On a quadratic equation of state and a universe mildly bouncing above the Planck temperature

A 1-parameter class of quadratic equations of state is confronted with the Hubble diagram of supernovae and Baryonic Acoustic Oscillations. The fit is found to be as good as the one using the Lambda CDM model. The corresponding universe has no initial singularity, only a mild bounce at a temperature well above the Planck temperature.