The paper presents new measurements of the cosmic expansion history using red-envelope galaxies in 24 galaxy clusters at redshifts between 0.2 and 1.0. High-quality spectra were obtained with the Keck-LRIS spectrograph, complemented by archival data from the SPICES and VVDS surveys. The authors provide two new determinations of the expansion history: \( H(z) = 97 \pm 62 \) km s\(^{-1}\) Mpc\(^{-1}\) at \( z \sim 0.5 \) and \( H(z) = 90 \pm 40 \) km s\(^{-1}\) Mpc\(^{-1}\) at \( z \sim 0.8 \). They discuss the uncertainties in these measurements due to stellar-population models and use these measurements, along with cosmic microwave background (CMB) data, to constrain cosmological parameters, particularly dark energy. The study demonstrates the utility of direct \( H(z) \) measurements in constraining the dark energy equation of state parameterized by \( w(z) \) and \( w_0 \), and shows that \( w(z) \) can be constrained for arbitrary curvature. Additionally, the number of relativistic degrees of freedom is constrained to be \( 4 \pm 0.5 \) and the total mass of relativistic species is constrained to be less than \( 0.2 \) eV at the 1\(\sigma\) level. The paper also discusses the statistical uncertainties in age determination and the importance of blue wavelength coverage for accurate age measurements.The paper presents new measurements of the cosmic expansion history using red-envelope galaxies in 24 galaxy clusters at redshifts between 0.2 and 1.0. High-quality spectra were obtained with the Keck-LRIS spectrograph, complemented by archival data from the SPICES and VVDS surveys. The authors provide two new determinations of the expansion history: \( H(z) = 97 \pm 62 \) km s\(^{-1}\) Mpc\(^{-1}\) at \( z \sim 0.5 \) and \( H(z) = 90 \pm 40 \) km s\(^{-1}\) Mpc\(^{-1}\) at \( z \sim 0.8 \). They discuss the uncertainties in these measurements due to stellar-population models and use these measurements, along with cosmic microwave background (CMB) data, to constrain cosmological parameters, particularly dark energy. The study demonstrates the utility of direct \( H(z) \) measurements in constraining the dark energy equation of state parameterized by \( w(z) \) and \( w_0 \), and shows that \( w(z) \) can be constrained for arbitrary curvature. Additionally, the number of relativistic degrees of freedom is constrained to be \( 4 \pm 0.5 \) and the total mass of relativistic species is constrained to be less than \( 0.2 \) eV at the 1\(\sigma\) level. The paper also discusses the statistical uncertainties in age determination and the importance of blue wavelength coverage for accurate age measurements.