UV/IR mode mixing and the CMB
  It is well understood that spatial non-commutativity, if indeed realized in
nature, is a phenomenon whose effects are not just felt at energy scales
comparable to the non-commutativity scale. Loop effects can transmit signatures
of any underlying non-commutativity to macroscopic scales (a manifestation of a
phenomenon that has come to be known as UV/IR mode mixing) and offer a
potential lever to constrain the amount of non-commutativity present in nature,
if present at all. Field theories defined on non-commutative spaces (realized
in string theory when D-branes are coupled to backgrounds of non-trivial RR
background flux), can exhibit strong UV/IR mode mixing, manifesting in a
non-local one loop effective action. In the context of inflation in the
presence of any background non-commutativity, we demonstrate how this UV/IR
mixing at the loop level can allow us to place severe constraints on the scale
of non-commutativity if we presume inflation is responsible for large scale
structure. We demonstrate that any amount of non-commutativity greatly
suppresses the CMB power at all observable scales, {\it independent} of the
scale of inflation, and independent of whether or not the non-commutativity
tensor redshifts during inflation, therefore nullifying a very salient and
successful prediction of inflation.
