  We generalize the `renormalized' perturbation theory (RPT) formalism of
Crocce & Scoccimarro (2006a) to deal with multiple fluids in the Universe and
here we present calculations up to the one-loop level. We apply the approach to
the non-linear evolution of baryon and cold dark matter (CDM) perturbations,
evolving from distinct sets of initial conditions. In current models of
structure formation, it is standard practice to treat baryons and CDM as an
effective single component fluid. In this approximation, one uses a weighed sum
of late-time baryon and CDM transfer functions to set initial conditions. Here,
we explore whether this approach can be used for high precision work. We show
that, even for a pure linear treatment, there is a large-scale scale-dependent
bias between baryons and CDM for WMAP5 cosmology. This bias is >1% until the
present day, when it is driven towards unity through gravitational relaxation.
Using the RPT formalism we test this approximation in the non-linear regime,
and show that the CDM power spectrum in the 2-component fluid differs from that
obtained from a 1-component fluid by ~3% on scales of order k~0.05 h/Mpc at
z=10, and by ~0.5% at z=0. However, for the case of baryons the situation is
worse and we find that the power spectrum is suppressed by ~15% on scales
k~0.05 h/Mpc at z=10, and by ~3-5% at z=0, relative to the total matter.
Importantly, besides the suppression of the spectrum, baryonic acoustic
oscillations (BAO) are amplified for baryon and damped for CDM spectra. Thus,
high precision modeling of baryons can not be probed through CDM only
simulations; detection significance of BAO will be amplified in probes that
study baryonic matter. Total mass can be modeled accurately using a 1-component
fluid approach at all times. (Abridged)
