This paper presents constraints on dark energy from cosmic age and supernova observations. Using the lower limit of cosmic age from globular clusters and white dwarfs (t₀ > 12 Gyr), along with recent high-redshift supernova data, the authors estimate the equation of state (W) of dark energy. They find that the cosmic age limit significantly reduces the upper bound on the variation amplitude of W. A new dark energy model called Quintom is proposed, which allows W to be greater than -1 in the past and less than -1 today, consistent with current observations. The paper discusses the implications of recent X-ray gas mass fraction data, which favor a negative running of the equation of state. The cosmic age limit plays a crucial role in constraining dark energy models. The authors use the WMAP data and other cosmological observations to analyze the behavior of dark energy. They find that the equation of state is consistent with a cosmological constant, but when not restricted to be constant, the fit to observational data improves. The paper also considers different parameterizations of the dark energy equation of state, such as W(z) = W + W'z and W(z) = W₁ + W_a z/(1+z). These models are tested against supernova data and the cosmic age limit. The results show that the cosmic age constraint significantly reduces the upper bound on the variation of W. The Quintom model is proposed as a possible explanation for the transition from W > -1 to W < -1, which is observed in current data. The paper also discusses the implications of X-ray gas mass fraction data from Chandra observations, which provide constraints on the equation of state. The results show that the equation of state may be decreasing, indicating a possible transition in dark energy behavior. The authors conclude that the cosmic age limit plays a significant role in constraining dark energy models and that the Quintom model provides a viable explanation for the observed behavior of dark energy.This paper presents constraints on dark energy from cosmic age and supernova observations. Using the lower limit of cosmic age from globular clusters and white dwarfs (t₀ > 12 Gyr), along with recent high-redshift supernova data, the authors estimate the equation of state (W) of dark energy. They find that the cosmic age limit significantly reduces the upper bound on the variation amplitude of W. A new dark energy model called Quintom is proposed, which allows W to be greater than -1 in the past and less than -1 today, consistent with current observations. The paper discusses the implications of recent X-ray gas mass fraction data, which favor a negative running of the equation of state. The cosmic age limit plays a crucial role in constraining dark energy models. The authors use the WMAP data and other cosmological observations to analyze the behavior of dark energy. They find that the equation of state is consistent with a cosmological constant, but when not restricted to be constant, the fit to observational data improves. The paper also considers different parameterizations of the dark energy equation of state, such as W(z) = W + W'z and W(z) = W₁ + W_a z/(1+z). These models are tested against supernova data and the cosmic age limit. The results show that the cosmic age constraint significantly reduces the upper bound on the variation of W. The Quintom model is proposed as a possible explanation for the transition from W > -1 to W < -1, which is observed in current data. The paper also discusses the implications of X-ray gas mass fraction data from Chandra observations, which provide constraints on the equation of state. The results show that the equation of state may be decreasing, indicating a possible transition in dark energy behavior. The authors conclude that the cosmic age limit plays a significant role in constraining dark energy models and that the Quintom model provides a viable explanation for the observed behavior of dark energy.