Quantifying the impact of future Sandage-Loeb test data on dark energy constraints

The Sandage-Loeb (SL) test is a unique method to probe dark energy in the "redshift desert" of $2\lesssim z\lesssim 5$, and thus it provides an important supplement to the other dark energy probes. Therefore, it is of great importance to quantify how the future SL test data impact on the dark energy constraints. To avoid the potential inconsistency in data, we use the best-fitting model based on the other geometric measurements as the fiducial model to produce 30 mock SL test data. The 10-yr, 20-yr, and 30-yr observations of SL test are analyzed and compared in detail. We show that compared to the current combined data of type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble constant, the 30-yr observation of SL test could improve the constraint on $\Omega_m$ by about $80$ and the constraint on $w$ by about $25$. Furthermore, the SL test can also improve the measurement of the possible direct interaction between dark energy and dark matter. We show that the SL test 30-yr data could improve the constraint on $\gamma$ by about $30$ and $10$ for the $Q=\gamma H\rho_c$ and $Q=\gamma H\rho_{de}$ models, respectively.Comment: 10 pages, 3 figure

Parameter estimation with Sandage-Loeb test

The Sandage-Loeb (SL) test directly measures the expansion rate of the universe in the redshift range of $2\lesssim z\lesssim 5$ by detecting redshift drift in the spectra of Lyman-$\alpha$ forest of distant quasars. We discuss the impact of the future SL test data on parameter estimation for the $\Lambda$CDM, the $w$CDM, and the $w_0w_a$CDM models. To avoid the potential inconsistency with other observational data, we take the best-fitting dark energy model constrained by the current observations as the fiducial model to produce 30 mock SL test data. The SL test data provide an important supplement to the other dark energy probes, since they are extremely helpful in breaking the existing parameter degeneracies. We show that the strong degeneracy between $\Omega_m$ and $H_0$ in all the three dark energy models is well broken by the SL test. Compared to the current combined data of type Ia supernovae, baryon acoustic oscillation, cosmic microwave background, and Hubble constant, the 30-yr observation of SL test could improve the constraints on $\Omega_m$ and $H_0$ by more than 60\% for all the three models. But the SL test can only moderately improve the constraint on the equation of state of dark energy. We show that a 30-yr observation of SL test could help improve the constraint on constant $w$ by about 25\%, and improve the constraints on $w_0$ and $w_a$ by about 20\% and 15\%, respectively. We also quantify the constraining power of the SL test in the future high-precision joint geometric constraints on dark energy. The mock future supernova and baryon acoustic oscillation data are simulated based on the space-based project JDEM. We find that the 30-yr observation of SL test would help improve the measurement precision of $\Omega_m$, $H_0$, and $w_a$ by more than 70\%, 20\%, and 60\%, respectively, for the $w_0w_a$CDM model.Comment: 16 pages, 9 figures, 3 tables; adding a new section to address future SN and BAO observations; accepted for publication in JCA

Neutrinos and dark energy after Planck and BICEP2: data consistency tests and cosmological parameter constraints

The detection of the B-mode polarization of the cosmic microwave background (CMB) by the BICEP2 experiment implies that the tensor-to-scalar ratio $r$ should be involved in the base standard cosmology. In this paper, we extend the $\Lambda$CDM+$r$+neutrino/dark radiation models by replacing the cosmological constant with the dynamical dark energy with constant $w$. Four neutrino plus dark energy models are considered, i.e., the $w$CDM+$r+\sum m_\nu$, $w$CDM+r + $N_{\rm eff}$, $w$CDM+r + $\sum m_\nu$ + $N_{\rm eff}$, and $w$CDM+r + $N_{\rm eff}$ + $m_{\nu,{\rm sterile}}^{\rm eff}$ models. The current observational data considered in this paper include the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, the cosmic shear data, and the BICEP2 polarization data. We test the data consistency in the four cosmological models, and then combine the consistent data sets to perform joint constraints on the models. We focus on the constraints on the parameters $w$, $\sum m_\nu$, $N_{\rm eff}$, and $m_{\nu,{\rm sterile}}^{\rm eff}$.Comment: 22 pages, 8 figures, 5 table

Unique Conservative Solutions to a Variational Wave Equation

Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation $u_{tt}-c(u) (c(u)u_x)_x=0$. Given a solution $u(t,x)$, even if the wave speed $c(u)$ is only H\"older continuous in the $t$-$x$ plane, one can still define forward and backward characteristics in a unique way. Using a new set of independent variables $X,Y$, constant along characteristics, we prove that $t,x,u$, together with other variables, satisfy a semilinear system with smooth coefficients. From the uniqueness of the solution to this semilinear system, one obtains the uniqueness of conservative solutions to the Cauchy problem for the wave equation with general initial data $u(0,\cdot)\in H^1(\mathbb{R})$, $u_t(0,\cdot)\in L^2(\mathbb{R})$

Dark radiation from a unified dark fluid model

We present a unified dark fluid model to describe the possible evolutionary behavior of $\Delta N_\mathrm{eff}$ in dark radiation. This model can be viewed as an interacting model for the dark sectors, in which dark matter interacts with dark radiation. We show that the evolution of $\Delta N_\mathrm{eff}$ can be nicely explained without some drawbacks, such as the blowup of $\Delta N_\mathrm{eff}$ and the non-vanishing interaction at the late time.Comment: 12 pages, 4 figures, revised version accepted by PTE

Redshift drift exploration for interacting dark energy

By detecting redshift drift in the spectra of Lyman-$\alpha$ forest of distant quasars, Sandage-Loeb (SL) test directly measures the expansion of the universe, covering the "redshift desert" of $2 \lesssim z \lesssim5$. Thus this method is definitely an important supplement to the other geometric measurements and will play a crucial role in cosmological constraints. In this paper, we quantify the ability of SL test signal by a CODEX-like spectrograph for constraining interacting dark energy. Four typical interacting dark energy models are considered: (i) $Q=\gamma H\rho_c$, (ii) $Q=\gamma H\rho_{de}$, (iii) $Q=\gamma H_0\rho_c$, and (iv) $Q=\gamma H_0\rho_{de}$. The results show that for all the considered interacting dark energy models, relative to the current joint SN+BAO+CMB+$H_0$ observations, the constraints on $\Omega_m$ and $H_0$ would be improved by about 60\% and 30--40\%, while the constraints on $w$ and $\gamma$ would be slightly improved, with a 30-yr observation of SL test. We also explore the impact of SL test on future joint geometric observations. In this analysis, we take the model with $Q=\gamma H\rho_c$ as an example, and simulate future SN and BAO data based on the space-based project WFIRST. We find that in the future geometric constraints, the redshift drift observations would help break the geometric degeneracies in a meaningful way, thus the measurement precisions of $\Omega_m$, $H_0$, $w$, and $\gamma$ could be substantially improved using future probes.Comment: 6 pages, 5 figures; accepted for publication in EPJC. arXiv admin note: text overlap with arXiv:1407.712