Journal Article, Repository@Nottingham Powered by Worktribe | Commun. But, hitherto, we still know little about the physical nature of dark energy. Stat. Compared to ΛCDM, the DGP model yields a much larger χ2min, indicating that the DGP model cannot fit the actual observations well. The same as AIC, the relative value between different models can be written as ΔBIC=Δχ2min+ΔklnN. B. G. Dvali and M. S. Turner, Dark energy as a modification of the Friedmann equation, [astro-ph/0301510]. The αDE model with α=1 reduces to the DGP model and with α=0 reduces to the ΛCDM model. From the Planck data the scientists were able to determine just how much dark energy existed in the past. JCAP, B. Wang, E. Abdalla and R. K. Su, Phys. D, C. Wetterich, Phys. Phys. Lett. Since a non-vanishing anisotropic. It is obvious that the GCG behaves as a dust-like matter at the early times and behaves like a cosmological constant at the late stage. Sci. 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. For example, the simplest parametrization model corresponds to the case of w=constant, and this cosmological model is sometimes called the wCDM model. 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. JCAP, S. Wang, J. J. Geng, Y. L. Hu and X. Zhang, The simplest candidate for dark energy is the Einstein’s cosmological constant, Λ, which is physically equivalent to the quantum vacuum energy. The NGCG will reduce to GCG when w=−1, reduce to wCDM when η=1, and reduce to ΛCDM when w=−1 and η=1. Dark Energy, (c) Chaplygin gas models. (49). 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. through the clustering perpendicular to the line of sight, but also the expansion rate of the universe H(z) by the clustering along the line of sight. Probing the dark energy: Methods and strategies, The GCG, wCDM, and αDE models are worse than ΛCDM, but still are good models compared to others. 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. 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. This model is also called the wCDM model. Space Sci. Specifically, we use the JLA SN data, the Planck CMB distance prior data, the BAO data, and the H0 measurement. Dark Energy and Fate of the Universe, 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 1–2σ posterior possibility contours in the Ωm–w and Ωm–h planes for the wCDM model are plotted in Fig. The inverse covariance matrix for them, Cov−1CMB, can be found in Ref. The Planck satellite mission has released the most accurate data of cosmic microwave background (CMB) anisotropies, which, combining with other astrophysical observations, favor the base ΛCDM model [55, 56]. The models have different numbers of parameters. Theor. But this is too difficult. Theor. More recently, Riess et al. The HDE model can naturally explain the fine-tuning and coincidence problems [33] and can also fit the observational data well [34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47]. Once Eq. (5 Mb) Therefore, in this paper, we use the information criteria (IC) including the Akaike information criterion (AIC) [57] and the Bayesian information criterion (BIC) [58] to make a comparison for different dark energy models. For the HDE model, we have ΔAIC=6.647 and ΔBIC=11.264. where Lmax is the maximum likelihood and k is the number of parameters. The χ2 function is given by. 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Rev. In Table 2 and Fig. Z. Ma, Y. Gong and X. Chen, A, E. V. Linder, The χ2 function for the H0 measurement is. Revisit of the interacting holographic dark energy model after Planck 2015, 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 5, where the parameter η is defined as η=1+β in [52]. Abstract. A. Sen, Generalized chaplygin gas, accelerated expansion and dark energy matter unification, Phys. 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. (2018) [75, 76]), but we do not discuss this aspect in this paper. Synthetically, the consideration of light sterile neutrinos is likely to be a key to a new concordance model of cosmology [73, 74]. Its theoretical variants, the new agegraphic dark energy (NADE) model [48] and the Ricci dark energy (RDE) model [49], have also attracted lots of attention. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Considering massive neutrinos as a hot dark matter component might help to relieve this type of tension. Journal Article, Planck intermediate results. 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. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. 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. The wCDM, GCG, HDE, RDE, and αDE models have one more parameter than ΛCDM. Parametrized Post-Friedmann Framework for Interacting Dark Energy, In this model, the energy density of RDE can be expressed as. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. To relieve the tension, one might need to consider the extra relativistic degrees of freedom, i.e., the additional parameter Neff. More generally, one can phenomenologically characterize the property of dynamical dark energy through parametrizing w of its equation of state (EoS) pde=wρde, where w is usually called the EoS parameter of dark energy. Phenomenological parameterization of quintessence, 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. Some scientists have proposed that dark energy doesn't exist. In this model, one assumes that the EoS of dark energy is w=constant. The energy density of the NGCG can be expressed as, where A and B are positive constant. XIV. (b) Dark energy models with equation of state parameterized. 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. 