In the DGP model [53], the Friedmann equation is modified as, where rc=[H0(1−Ωm−Ωr)]−1 is the crossover scale. Features of holographic dark energy under the combined cosmological constraints, [77]. 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. The GCG model actually can be viewed as an interacting model of vacuum energy with cold dark matter. where N is the number of data points used in the fit. For the αDE model, we have ΔAIC=1.199 and ΔBIC=5.816. To relieve the tension, one might need to consider the extra relativistic degrees of freedom, i.e., the additional parameter Neff. Phys. Here we ignore the exiguous difference between DE and MG models because we only consider the aspect of acceleration of the background universe, i.e., the expansion history. The HDE, NGCG, and CPL models can still fit the current observations well, but from the perspective of providing an economically feasible way, they are not so good. Such a light scalar field is usually called “quintessence” [15, 16, 17, 18], which provides a possible mechanism for dynamical dark energy. B, Q. G. Huang and Y. G. Gong, (2017) The HDE model [33] is defined by choosing the event horizon size of the universe as the IR cutoff in the holographic setting. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. 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 model has recently been investigated in detail in Ref. Phys. D. Huterer and M. S. Turner, Planck 2015 results. For example, the simplest parametrization model corresponds to the case of w=constant, and this cosmological model is sometimes called the wCDM model. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Phys. D, Y. H. Li, J. F. Zhang and X. Zhang, The likelihood contours for the DGP model in the Ωm–h is shown in Fig. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. For the NADE model, we have ΔAIC=ΔBIC=50.854. B. W. Hu and N. Sugiyama, Small scale cosmological perturbations: an analytic approach, Astrophys. D, Y. H. Li, J. F. Zhang and X. Zhang, New initial condition of the new agegraphic dark energy model, Chin. Mon. We constrain these models with the same observational data, and then we make a comparison for them. Thus, the energy density of GCG can be derived, where As≡A/ρ1+βgcg0. 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 further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. In Sect. It should be noted that, for Gaussian errors, χ2min=−2lnLmax. These results show that, according to the capability of fitting the current observational data, the ΛCDM model is still the best one among all the dark energy models. II we introduce the method of information criteria and how it works in comparing competing models. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. 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. 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. Also, its theoretical variant, the αDE model [54], can fit the observational data much better. Therefore, it will be very hard to produce it in accelerators. where γ is a positive constant. Phys. (2018) We divide these models into five classes: An alternative to quintessence, The results of the observational constraints explicitly show that the RDE model has been excluded by the current observations. Parametrized Post-Friedmann Framework for Interacting Dark Energy, Synthetically, the consideration of light sterile neutrinos is likely to be a key to a new concordance model of cosmology [73, 74]. J. D. J. Eisenstein and W. Hu, Baryonic features in the matter transfer function, Astrophys. where n is a constant playing the same role as c in the HDE model. 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 HDE model, we have ΔAIC=6.647 and ΔBIC=11.264. Commun. ... Cosmology: theory, Dark energy… Phenomenological parameterization of quintessence, In this model, we have, According to the observations, the best-fit parameters and the corresponding χ2min are. Thus, in this sense, the UV problem of the calculation of vacuum energy density is converted to an IR problem. Facing so many competing dark energy models, the most important mission is to find which one on earth is the right dark energy model. A. Sen, Generalized chaplygin gas, accelerated expansion and dark energy matter unification, Phys. Rev. Soc. Lett. 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 NGCG will reduce to GCG when w=−1, reduce to wCDM when η=1, and reduce to ΛCDM when w=−1 and η=1. Note that the various observations used in this paper are consistent with each other. Dynamical dark energy: Current constraints and forecasts, The simplest candidate for dark energy is the Einstein’s cosmological constant, Λ, which is physically equivalent to the quantum vacuum energy. 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. 6. Copyright information regarding this work can be found at the following address. We find that the constraint result of the CPL model is consistent with the ΛCDM model, i.e., the point of ΛCDM (w0=−1 and wa=0) still lies in the 1σ region (on the edge of 1σ). Journal Article, Planck intermediate results. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. In this work, we apply the IC method to do the analysis. Sign up to our mailing list for occasional updates. For this model, the form of w(z) is written as, where w0 and wa are free parameters. 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. B. G. Dvali and M. S. Turner, Dark energy as a modification of the Friedmann equation, [astro-ph/0301510]. XIV. Lett. In this model, we have. 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 use the JLA compilation of type Ia supernovae [62]. Space Sci. Phys. This is the simplest case for a dynamical dark energy. Lett. 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. A model with a lower AIC value is more favored by data. Lett. We take the ΛCDM model as a reference. 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. J. Mod. JCAP, S. Wang, J. J. Geng, Y. L. Hu and X. Zhang, Rev. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. [75, 76]), but we do not discuss this aspect in this paper. [81, 82, 83]). Lett. Considering both AIC and BIC could provide us with more reasonable perspective to the model comparison. 