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In this paper, the generalized equation of state (GEoS) for dark energy (\(w_\beta =w_0-w_{\beta }[(1+z)^{-\beta }-1]/\beta \)) is investigated with the combined standard ruler data from the observations of intermediate-luminosity radio quasars, galaxy clusters, BAO and CMB. The constraint results show that the best-fit EoS parameters are \(w_0=-\,0.94^{+0.57}_{-0.41}\), \(w_\beta =-\,0.17^{+2.45}_{-4.81}\) and \(\beta =-1.42\) (with a lower limit of \(\beta >-\,2.70\) at 68.3% C.L.), which implies that at early times the dark energy vanishes. In the framework of nine truncated GEoS models with different \(\beta \) parameters, our findings present very clear evidence disfavoring the case that dark energy always dominates over the other material components in the early universe. Moreover, stringent constraints can be obtained in combination with the latest measurements of Hubble parameter at different redshifts: \(w_0=-1.01^{+0.56}_{-0.31}\), \(w_\beta =0.01^{+2.33}_{-4.52}\) and \(\beta =-0.42\) (with a lower limit of \(\beta >-2.40\) at 68.3% C.L.). Finally, the results obtained from the transition redshift (\(z_t\)) and Om(z) diagnostic indicate that: (1) The above constraints on the GEoS model agree very well with the transition redshift interval \(0.49 \le z_t \le 0.88\) within \(1\sigma \) error region. (2) At the current observational level, the GEoS model is practically indistinguishable from \(\Lambda \)CDM, although a small deviation from \(\Lambda \)CDM cosmology is present in the combined standard ruler data.

The generalized cosmic equation of state: a revised study with cosmological standard rulers