When performing cosmological inference, standard analyses of the
Lyman-α (Lyα) three-dimensional correlation functions only
consider the information carried by the distinct peak produced by baryon
acoustic oscillations (BAO). In this work, we address whether this compression
is sufficient to capture all the relevant cosmological information carried by
these functions. We do this by performing a direct fit to the full shape,
including all physical scales without compression, of synthetic Lyα
auto-correlation functions and cross-correlations with quasars at effective
redshift zeff=2.3, assuming a DESI-like survey, and providing a
comparison to the classic method applied to the same dataset. Our approach
leads to a 3.5% constraint on the matter density ΩM, which is
about three to four times better than what BAO alone can probe. The growth term
fσ8(zeff) is constrained to the 10% level, and the
spectral index ns to ∼3−4%. We demonstrate that the extra
information resulting from our `direct fit' approach, except for the
ns constraint, can be traced back to the Alcock-Paczy\'nski effect
and redshift space distortion information.Comment: Submitted to MNRA