The cosmological model-independent method known as the Gaussian process (GP) has been widely used in the reconstruction of the Hubble constant H 0, and the hyperparameters inside GP influence the reconstructed result derived from GP. Different hyperparameters inside GP are used in the constraint of H 0 derived from GP with observational Hubble parameter H(z) data, and the influence of the hyperparameters inside GP on the reconstruction of H 0 with GP is discussed. The discussion about the hyperparameters inside GP and the forecasts for future data show that the consideration of the lower and upper bounds on the GP’s hyperparameters are necessary in order to get an extrapolated result of H 0 from GP reliably and robustly.

HI absorption systems are great targets for direct measurement of the Sandage-Loeb (SL) effect throughout a wide range of redshift for ground-based radio telescopes. We demonstrate the significance of improving the accuracy of SL effect measurement in cosmological model selection. With its wide sky coverage and high sensitivity, we forecast that for 1 year of the upcoming commensal survey (CRAFTS) the FAST telescope is capable of discovering about 800 HI absorption systems thereby improving the SL measurement accuracy. Aiming to measurement the cosmic redshift drift rate at the precision of ż ∼ 10−10 decade−1, we propose combined observation mode with blind-searching and targeted observation. For a decade of consecutive targeted spectroscopic observation with the frequency resolution at a level of sub-0.1 Hz, we could detect the first-order derivative of the cosmological redshift with the expected precision.

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In this work, we perform a full-spectrum fitting of 350 massive and passive galaxies selected as cosmic chronometers from the LEGA-C ESO public survey to derive their stellar ages, metallicities, and star formation histories. We extensively test our results by assessing their dependence on the possible contribution of dust, calibration of noise and signal, and use of photometric data in addition to spectral information; we also identify indicators of the correct convergence of the results, including the shape of the posterior distributions, the analysis of specific spectral features, and the correct reproduction of the observed spectrum. We derive a clear age–redshift trend compatible with the aging in a standard cosmological model showing a clear downsizing pattern, with more massive galaxies being formed at higher redshift (z f ∼ 2.5) with respect to less massive ones (z f ∼ 2). From these data, we measure the differential aging of this population of cosmic chronometers to derive a new measurement of the Hubble parameter, obtaining H ( z = 0.8 ) = 113.1 ± 15.1 ( stat . ) − 11.3 + 29.1 ( syst . ) . This analysis allows us to compare for the first time the differential ages of cosmic chronometers measured on the same sample with two completely different methods, the full-spectrum fit (this work) and the analysis of Lick indices, known to correlate with the age and metallicity of the stellar populations. Albeit an understood offset in the absolute ages, the differential ages have proven to be extremely compatible between the two methods, despite the very different data, assumptions, and models considered, demonstrating the robustness of the method.

Damped Lyman-α Absorber (DLA), or HI 21cm Absorber (H21A), is an important probe to model-independently measure the acceleration of spectroscopic velocity (vS) via the Sandage-Loeb (SL) effect. Confined by the shortage of DLAs and Background Radio Sources (BRSs) with adequate information, the detectable amount of DLAs is ambiguous in the bulk of previous work. After differing the acceleration of scale factor ($\ddot{a}$) from the first order time derivative of spectroscopic velocity ($\dot{v}_\mathrm{S}$), we make a statistical investigation of the amount of potential DLAs in the most of this paper. Using Kernel Density Estimation (KDE) to depict general redshift distributions of BRSs, observed DLAs and a DLA detection rate with different limitations (1.4GHz flux, HI column density and spin temperature), we provide fitted multi-Gaussian expressions of the three components and their 1σ regions by bootstrap, with a proportional constant of H21As in detected DLAs, leading to the measurable number predictions of H21As for FAST, ASKAP and SKA1-Mid in HI absorption blind survey. In our most optimistic condition (F1.4GHz>10mJy, NHI > 2 × 1020cm−2 and TS>500K), the FAST, AKSAP and SKA1-Mid would probe about 80, 500 and 600 H21As respectively.