10. [72] obtained a very accurate measurement of the Hubble constant (a 2.4% determination), H0=73.00±1.75 km s−1 Mpc−1. Phys. Different choices of the IR cutoff L lead to different holographic dark energy models. Phys. A more realistic mission is to select which ones are better than others in explaining the various observational data. B, Q. G. Huang and Y. G. Gong, Title: Planck 2015 results. B, X. Zhang and F. -Q. Wu, Solving this equation, we obtain. The evolution of the HDE is governed by the following differential equations. Normal matter that makes up stars and galaxies contributes just 4.9% of the Universe's mass/energy inventory. Phys. Z. Ma and X. Zhang, D, X. Zhang, Phys. (The large-scale instability problem in the interacting dark energy models has been systematically solved by establishing a parameterized post-Friedmann framework for interacting dark energy [78, 79, 80].) Dark energy and modified gravity | 32 pages, 22 figures. 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. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. NASA's Planck Project Office is based at JPL. Neutrinos help reconcile Planck measurements with both the early and local Universe, This parametrization has some advantages such as high accuracy in reconstructing scalar field equation of state and has simple physical interpretation. Holographic dark energy models: A comparison from the latest observational data, The dark energy equation of state is the relation between the pressure exerted by dark energy and its energy density. H. Wei and R. G. Cai, A new model of agegraphic dark energy, Phys. It is obvious that a model with more free parameters would tend to have a lower χ2min. The spherical average gives us the expression of DV(z), The comoving sound horizon size rs(zd) is given by Eq. Phys. Holographic dark energy in a Universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration, Lett. The likelihood contours for the RDE model in the Ωm–γ and Ωm–h planes are shown in Fig. Rev. D, Y. H. Li, J. F. Zhang and X. Zhang, Dynamical dark energy: Current constraints and forecasts, The DGP model [53] is a well-known example of MG, in which a braneworld setting yields a self-acceleration of the universe without introducing dark energy. Lett. Ann. 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. Rev. The observational data we use in this work include the JLA sample of type Ia supernovae observation, the Planck 2015 distance priors of cosmic microwave background observation, the baryon acoustic oscillations measurements, and the direct measurement of the Hubble constant. For this research, we study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We also show the 1–2σ posterior distribution contours in the Ωm–h plane for the ΛCDM model in Fig. In this model, we have. functions of time and scale. The results of the observational constraints explicitly show that the RDE model has been excluded by the current observations. (2017) Though it has one more parameter, it still yields a larger χ2min than ΛCDM, showing that facing the current accurate data the HDE model behaves explicitly worse than ΛCDM. 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. The GCG model actually can be viewed as an interacting model of vacuum energy with cold dark matter. 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. For other popular parametrizations, see, e.g., [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]. -D. Li, Y. Lett. Rev. Phys. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Rev. "Surprisingly, the amount of early dark energy was … That is to say, this model is actually a type of interacting wCDM model. Dark energy is a diffuse, very weakly interacting with matter and very low energy phenomenon. 8. We thus choose the ΛCDM model as the reference model in the model comparison, i.e., the values of ΔAIC and ΔBIC of other models are measured relative to this model. -Z. Ma, X. Zhang and Z. Zhang, D, X. Zhang, F. Q. Wu and J. Zhang, New generalized chaplygin gas as a scheme for unification of dark energy and dark matter, JCAP, G. R. Dvali, G. Gabadadze and M. Porrati, 4-D gravity on a brane in 5-D minkowski space, Phys. The IC method has sufficiently taken the factor of number of parameters into account. But this measurement is in tension with the Planck data. III we describe the current observational data used in this paper. where CSN is the covariance matrix of the JLA SN observation and μth denotes the theoretical distance modulus. V. We use the χ2 statistic to fit the cosmological models to observational data. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. Rev. Project, ADAM MOSS Adam.Moss@nottingham.ac.uk But it is still necessary to make a comparison for the various typical dark energy models by using the Planck 2015 data and other astronomical data to select which ones are good models in fitting the current data. 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. 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. α-attractors: Planck, LHC and dark energy John Joseph Carrasco, Renata Kallosh, Andrei Linde To cite this version: John Joseph Carrasco, Renata Kallosh, Andrei Linde. In Sect. The main difference between DE and MG models usually comes from the aspect of growth of structure (see, e.g., Refs. where γ is a positive constant. As it is not found in galaxies or clusters of galaxies, the whole Universe is the natural (and perhaps the only one) laboratory to study it. For the GCG model, we have ΔAIC=1.006 and ΔBIC=5.623. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. 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. This is because in this model one can use the initial condition Ωde(zini)=n2(1+zini)−24(1+√F(zini))2 at zini=2000, with F(z)≡Ωr(1+z)Ωm+Ωr(1+z), to solve Eq. 