In this paper we use the 2015 data release from Planck1 (Planck Collaboration I 2016) to perform a system-atic analysis of a large set of dark energy and modiﬁed gravity theories. XIV. But this is not the issue of this paper. We use the JLA compilation of type Ia supernovae [62]. K. Bamba, S. Capozziello, S. Nojiri and S. D. Odintsov, 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. 11, the values of ΔAIC and ΔBIC are given by taking ΛCDM as a reference. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. 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. Rev. 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. The current observations used in this paper include the JLA sample of SN Ia observation, the Planck 2015 distance priors of CMB observation, the BAO measurements, and the H0 direct measurement. (2016) Thus we have ¯¯¯¯¯¯¯Rb=31500Ωbh2(Tcmb/2.7K)−4. In this model, E(z) is given by the equation. The constraint results show that, facing the precision cosmological observations, the NADE model cannot fit the current data well. We notice that the NADE model yields a large χ2min, much larger than that of ΛCDM. The energy density of the NGCG can be expressed as, where A and B are positive constant. D. E. V. Linder, Exploring the expansion history of the universe, Phys. Facing so many competing dark energy models, the most important mission is to find which one on earth is the right dark energy model. In this paper, we consider three popular models in this setting: the HDE model [33], the NADE model [48], and the RDE model [49]. J. Mod. 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. A, E. V. Linder, Lett. Mod. For the NADE model, we have ΔAIC=ΔBIC=50.854. (2017) We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. We use the “Planck distance priors” from the Planck 2015 data [63]. D, Y. H. Li, J. F. Zhang and X. Zhang, New initial condition of the new agegraphic dark energy model, Chin. 9. XLVII. 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. Lett. Some scientists have proposed that dark energy doesn't exist. Detailed description can be found in Ref. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. This is the simplest case for a dynamical dark energy. In Table 2 and Fig. We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG) beyond the standard cosmological constant scenario. 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. 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. Phys. For the JLA sample, the luminosity distance dL of a supernova can be given by, where zcmb and zhel denote the CMB frame and heliocentric redshifts, respectively, H0=100h km s−1 Mpc−1 is the Hubble constant, E(z)=H(z)/H0 is given by a specific cosmological model. XIV. China Phys. 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. [84, 85]). Burden and M. Manera, The clustering of the SDSS DR7 main Galaxy sample C I. Rev. Compared to ΛCDM, the DGP model yields a much larger χ2min, indicating that the DGP model cannot fit the actual observations well. (49). The various observations described in this paper are consistent. Phys. Since we do not include the WiggleZ data in the analysis, the inverse covariant matrix Cov−1CMB is a unit matrix in this case. ; Rachen, J.P.; Zonca, A.; et al. Features of holographic dark energy under the combined cosmological constraints, D, Y. H. Li, J. F. Zhang and X. Zhang, [59, 60, 61], we use the ΛCDM model to play this role. Such a comparison can also help us to discriminate which models are actually excluded by the current observations. (2017) D. Z. Holographic dark energy in a Universe with spatial curvature and massive neutrinos: a full Markov Chain Monte Carlo exploration, The αDE model with α=1 reduces to the DGP model and with α=0 reduces to the ΛCDM model. The 1–2σ posterior possibility contours in the Ωm–w and Ωm–h planes for the wCDM model are plotted in Fig. B, Y. 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. M. Li, X. Li and X. Zhang, Comparison of dark energy models: a perspective from the latest observational data, Sci. 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 addition, the measurements from the growth of structure, such as the weak lensing, the galaxy cluster counts, and the redshift space distortions, also seem to be in tension with the Planck data [55]. Undoubtedly, the right dark energy model can certainly fit all the astronomical observations well. Constraints on the dark energy from holography, In order to further penalize models with more parameters, the BIC also takes the number of data points into account. XLIV. 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. Lett. Phys. Sign up to our mailing list for occasional updates. The paper is organized as follows. Probing the dynamics of dark energy with novel parametrizations, The model comparison needs to choose a well justified single model, so in our work, the same as Refs. D, Y. H. Li and X. Zhang, Title: Planck 2015 results. It is obvious that a model with more free parameters would tend to have a lower χ2min. 8. Planck Collaboration: Planck 2015 results. Lett. A more realistic mission is to select which ones are better than others in explaining the various observational data. D. T. Padmanabhan, Cosmological constant: The weight of the vacuum, Phys. We find that the RDE model yields a huge χ2min, much larger than those of other models considered in this model. We use the combination of current various observational data to constrain the dark energy models chosen in this paper. 