A parton picture of de Sitter space during slow-roll inflation

It is well-known that expectation values in de Sitter space are afflicted by infra-red divergences. Long ago, Starobinsky proposed that infra-red effects in de Sitter space could be accommodated by evolving the long-wavelength part of the field according to the classical field equations plus a stochastic source term. I argue that--when quantum-mechanical loop corrections are taken into account--the separate-universe picture of superhorizon evolution in de Sitter space is equivalent, in a certain leading-logarithm approximation, to Starobinsky's stochastic approach. In particular, the time evolution of a box of de Sitter space can be understood in exact analogy with the DGLAP evolution of partons within a hadron, which describes a slow logarithmic evolution in the distribution of the hadron's constituent partons with the energy scale at which they are probed.Comment: 36 pages; uses iopart.cls and feynmp.sty. v2: Minor typos corrected. Matches version published in JCA

Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity

Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars \phi are naturally coupled to gauge fields through c \phi F \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological signatures are highly distinctive: large nongaussianity of (nearly) equilateral shape, in addition to detectably large values of both the scalar spectral tilt and tensor-to-scalar ratio (both being typical of large field inflation). The WMAP bound on nongaussianity implies that the coupling, c, of the pseudo-scalar inflaton to any gauge field must be smaller than about 10^{2} M_p^{-1}.Comment: 45 pages, 7 figure

Stress tensor fluctuations in de Sitter spacetime

The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m^2/H^2. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.Comment: 35 pages, 4 figure

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde