An open problem in cosmology is the determination of the precise thermal history of the Universe. One way which we can try to measure it is through the broadening of absorption lines in the Lyman-alpha forest. This allows the study of the intergalactic medium at high redshifts (from z=2 to z=4).

The broadening is the sum of two components: thermal broadening, characterised by the 'equation of state' of the IGM, and 'Jeans broadening', an effect arising form the Hubble flow in the filaments of the cosmic web. Most previous studies of the Lyman-alpha forest have focused on the former, modelling the equation of state as a power-law, and using quasar spectra to constrain the two parameters of the power-law. It has been argued in the literature (e.g. arXiv:1502.05715) that one should include a third parameter (f_J) to model the Jeans broadening. Since f_J measures the scale of baryonic matter density fluctuations, it depends not just on the current thermal state of the IGM, but on its whole thermal history.

In this talk, I will present our analysis of mock spectra generated from a range of state-of-the-art cosmological simulations taken from the EAGLE suite (Schaye+2015, Crain+2015) and how we assess the validity of this model and measure the level of systematic errors. We then apply the same pipeline to a series of high-resolution quasar spectra.