TianQin is a planned space-based gravitational wave (GW) observatory consisting of three Earth-orbiting satellites with an orbital radius of about $10^5 \, {\rm km}$. The satellites will form an equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4} \, {\rm Hz}$ and $1 \, {\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe and exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new-generation $17 \, {\rm cm}$ single-body hollow corner-cube retro-reflector which was launched with the QueQiao satellite on 21 May 2018; a new laser-ranging station equipped with a $1.2 \, {\rm m}$ telescope has been constructed and the station has successfully ranged to all five retro-reflectors on the Moon; and the TianQin-1 experimental satellite was launched on 20 December 2019—the first-round result shows that the satellite has exceeded all of its mission requirements.

In this paper, we use the type Ia supernovae data to constrain the holographic dark energy model proposed by Li. We also apply a cosmic age test to this analysis. We consider in this paper a spatially flat Friedmann-Robertson-Walker universe with a matter component and a holographic dark energy component. The fit result shows that the case $c<1$ ($c=0.21$) is favored, which implies that the holographic dark energy behaves as a quintom-type dark energy. Furthermore, we also perform a joint analysis of $\mathrm{SNe}+\mathrm{CMB}+\mathrm{LSS}$ to this model; the result is well improved and still upholds the quintom dark energy conclusion. The best fit results in our analysis are $c=0.81$, ${\Omega }_m^0=0.28$, and $h=0.65$, which lead to the present equation of state of dark energy $w_0=-1.03$ and the deceleration/acceleration transition redshift $z_T=0.63$. Finally, an expected supernova/acceleration probe simulation using $\Lambda \mathrm{CDM}$ as a fiducial model is performed on this model, and the result shows that the holographic dark energy model takes on $c<1$ ($c=0.92$) even though the dark energy is indeed a cosmological constant.

The holographic principle of quantum gravity theory has been applied to the dark energy (DE) problem, and so far three holographic DE models have been proposed: the original holographic dark energy (HDE) model, the agegraphic dark energy (ADE) model, and the holographic Ricci dark energy (RDE) model. In this work, we perform the best-fit analysis on these three models, by using the latest observational data including the Union+CFA3 sample of 397 Type Ia supernovae (SNIa), the shift parameter of the cosmic microwave background (CMB) given by the five-year Wilkinson Microwave Anisotropy Probe (WMAP5) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). The analysis shows that for HDE, $\chi_{min}^{2}=465.912$; for RDE, $\chi_{min}^{2}=483.130$; for ADE, $\chi_{min}^{2}=481.694$. Among these models, HDE model can give the smallest $\chi^2_{min}$. Besides, we also use the Bayesian evidence (BE) as a model selection criterion to make a comparison. It is found that for HDE, ADE, and RDE, $\Delta \ln \mathrm{BE}= -0.86$, -5.17, and -8.14, respectively. So, it seems that the HDE model is more favored by the observational data.

The holographic dark energy model is proposed by Li as an attempt for probing the nature of dark energy within the framework of quantum gravity. The main characteristic of holographic dark energy is governed by a numerical parameter $c$ in the model. The parameter $c$ can only be determined by observations. Thus, in order to characterize the evolving feature of dark energy and to predict the fate of the Universe, it is of extraordinary importance to constrain the parameter $c$ by using the currently available observational data. In this paper, we derive constraints on the holographic dark energy model from the latest observational data including the gold sample of 182 type Ia supernovae (SNIa), the shift parameter of the cosmic microwave background (CMB) given by the three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations, and the baryon acoustic oscillation (BAO) measurement from the Sloan Digital Sky Survey (SDSS). The joint analysis gives the fit results in $1\mathrm{\text{−}}\sigma$: $c={0.91}_{-0.18}^{+0.26}$ and ${\Omega }_{\mathrm{m}0}=0.29\pm 0.03$. That is to say, though the possibility of $c<1$ is more favored, the possibility of $c>1$ cannot be excluded in one-sigma error range, which is somewhat different from the result derived from previous investigations using earlier data. So, according to the new data, the evidence for the quintom feature in the holographic dark energy model is not as strong as before.