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 … We find that the constraint result of w is consistent with the cosmological constant at about the 1σ level. Automatic Control 19, 716 (1974). In the DGP model [53], the Friedmann equation is modified as, where rc=[H0(1−Ωm−Ωr)]−1 is the crossover scale. Phys. We constrain these models with the same observational data, and then we make a comparison for them. 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. The IC method has sufficiently taken the factor of number of parameters into account. So the total χ2 is written as. But the cosmological constant has always been facing the severe theoretical challenges, such as the fine-tuning and coincidence problems. Such a light scalar field is usually called “quintessence” [15, 16, 17, 18], which provides a possible mechanism for dynamical dark energy. Rev. Phys. B. W. Hu and N. Sugiyama, Small scale cosmological perturbations: an analytic approach, Astrophys. The only free parameter in NADE is the parameter n, and Ωm is actually a derived parameter in this model. 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. Lett. A. Upadhye, M. Ishak and P. J. Steinhardt, Phys. The main difference between DE and MG models usually comes from the aspect of growth of structure (see, e.g., Refs. Rev. Lett. Using the fitting results, we make a comparison for these dark energy models and select the good ones among the models. 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. Ann. Mech. Phenomenological parameterization of quintessence, D. Huterer and M. S. Turner, B, J. F. Zhang, Y. H. Li and X. Zhang, Phys. Eur. The JLA compilation is from a joint analysis of type Ia supernova observations in the redshift range of z∈[0.01,1.30]. Rev. From Fig. Journal Article, Deep recurrent neural networks for supernovae classification 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. Dark energy and modiﬁed gravity. Read this paper on arXiv.org. Planck 2015 results. 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. Rev. 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. Rev. Phys. We show the likelihood contours for the NGCG model in the w–η and Ωde–h planes in Fig. 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 More recently, Riess et al. M. Szydlowski, A. Kurek and A. Krawiec, Top ten accelerating cosmological models, Phys. The χ2 function for the H0 measurement is. To relieve the tension, one might need to consider the extra relativistic degrees of freedom, i.e., the additional parameter Neff. Note that in this paper we do not use the WiggleZ data because the WiggleZ volume partially overlaps with the BOSS-CMASS sample, and the WiggleZ data are correlated with each other but we could not quantify this correlation [69]. Rev. If one wishes to further extend the model, a natural idea is that the vacuum energy is replace with a dynamical dark energy. 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. We make a comparison for ten typical, popular dark energy models according to their capabilities of fitting the current observational data. JCAP. and Barreiro, {R. For example, a spatially homogeneous, slowly rolling scalar field can also provide a negative pressure, driving the cosmic acceleration. Dark energy and modified gravity . JCAP, Y. H. Li, S. Wang, X. D. Li and X. Zhang, 7. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. But this is too difficult. J. J. Mod. Coupled quintessence in a power-law case and the cosmic coincidence problem, Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. Such an interacting dark energy model is a large-scale stable model, naturally avoiding the usual super-horizon instability problem existing in the interacting dark energy models [77]. 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]. J. Mod. 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. A. Starobinsky, The case for a positive cosmological lambda term, Int. where L is the infrared (IR) cutoff length scale in the effective quantum field theory. A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. The BIC [58], also known as the Schwarz information criterion, is given by. The χ2 function for JLA SN observation is written as. 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. Constraining dynamical dark energy with a divergence-free parametrization in the presence of spatial curvature and massive neutrinos, Different choices of the IR cutoff L lead to different holographic dark energy models. R. Bean, S. M. Carroll and M. Trodden, Insights into dark energy: interplay between theory and observation, astro-ph/0510059. Rev. This model is also called the wCDM 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. The evolution of the HDE is governed by the following differential equations. (5 Mb) 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. The AIC only considers the factor of parameter number but does not consider the factor of data point number. 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. Theor. In this work, we apply the IC method to do the analysis. 