  We develop a theory of self-resonance after inflation. We study a large class
of models involving multiple scalar fields with an internal symmetry. For
illustration, we often specialize to dimension 4 potentials, but we derive
results for general potentials. This is the first part of a two part series of
papers. Here in Part 1 we especially focus on the behavior of long wavelengths
modes, which are found to govern most of the important physics. Since the
inflaton background spontaneously breaks the time translation symmetry and the
internal symmetry, we obtain Goldstone modes; these are the adiabatic and
isocurvature modes. We find general conditions on the potential for when a
large instability band exists for these modes at long wavelengths. For the
adiabatic mode, this is determined by a sound speed derived from the time
averaged potential. While for the isocurvature mode, this is determined by a
speed derived from a time averaged auxiliary potential. Interestingly, we find
that this instability band usually exists for one of these classes of modes,
rather than both simultaneously. We focus on backgrounds that evolve radially
in field space, as setup by inflation, and also mention circular orbits, as
relevant to Q-balls. In Part 2 [1] we derive the central behavior from the
underlying description of many particle quantum mechanics, and introduce a weak
breaking of the symmetry to study corrections to particle-antiparticle
production from preheating.