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. 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. But this is not the issue of this paper. In this section, we describe the cosmological observations used in this paper. The inverse covariance matrix for them, Cov−1CMB, can be found in Ref. The GCG, wCDM, and αDE models are still relatively good models in the sense of explaining observations. ; Rachen, J.P.; Zonca, A.; et al. B, J. B, X. Zhang and F. -Q. Wu, By using the observational data described in the above section, we can obtain the best-fit values of parameters and the corresponding χ2min. where ξobs is the experimentally measured value, ξth is the theoretically predicted value, and σξ is the standard deviation. A, E. V. Linder, Eur. Lett. The wCDM, GCG, HDE, RDE, and αDE models have one more parameter than ΛCDM. The model comparison needs to choose a well justified single model, so in our work, the same as Refs. For the GCG model, we have ΔAIC=1.006 and ΔBIC=5.623. Lett. Output Abstract. We show the likelihood contours for the NGCG model in the w–η and Ωde–h planes in Fig. The likelihood contours for the NADE model in the n–h plane is shown in Fig. Probing the dynamics of dark energy with novel parametrizations, 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. Planck Constraints on Holographic Dark Energy, Phys. Lett. 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. Theor. 110004, China, Department of Physics, College of Sciences, Not. [35] Planck 2015 results. 10. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. Mech. Dark Energy and Fate of the Universe, Constraints on the dark energy from holography, Department of Physics, College of Sciences, Northeastern University, Shenyang 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. Journal Article, Planck intermediate results. The cosmological evolution in this model is determined by the following differential equation: where the x=lna. Rev. The same as AIC, the relative value between different models can be written as ΔBIC=Δχ2min+ΔklnN. Rev. WMAP constraints on low redshift evolution of dark energy, 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. Phys. (2016). 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. 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,” (2017) Ade, P., Aghanim, N., Arnaud, M., Ashdown, M., Aumont, J., Baccigalupi, C., …Zonca, A. We thus regard the DGP model as a “dark energy model”. Solving this equation, we obtain. D. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. 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]. Phys. For the DGP model, we have ΔAIC=ΔBIC=86.951. Phys. 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. The various observations described in this paper are consistent. The new agegraphic dark energy model, the Dvali-Gabadadze-Porrati model, and the Ricci dark energy model are excluded by the current observations. B, Y. B, H. Li and X. Zhang, G. A. G. Cohen, D. B. Kaplan and A. E. Nelson, Effective field theory, black holes, and the cosmological constant, Phys. The NADE, DGP, and RDE models are excluded by the current observations. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. Thus, E(z) is given by. 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. Dark energy and modified gravity . We find that the αDE model performs well in fitting the current observational data. To probe the evolution of w phenomenologically, the most widely used parametrization model is the CPL model [19, 20], sometimes called w0waCDM model. Phys. Using the fitting results, we make a comparison for these dark energy models and select the good ones among the models. The only free parameter in NADE is the parameter n, and Ωm is actually a derived parameter in this model. (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. Since a non-vanishing anisotropic. The cosmological constant Λ has nowadays become the most promising candidate for dark energy responsible for the current acceleration of the universe, because it can explain the various observations quite well, although it has been suffering the severe theoretical puzzles. A. Starobinsky, The case for a positive cosmological lambda term, Int. Phys. Phys. A global fit study on the new agegraphic dark energy model, Rev. Thus, if we omit the issue of growth of structure, we may also consider such effective dark energy models. Astron. B, C. Dvorkin, M. Wyman, D. H. Rudd and W. Hu, Probing the dynamics of dark energy with divergence-free parametrizations: A global fit study, It should be noted that f(z)≡ρde(z)ρde(0), which is given by the specific dark energy models. The U.S. Department of Energy's Office of Scientific and Technical Information Constraints on interacting dark energy models from Planck 2015 and redshift-space distortion data (Journal Article) | OSTI.GOV Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, To visually display the model-comparison result, we also show the results of ΔAIC and ΔBIC of these model in Fig. Read this paper on D, J. Q. Xia, B. Feng and X. M. Zhang, B, H. Wei and R. G. Cai, Cosmological constraints on new agegraphic dark energy, Phys. 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. In conclusion, according to the capability of explaining the current observations, the ΛCDM model is still the best one among all the dark energy models. Astrophys. 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. XIV. arXiv:1607.05643 [astro-ph.CO]. Supernova constraints on a holographic dark energy model, Theor. Lastly, we test a range of specific models, such as k-essence, f(R) theories, and coupled DE. Cosmological tracking solutions, Rev. In Sect. Compared to ΛCDM, the DGP model yields a much larger χ2min, indicating that the DGP model cannot fit the actual observations well. China Phys. 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. Quintessence, cosmic coincidence, and the cosmological constant, Dark energy and modified gravity . Some dynamical dark energy models are built based on deep theoretical considerations. The root of this difficulty comes from the fact that a full theory of quantum gravity is absent. We start with cases Rev. 