We wish to investigate whether there is an extension to the base ΛCDM cosmology that can resolve the tension between the Planck observation of the cosmic microwave background anisotropies and the local measurement of the Hubble constant. We consider various plausible extended models in this work, and we use the Planck 2015 observations, combined with the baryon acoustic oscillation data, the JLA type Ia supernovae data, and the local measurement of the Hubble constant , to make an analysis. We find that the holographic dark energy plus sterile neutrino model can reduce the tension to be at the 1.11σ level, but this model is obviously not favored by the current observations. Among these extended models, the ΛCDM+N eff model is most favored by the current observations, and this model can reduce the tension to be at the 1.87σ level. By a careful test, we conclude that none of these extended models can convincingly resolve the H 0 tension.

We investigate the constraints on total neutrino mass in the scenario of vacuum energy interacting with cold dark matter. We focus on two typical interaction forms, i.e., Q = βHρc and Q = βHρΛ. To avoid the occurrence of large-scale instability in interacting dark energy cosmology, we adopt the parameterized post-Friedmann approach to calculate the perturbation evolution of dark energy. We employ observational data, including the Planck cosmic microwave background temperature and polarization data, baryon acoustic oscillation data, a JLA sample of type Ia supernovae observation, direct measurement of the Hubble constant, and redshift space distortion data. We find that, compared with those in the ΛCDM model, much looser constraints on mν are obtained in the Q = βHρc model, whereas slightly tighter constraints are obtained in the Q = βHρΛ model. Consideration of the possible mass hierarchies of neutrinos reveals that the smallest upper limit of mν appears in the degenerate hierarchy case. By comparing the values of χ 2 min , we find that the normal hierarchy case is favored over the inverted one. In particular, we find that the difference ∆χ 2 min ≡ χ 2 IH;min −χ 2 NH;min > 2 in the Q = βHρc model. In addition, we find that β = 0 is consistent with the current observations in the Q = βHρc model, and β < 0 is favored at more than the 1σ level in the Q = βHρΛ model.

We constrain the neutrino mass in the scenario of vacuum energy interacting with cold dark matter by using current cosmological observations. To avoid the large-scale instability problem in interacting dark energy models, we employ the parameterized post-Friedmann (PPF) approach to do the calculation of perturbation evolution, for the Q = βHρ c and Q = βHρ Λ models. The current observational data sets used in this work include Planck (cosmic microwave background), BSH (baryon acoustic oscillations, type Ia supernovae, and Hubble constant), and LSS (redshift space distortions and weak lensing). According to the constraint results, we find that β > 0 at more than 1σ level for the Q = βHρ c model, which indicates that cold dark matter decays into vacuum energy; while β = 0 is consistent with the current data at 1σ level for the Q = βHρ Λ model. Taking the ΛCDM model as a baseline model, we find that a smaller upper limit, m ν < 0.11 eV (2σ), is induced by the latest BAO BOSS DR12 data and the Hubble constant measurement H 0 = 73.00 ± 1.75 km s −1 Mpc −1 .Since the discovery of accelerated expansion of the universe, it has been proposed that there is a mysterious ingredient in the universe, called "dark energy", which is a component with negative pressure; in other words, it is the source to produce repulsive gravity to drive the acceleration of the universe's expansion (for reviews of cosmic acceleration and dark energy, see e.g. [1][2][3][4][5][6][7][8][9][10]). Dark energy is now a dominant component (it occupies about 70% of the total energy density) in today's universe. Also, dark energy is undoubtedly the most popular explanation for the cosmic accelerated expansion. Though the cosmological constant Λ is the simplest model of dark energy, it can explain almost all the current observations well. So, the cosmological constant model (usually dubbed the ΛCDM model) is always viewed as the primary candidate of the cosmological standard model. However, the cosmological constant Λ has always been facing significant challenges, such as the "coincidence problem" [2], which states that dark matter and dark energy just have the same order of magnitude today, while the order difference between them can be up to 10 30 in the early universe.The "interacting dark energy" (IDE) scenario, in which it is considered that there is some direct, non-gravitational coupling between dark energy and dark matter, is proposed and studied widely . It has been shown that the coincidence problem can be well alleviated in the IDE scenario [13-15, 23, 25]. But the more important question is how to detect such a direct coupling between dark energy and dark matter through the cosmological observations. This requires us to precisely know how the interaction affects the evolution of the universe, including the expansion history and the growth of structure of the universe. The impacts on the cosmic microwave background (CMB) [25,46] and large-scale structure formation [12,20,24,26,37,46] in the IDE scenario have been investigated in detail.The fact...

The nature of dark energy affects the Hubble expansion rate (namely, the expansion history) H (z) by an integral over w(z). However, the usual observables are the luminosity distances or the angular diameter distances, which measure the distance-redshift relation. Actually, the property of dark energy affects the distances (and the growth factor) by a further integration over functions of H (z). Thus, the direct measurements of the Hubble parameter H (z) at different redshifts are of great importance for constraining the properties of dark energy. In this paper, we show how the typical dark energy models, for example, the CDM, wCDM, CPL, and holographic dark energy models, can be constrained by the current direct measurements of H (z) (31 data used in total in this paper, covering the redshift range of z ∈ [0.07, 2.34]). In fact, the future redshift-drift observations (also referred to as the Sandage-Loeb test) can also directly measure H (z) at higher redshifts, covering the range of z ∈ [2, 5]. We thus discuss what role the redshift-drift observations can play in constraining dark energy with the Hubble parameter measurements. We show that the constraints on dark energy can be improved greatly with the H (z) data from only a 10-year observation of redshift drift.

We explore the impact of the Sandage-Loeb (SL) test on the precision of cosmological constraints for $f(T)$ gravity theories. The SL test is an important supplement to current cosmological observations because it measures the redshift drift in the Lyman-$\alpha$ forest in the spectra of distant quasars, covering the "redshift desert" of $2 \lesssim z \lesssim5$. To avoid data inconsistency, we use the best-fit models based on current combined observational data as fiducial models to simulate 30 mock SL test data. We quantify the impact of these SL test data on parameter estimation for $f(T)$ gravity theories. Two typical $f(T)$ models are considered, the power-law model $f(T)_{PL}$ and the exponential-form model $f(T)_{EXP}$. The results show that the SL test can effectively break the existing strong degeneracy between the present-day matter density $\Omega_m$ and the Hubble constant $H_0$ in other cosmological observations. For the considered $f(T)$ models, a 30-year observation of the SL test can improve the constraint precision of $\Omega_m$ and $H_0$ enormously but cannot effectively improve the constraint precision of the model parameters.Comment: 5 pages, 2 figure