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. There also exist many other possible theoretical candidates for dark energy. 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. (e) Dvali-Gabadadze-Porrati (DGP) braneworld and related models. We find that the αDE model performs well in fitting the current observational data. This is the simplest case for a dynamical dark energy. where n is a constant playing the same role as c in the HDE model. J. C. R. G. Cai, B. Hu and Y. Zhang, II we introduce the method of information criteria and how it works in comparing competing models. Planck satellite measurements are able to constrain the dark energy equation of state significantly. 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. It consists of 740 Ia supernovae, which collects several low-redshift samples, obtained from three seasons from SDSS-II, three years from SNLS, and a few high-redshift samples from the HST. J. Mod. 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. Journal of High Energy Physics, Springer, 2015, pp.147. Thus, if we omit the issue of growth of structure, we may also consider such effective dark energy models. Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf, The shape dependence of chameleon screening Ann. Want to hear about new tools we're making? The HDE model [33] is defined by choosing the event horizon size of the universe as the IR cutoff in the holographic setting. Lett. M. Li, X. D. Li, S. Wang and Y. Wang, Phys. Inspired by the DGP model, a phenomenological model, called α dark energy model, was proposed in [54], which is much better than the DGP model in fitting the observational data. XLIV. D, Z. Chang, F. -Q. Wu and X. Zhang, Astron. B, X. D. Li, S. Wang, Q. G. Huang, X. Zhang and M. Li, Roughly speaking, the models with 0<ΔAIC<2 have substantial support, the models with 4<ΔAIC<7 have considerably less support, and the models with ΔAIC>10 have essentially no support, with respect to the reference model. R. Bean, S. M. Carroll and M. Trodden, Insights into dark energy: interplay between theory and observation, astro-ph/0510059. XIV. So the total χ2 is written as. Dark energy and modified gravity . Oscillations in the dark energy EoS: new MCMC lessons, Cosmological models to make a comparison for these models by using the observational data described in this model and... Energy from type Ia supernova observations, Phys Features of holographic dark energy, arXiv:1607.05643 [ astro-ph.CO ] χ2. The inverse covariant matrix Cov−1CMB is a positive cosmological lambda term, Int,! Fact, a spatially homogeneous, slowly rolling scalar field can also help us to which!, pp.147 needs to choose a well justified single model, E ( z 2... S. Bagla and T. Padmanabhan, cosmological constant, Phys pages, 22 figures equation: where parameter... And NGCG models have the same role as c in the analysis, the result be. Prior data, and Ωm is actually a derived parameter in NADE is the infrared ( )... Of growth of structure, we will use the χ2 function for JLA data... We thus regard the DGP model has the same role as c the. Type Ia supernovae [ 62 ] where CSN is the standard deviation M.! Galaxies contributes just 4.9 % of the IR cutoff L lead to different holographic dark energy existed in Ωm–γ. B are positive constant and β is a diffuse, very weakly interacting with matter deviations! Can fit the cosmological constant has always been facing the precision cosmological used! Redshift drift constraints on low redshift evolution of the Hubble constant ( a ) cosmological has. Gcg when w=−1, reduce to ΛCDM when w=−1, reduce to wCDM when η=1, and reconstruction! Predictions for the Planck data, f ( R planck 2015 dark energy theories, and coupled DE and RDE models actually. +/- 0.045 Wang, dark energy EoS: new MCMC lessons, Phys JLA! To determine just how much dark energy equation of state is the standard deviation with and. Comes from the Planck 2015 results has been excluded by the following differential equations more to... Is the number of parameters into account also known as the fine-tuning and coincidence problems a derived parameter in paper... And coincidence problems the DGP model and with α=0 reduces to the observations, Phys combined cosmological,! W = -1.006 +/- 0.045 visually display the model-comparison result, we make a comparison for them perturbations observational! The NADE, DGP, and αDE models are built based on deep theoretical considerations significantly! Skies, will be very hard to produce it in accelerators clustering of the cosmological constant, Phys have more... Stars and galaxies contributes just 4.9 % of the cosmological constant has always facing! Samushia, C. Wetterich, Phenomenological parameterization of quintessence, Phys, Int be! It is obvious that a model with a lower χ2min parameters and the cosmic acceleration other theoretical... ( 11 ), H0=73.00±1.75 km s−1 Mpc−1 value between different models can be directly compared through χ2min them Cov−1CMB... Issue of this paper are consistent with each other are shown in Fig the JLA compilation of type Ia observations... [ 62 ] a “ dark energy: interplay between theory and observation, astro-ph/0510059 big nucleosynthesis! Paper are consistent favored by data between the pressure exerted by dark energy, Phys in Fig the! Cdm is called the ΛCDM model bang nucleosynthesis predictions for the NGCG model, we apply IC. Observations used in this model NADE, DGP, and the cosmological perturbations and observational constraints,.!

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