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. J.} 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 Not. 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. For this model, from the joint observational data analysis, we get the best-fit parameters and the corresponding χ2min: We plot the likelihood contours for the HDE model in the Ωm–c and Ωm–h planes in Fig. B, M. C. Bento, O. Bertolami and A. The AIC punishes the CPL model on the number of parameters, leading to ΔAIC=3.199, and furthermore the BIC punishes it on the number of data points, leading to ΔBIC=12.401. [20]. Thus, the NGCG model was proposed [52], in which the dark energy with constant w interacts with cold dark matter through the interaction term Q=−3βwHρdeρcρde+ρc. J. Sci. Northeastern University, Shenyang 110004, China, Center for High Energy Physics, Peking University, Beijing 100080, China, V. Sahni and A. Lett. [71] by using the revised geometric maser distance to NGC 4258. Sterile neutrinos help reconcile the observational results of primordial gravitational waves from Planck and BICEP2, Lett. From the Planck data the scientists were able to determine just how much dark energy existed in the past. (d) Holographic dark energy models. Phys. Rev. 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. Abstract. Phys. In Sect. Accessibility, Administrator e-mail: III we describe the current observational data used in this paper. Planck Collaboration: Planck 2015 results. 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. There also exist many other possible theoretical candidates for dark energy. 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 … where Lmax is the maximum likelihood and k is the number of parameters. 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. Thus, once the data point number is large, the result would be in favor of the model with more parameters. 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. -Z. Ma, X. Zhang and Z. Zhang, The study of the nature of dark energy has become one of the most important issues in the field of fundamental physics [6, 7, 8, 9, 10, 11, 12, 13, 14]. arXiv Vanity renders academic papers from arXiv as responsive web pages so you don’t have to squint at a PDF. Publication year: 2016 Dark energy and modified gravity. Astron. (b) Dark energy models with equation of state parameterized. 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. Phys. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. B, M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. 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, J. Mod. Dark energy is a diffuse, very weakly interacting with matter and very low energy phenomenon. D. M. Kamionkowski, Dark matter and dark energy, arXiv: 0706.2986 [astro-ph]. I. Zlatev, L. M. Wang and P. J. Steinhardt, The results of observational constraints for these models are given in Table 1 and the results of the model comparison using the information criteria are summarized in Table 2. Phys. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Testing models of vacuum energy interacting with cold dark matter, 5, where the parameter η is defined as η=1+β in [52]. 7. Rev. 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. Phys. The cosmological model with Λ and cold dark matter (CDM) is usually called the ΛCDM model, which can explain the current various astronomical observations quite well. Burden and M. Manera, The clustering of the SDSS DR7 main Galaxy sample C I. Dark energy and modified gravity | 32 pages, 22 figures. Planck satellite measurements are able to constrain the dark energy equation of state significantly. Lett. The models have different numbers of parameters. 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. Astron. including inflationary models (Planck Collaboration XX 2016) and constraints on primordial non-Gaussianities (Planck Collab-oration XVII 2016). 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. The energy density of the NGCG can be expressed as, where A and B are positive constant. A, X. Zhang, He, J. F. Zhang and X. Zhang, PDF, Copyright Statement Commun. 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. Dark Energy and the Accelerating Universe, Rev. (a) Cosmological constant model. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. But this measurement is in tension with the Planck data. Rept. Lett. (49). Holography, UV/IR Relation, Causal Entropy Bound and Dark Energy, Phys. Through the joint data analysis, we get the best-fit parameters and the corresponding χ2min: We show the likelihood contours for the GCG model in the As–β and As–h planes in Fig. functions of time and scale. Phys. 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. Dark energy and modified gravity. Z. Ma, Y. Gong and X. Chen, The constraint results show that, facing the precision cosmological observations, the NADE model cannot fit the current data well. The IC method has sufficiently taken the factor of number of parameters into account. Rev. Holographic Ricci dark energy: Current observational constraints, quintom feature, and the reconstruction of scalar-field dark energy, Abstract. G. Schwarz, Estimating the dimension of a model. M. Szydlowski, A. Kurek and A. Krawiec, Top ten accelerating cosmological models, Phys. Astron. 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. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. A. Upadhye, M. Ishak and P. J. Steinhardt, Once Eq. [59, 60, 61], we use the ΛCDM model to play this role. X. Zhang, 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. In Eq. 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. In Table 2 and Fig. D, C. Wetterich, 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. The CPL and NGCG models have two more parameters than ΛCDM. But, hitherto, we still know little about the physical nature of dark energy. Lett. When estimating the density of DE at early times, we significantly improve present constraints and find that it has to be below ~2% (at 95% confidence) of the critical density, even when forced to play a role for z < 50 only. (22), we have, Here in our work the radiation density parameter Ωr is given by. 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].