Parameterized post-Friedmann Approach Research Articles

IDECAMB: an implementation of interacting dark energy cosmology in CAMB

Interacting dark energy (IDE) scenario is a natural and important extension to the standard ΛCDM cosmology. We develop a full numerical routine, called IDECAMB, as a patch to the public Einstein-Boltzmann solver CAMB, to solve the background and perturbation equations of the IDE models. The IDECAMB solver provides a unified interface for the widely studied IDE models by employing a parametrization model with five free functions. By configuring these five functions, one can easily map the coupled quintessence (CQ) and coupled fluid (CF) models into the parametrization. We handle the perturbation evolutions of the CF models with the parametrized post-Friedmann (PPF) approach to avoid the possible large-scale instability. Compared with the previous established PPF approach whose form depends on a specific IDE model, the PPF approach in this work are model-independent, making it easy to use. We constrain a specific CQ model with the IDECAMB package. The fitting results are consistent with those obtained by Planck Collaboration, which confirms the validity of the package.

Fast and accurate predictions of the non-linear matter power spectrum for general models of Dark Energy and Modified Gravity

ABSTRACT We embed linear and non-linear parametrizations of beyond standard cosmological physics in the halo model reaction framework, providing a model-independent prescription for the non-linear matter power spectrum. As an application, we focus on Horndeski theories, using the Effective Field Theory of Dark Energy (EFTofDE) to parametrize linear and quasi-non-linear perturbations. In the non-linear regime, we investigate both a non-linear parametrized post-Friedmann (nPPF) approach as well as a physically motivated and approximate phenomenological model based on the error function (Erf). We compare the parametrized approaches’ predictions of the non-linear matter power spectrum to the exact solutions, as well as state-of-the-art emulators, in an evolving dark energy scenario and two well-studied modified gravity models, finding sub-per cent agreement in the reaction using the Erf model at z ≤ 1 and k ≤ 5 h Mpc−1. This suggests only an additional three free constants, above the background and linear theory parameters, are sufficient to model non-linear, non-standard cosmology in the matter power spectrum at scales down to k ≤ 3h Mpc−1 within $2{{\ \rm per\ cent}}$ accuracy. We implement the parametrizations into ver.2.0 of the ReACT code: ACTio et ReACTio.

Search for sterile neutrinos in a universe of vacuum energy interacting with cold dark matter

We investigate the cosmological constraints on sterile neutrinos in a universe in which vacuum energy interacts with cold dark matter by using latest observational data. We focus on two specific interaction models, $Q=\beta H\rho_{\rm v}$ and $Q=\beta H\rho_{\rm c}$. To overcome the problem of large-scale instability in the interacting dark energy scenario, we employ the parametrized post-Friedmann (PPF) approach for interacting dark energy to do the calculation of perturbation evolution. The observational data sets used in this work include the Planck 2015 temperature and polarization data, the baryon acoustic oscillation measurements, the type-Ia supernova data, the Hubble constant direct measurement, the galaxy weak lensing data, the redshift space distortion data, and the Planck lensing data. Using the all-data combination, we obtain $N_{\rm eff}<3.522$ and $m_{\nu,{\rm sterile}}^{\rm eff}<0.576$ eV for the $Q=\beta H\rho_{\rm v}$ model, and $N_{\rm eff}=3.204^{+0.049}_{-0.135}$ and $m_{\nu,{\rm sterile}}^{\rm eff}=0.410^{+0.150}_{-0.330}$ eV for the $Q=\beta H\rho_{\rm c}$ model. The latter indicates $\Delta N_{\rm eff}>0$ at the 1.17$\sigma$ level and a nonzero mass of sterile neutrino at the 1.24$\sigma$ level. In addition, for the $Q=\beta H\rho_{\rm v}$ model, we find that $\beta=0$ is consistent with the current data, and for the $Q=\beta H\rho_{\rm c}$ model, we find that $\beta>0$ is obtained at more than 1$\sigma$ level.

Probing the interaction between dark energy and dark matter with the parametrized post-Friedmann approach

There possibly exists some direct, non-gravitational coupling between dark energy and dark matter. This possibility should be seriously tested by using observations, which requires us to understand such a scenario from the aspects of both expansion history and growth of structure. It is found that once calculating the perturbations in the interacting dark energy (IDE) scenario, for most cases the curvature perturbation on superhorizon scales is divergent, which is a catastrophe for the IDE cosmology. We found a solution to this issue, which is to establish an effective theory to treat the dark energy perturbations totally based on the basic facts of dark energy. This scheme generalizes the parametrized post-Friedmann framework of uncoupled dark energy and can be used to cure the instability of the IDE cosmology. The whole parameter space of IDE models can henceforward be explored by observational data. The IDE scenario can thus be tested or falsified with current and future observational data by using the PPF approach. We expect that the future highly accurate observational data would offer the certain answer to the question whether there is a direct coupling between dark energy and dark matter.