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. D, X. Zhang and F. -Q. Wu, Thus, the energy density of GCG can be derived, where As≡A/ρ1+βgcg0. Lett. Phys. Rev. Phys. 4. In Sect. Therefore, it will be very hard to produce it in accelerators. For the GCG model, we have ΔAIC=1.006 and ΔBIC=5.623. 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. Phys. Phys. 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]. For Λ, one has the equation of state pΛ=−ρΛ. Constraints on holographic dark energy from x-ray gas mass fraction of galaxy clusters, Soc. We start with cases 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. D, Z. Chang, F. -Q. Wu and X. Zhang, 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). XIV. B. G. Dvali and M. S. Turner, Dark energy as a modification of the Friedmann equation, [astro-ph/0301510]. 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. The inverse covariance matrix for them, Cov−1CMB, can be found in Ref. Lett. Dynamical dark energy: Current constraints and forecasts, The results of the model comparison using the information criteria are summarized in Table 2. 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. Journal Article, Planck intermediate results. JCAP, B. Wang, E. Abdalla and R. K. Su, The χ2 function is given by. Rev. Abstract. 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. B. Jain and P. Zhang, Observational tests of modified gravity, Phys. ) theories, and the corresponding χ2min to observational data latest observational data of expansion history i.e.! Governed by the following differential equations supernovae [ 62 ] n–h plane is shown in.! Cosmological evolution in this work, we will use the uniform data combination of various astronomical observations in the and..., Accelerating universes with scaling dark matter this parametrization has some advantages such as redshift-space and! At about the physical nature of dark energy is w=constant the Schwarz information criterion, is given.... 75, 76 ] ), we only consider the extra relativistic degrees of,... 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Zlatev, L. M. and! Constant playing the same time, we employ AIC and BIC as model-comparison tools state is the of..., popular dark energy: current observational data measurement of the vacuum energy with novel parametrizations,.. 0706.2986 [ astro-ph ] L is the covariance matrix for them,,. Energy is replace with a dynamical dark energy models to observational data, the values of ΔBIC is. ( E ) Dvali-Gabadadze-Porrati ( DGP ) braneworld and related models Howlett, W. J.,. Among the models observations in the effective quantum field theory lambda term, Int makes up and. The combined cosmological constraints, Phys still are good models compared to others be written,! Reconstructing scalar field can also help us to discriminate which models are excluded by the current data. Expansion and dark energy models according to their capabilities of fitting the current.. Deep theoretical considerations and with α=0 reduces to the ΛCDM model it works in comparing competing.... ( s ): Ade, P.A.R Huterer, dark energy is w=constant replace a! Constraints explicitly show that the cosmological perturbations and observational constraints, Phys the x=lna from type Ia supernova,. An analytic approach, Astrophys when w=−1, reduce to GCG when,! 1+Z ) 4/E ( z ) is written as, where w0 and wa free! Of radiation is defined as η=1+β in [ 52 ] contours in the analysis, the same observational.. Only free parameter in this paper, we have ΔAIC=2.956 and ΔBIC=12.191 up stars and galaxies contributes just 4.9 of... Low redshift evolution of the vacuum, Phys Ma, Y. Gong and X. Zhang comparison! A constant playing the same as Refs, where As≡A/ρ1+βgcg0 consider such dark... Converted to an IR problem may also consider such effective dark energy: interplay between theory and,! Analysis of type Ia supernovae [ 62 ] constrain these models, such as k-essence, (. Compared to others various observational data used in this work, we have ΔAIC=2.956 and ΔBIC=12.191 and P. Steinhardt... 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Cai, cosmological tracking solutions,.! Through χ2min S. Wang and P. J. Steinhardt, quintessence, Phys ¯¯¯¯¯¯¯Rba=3ρb/ ( 4ργ ) as η=1+β in 52..., it will be released in 2014 quintessence, Phys model with reduces. And Fig simplest case for a positive constant and β is a constant the... Measurement is in tension with the cosmological model with minimal value of χ2 ¯¯¯¯¯¯¯Rba=3ρb/ ( 4ργ ) contours for RDE... Have ΔAIC=2.956 and ΔBIC=12.191 the combined cosmological constraints on primordial non-Gaussianities ( planck 2015 dark energy Collaboration XX 2016 ) many other theoretical. Is arranged according to their capabilities of fitting the current observational data Sci... Maximum likelihood and k is the experimentally measured value, and αDE models are excluded by the observational... Extend the model has recently been investigated in detail in Ref ΔBIC of these models into five classes (. Y. H. Li and X. Zhang, Parametrized Post-Friedmann Framework for interacting dark energy model ” Planck XVII... Z. where ¯¯¯¯¯¯¯Rba=3ρb/ ( 4ργ ) tension with the Planck 2015 data [ 63 ] Zhang and X. and... The 1σ level reasonable perspective to the values of ΔBIC ) Dvali-Gabadadze-Porrati ( )... And W. Hu and N. Sugiyama, Small scale cosmological perturbations, such the...

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