Hybrid inflation models are especially interesting as they lead to a spike in the density power spectrum on small scales, compared to the CMB, while also satisfying current bounds on tensor modes. Here we study hybrid inflation with $N$ waterfall fie
lds sharing a global $SO(N)$ symmetry. The inclusion of many waterfall fields has the obvious advantage of avoiding topologically stable defects for $N>3$. We find that it also has another advantage: it is easier to engineer models that can simultaneously (i) be compatible with constraints on the primordial spectral index, which tends to otherwise disfavor hybrid models, and (ii) produce a spike on astrophysically large length scales. The latter may have significant consequences, possibly seeding the formation of astrophysically large black holes. We calculate correlation functions of the time-delay, a measure of density perturbations, produced by the waterfall fields, as a convergent power series in both $1/N$ and the fields correlation function $Delta(x)$. We show that for large $N$, the two-point function is $<delta t({bf x}),delta t({bf 0})>,proptoDelta^2(|{bf x}|)/N$ and the three-point function is $<delta t({bf x}),delta t({bf y}),delta t({bf 0})>,proptoDelta(|{bf x}-{bf y}|)Delta(|{bf x}|)Delta(|{bf y}|)/N^2$. In accordance with the central limit theorem, the density perturbations on the scale of the spike are Gaussian for large $N$ and non-Gaussian for small $N$.
We further develop a theory of self-resonance after inflation in a large class of models involving multiple scalar fields. We concentrate on inflaton potentials that carry an internal symmetry, but also analyze weak breaking of this symmetry. This is
the second part of a two part series of papers. Here in Part 2 we develop an understanding of the resonance structure from the underlying many particle quantum mechanics. We begin by a small amplitude analysis, which obtains the central resonant wave numbers, and relate it to perturbative processes. We show that the dominant resonance structure is determined by (i) the nonrelativistic scattering of many quantum particles and (ii) the application of Bose-Einstein statistics to the adiabatic and isocurvature modes, as introduced in Part 1 [1]. Other resonance structure is understood in terms of annihilations and decays. We setup Bunch-Davies vacuum initial conditions during inflation and track the evolution of modes including Hubble expansion. In the case of a complex inflaton carrying an internal U(1) symmetry, we show that when the isocurvature instability is active, the inflaton fragments into separate regions of phi-particles and anti-phi-particles. We then introduce a weak breaking of the U(1) symmetry; this can lead to baryogenesis, as shown by some of us recently [2,3]. Then using our results, we compute corrections to the particle-antiparticle asymmetry from this preheating era.
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 pot
entials. 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.
We survey observational constraints on the parameter space of inflation and axions and map out two allowed windows: the classic window and the inflationary anthropic window. The cosmology of the latter is particularly interesting; inflationary axion
cosmology predicts the existence of isocurvature fluctuations in the CMB, with an amplitude that grows with both the energy scale of inflation and the fraction of dark matter in axions. Statistical arguments favor a substantial value for the latter, and so current bounds on isocurvature fluctuations imply tight constraints on inflation. For example, an axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy scale > 3.8*10^14 GeV (r > 2*10^(-9)) at 95% confidence, and so implies negligible gravitational waves from inflation, but suggests appreciable isocurvature fluctuations.
