension of a model. Parametrized Post-Friedmann Framework for Interacting Dark Energy, Request PDF | Planck 2015 results. Dark energy and modified gravity: Author(s): Ade, P.A.R. [72] obtained a very accurate measurement of the Hubble constant (a 2.4% determination), H0=73.00±1.75 km s−1 Mpc−1. Thus we have ¯¯¯¯¯¯¯Rb=31500Ωbh2(Tcmb/2.7K)−4. Journal Article, Repository@Nottingham Powered by Worktribe | Journal Article, Planck intermediate results. The Chaplygin gas model [50], which is commonly viewed as arising from the d-brane theory, can describe the cosmic acceleration, and it provides a unification scheme for vacuum energy and cold dark matter. Automatic Control 19, 716 (1974). Considering massive neutrinos as a hot dark matter component might help to relieve this type of tension. Rev. All For this model, we have. Cosmological tracking solutions, B. Jain and P. Zhang, Observational tests of modified gravity, Phys. The generalized Chaplygin gas model, the constant w model, and the α dark energy model are worse than the cosmological constant model, but still are good models compared to others. A. Upadhye, M. Ishak and P. J. Steinhardt, But, hitherto, we still know little about the physical nature of dark energy. J. D. J. Eisenstein and W. Hu, Baryonic features in the matter transfer function, Astrophys. We use the result of direct measurement of the Hubble constant, given by Efstathiou [70], H0=70.6±3.3 km s−1 Mpc−1, which is derived from a re-analysis of Cepheid data of Riess et al. Complete results from Planck, which still is scanning the skies, will be released in 2014. (11), rs(z) is the comoving sound horizon at z. where ¯¯¯¯¯¯¯Rba=3ρb/(4ργ). Exploring the full parameter space for an interacting dark energy model with recent observations including redshift-space distortions: Application of the parametrized post-Friedmann approach, In practice, we do not care about the absolute value of the criterion, and we actually pay more attention to the relative values between different models, i.e., ΔAIC=Δχ2min+2Δk. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. The inverse covariance matrix for them, Cov−1CMB, can be found in Ref. Among the models discussed in this paper, the ΛCDM model has the lowest AIC and BIC values, which shows that this model is still the most favored cosmological model by current data nowadays. A. Starobinsky, The case for a positive cosmological lambda term, Int. D, A. Y. Kamenshchik, U. Moschella and V. Pasquier, 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 [, , ]. The NADE, DGP, and RDE models are excluded by the current observations. For the NADE model, we have ΔAIC=ΔBIC=50.854. In this work, we mainly consider the smooth dark energy models, and thus the combination of the SN, CMB, BAO, and H0 data is sufficient for our mission. In this work, we focus on the smooth dark energy models, in which dark energy mainly affects the expansion history of the universe. It should be noted that f(z)≡ρde(z)ρde(0), which is given by the specific dark energy models. From the constraint results, we can see that the value of β is close to zero, which implies that the ΛCDM limit of this model is favored. A model with a lower AIC value is more favored by data. Mod. The IC method has sufficiently taken the factor of number of parameters into account. We take the ΛCDM model as a reference. Title: Planck 2015 results. XLVII. Solving this equation, we obtain. Astron. We show the likelihood contours for the NGCG model in the w–η and Ωde–h planes in Fig. The root of this difficulty comes from the fact that a full theory of quantum gravity is absent. Although cosmic microwave background (CMB) anisotropy data alone cannot constrain simultaneously the spatial curvature and the equation of state of dark energy, CMB data provide a valuable addition to other experimental results. 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. Project, ADAM MOSS Adam.Moss@nottingham.ac.uk 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 analysis results show that, according to the capability of explaining observations, the cosmological constant model is still the best one among all the dark energy models. D, X. Zhang, 9. 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