相互作用暗能量模型的研究现状

本文简要介绍了相互作用暗能量模型研究的最新进展。首先介绍了几种目前比较流行的相互作用暗能量模型，接着详细分析了国内外在该领域的研究现状及发展动态。其中，针对大尺度不稳定性问题，本文着重强调了用来处理相互作用暗能量宇宙学扰动的参数化后弗里德曼(parametrized post-Friedmann，简称PPF)方法。研究表明该方法能够成功地在相互作用暗能量模型全部参数空间中消除其大尺度不稳定性问题。 In this paper, we briefly introduce the present status of the study of interacting dark energy (IDE) models. Firstly, we introduce several currently popular models of dark energy interacting with dark matter. Then, we analyze the research status in this field and development tendency at home and abroad. Note here that, in order to solve the large-scale instability of IDE, we describe the para-metrized post-Friedmann (PPF) approach, which could handle the cosmological perturbations of IDE. It has been proved that the PPF framework of IDE can successfully solve the large-scale insta-bility issue in the whole parameter space.

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

Dark energy can modify the dynamics of dark matter if there exists a direct interaction between them. Thus a measurement of the structure growth, e.g., redshift-space distortions (RSD), can provide a powerful tool to constrain the interacting dark energy (IDE) models. For the widely studied $Q=3\beta H\rho_{de}$ model, previous works showed that only a very small coupling ($\beta\sim\mathcal{O}(10^{-3})$) can survive in current RSD data. However, all these analyses had to assume $w>-1$ and $\beta>0$ due to the existence of the large-scale instability in the IDE scenario. In our recent work [Phys. Rev. D 90, 063005 (2014)], we successfully solved this large-scale instability problem by establishing a parametrized post-Friedmann (PPF) framework for the IDE scenario. So we, for the first time, have the ability to explore the full parameter space of the IDE models. In this work, we reexamine the observational constraints on the $Q=3\beta H\rho_{de}$ model within the PPF framework. By using the Planck data, the baryon acoustic oscillation data, the JLA sample of supernovae, and the Hubble constant measurement, we get $\beta=-0.010^{+0.037}_{-0.033}$ ($1\sigma$). The fit result becomes $\beta=-0.0148^{+0.0100}_{-0.0089}$ ($1\sigma$) once we further incorporate the RSD data in the analysis. The error of $\beta$ is substantially reduced with the help of the RSD data. Compared with the previous results, our results show that a negative $\beta$ is favored by current observations, and a relatively larger interaction rate is permitted by current RSD data.

Parametrized post-Friedmann framework for interacting dark energy

Dark energy might directly interact with cold dark matter. However, in such a scenario, an early-time large-scale instability occurs occasionally, which may be due to the incorrect treatment for the pressure perturbation of dark energy as a nonadiabatic fluid. To avoid this nonphysical instability, we establish a new framework to correctly calculate the cosmological perturbations in the interacting dark energy models. Inspired by the well-known parametrized post-Friedmann approach, the condition of the dark energy pressure perturbation is replaced with the relationship between the momentum density of dark energy and that of other components on large scales. By reconciling the perturbation evolutions on the large and small scales, one can complete the perturbation equations system. The large-scale instability can be successfully avoided and the well-behaved density and metric perturbations are obtained within this framework. Our test results show that this new framework works very well and is applicable to all the interacting dark energy models.

Testing general relativity with cosmology: a synopsis of the parametrized post-Friedmann approach

More than half a century after the Chapel Hill meeting of 1957, the landscape of general relativity has been transformed. In relativistic cosmology we are entering an era in which we can seriously consider testing some of the most fundamental assumptions that go into our view of the Universe. We propose that precision tests of gravity on cosmological scales may be feasible with up-and-coming surveys of galaxies. To achieve the most accurate general constraints yet we briefly describe a formalism which is applicable on the largest scales: the parametrized post-Friedmann approach. We sketch out the steps that need to be taken to link realistic, cosmological observables with fundamental properties of general relativity.