Several interesting luminosity correlations among gamma‐ray burst (GRB) variables have been recently discussed extensively. In this paper, we derive six luminosity correlations (τlag–L, V–L, Epeak–L, Epeak–Eγ, τRT–L, Epeak–Eγ, iso) from the light curves and spectra of the latest 116 long GRBs, including the time lag (τlag) between low and high photon energy light curves, the variability (V) of the light curve, the peak energy of the spectrum (Epeak) and the minimum rise time (τRT) of the peaks. We find using the latest GRB data that the intrinsic scatter of the V–L correlation is too large and that there seems to be no inherent correlation between the two parameters. The other five correlations indeed exist when the sample is enlarged. The Epeak–Eγ correlation has a significantly lower intrinsic scatter compared to the other correlations. We divide the full data into four redshift bins when testing possible evolution of the correlations with redshift. We find no statistically significant evidence for the redshift evolution of the luminosity correlations. To avoid the circularity problem when constraining the cosmological parameters, we simultaneously minimize χ2 with respect to both the correlation parameters a, b and the cosmological parameters using the maximum likelihood method. For the flat ΛCDM, the best fit is Ωm= 0.31+0.13− 0.10. We also constrain the possible evolution of the equation of state (EOS) of the dark energy using the GRBs together with the Union2 compilation of type Ia supernovae (SNe Ia) and the H(z) data. The result is consistent with the cosmological constant at 2σ confidence level and, mainly due to the GRB data, the dark energy EOS shows slight deviation from −1 at z ≥ 0.5 as was persistently presented in many previous data sets.
By generating a Brillouin laser in an optical microresonator, we realize a soliton Kerr microcomb through exciting the Kerr frequency comb using the generated Brillouin laser in the same cavity. The intracavity Brillouin laser pumping scheme enables us to access the soliton states with a blue-detuned input pump. Due to the ultra-narrow linewidth and the low-noise properties of the generated Brillouin laser, the observed soliton microcomb exhibits narrow-linewidth comb lines and stable repetition rate even by using a diode laser with relatively broad linewidth. Also, we demonstrate a low-noise microwave signal with phase noise levels of -24 dBc/Hz at 10 Hz, -111 dBc/Hz at 10 kHz, and -147 dBc/Hz at 1 MHz offsets for a 11.14 GHz carrier with only a free-running input pump. The easy operation of the Brillouin-Kerr soliton microcomb with excellent performance makes our scheme promising for practical applications.
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