We develop a theory of nonlinear cosmological perturbations on superhorizon scales for a single scalar field with a general kinetic term and a general form of the potential. We employ the ADM formalism and the spatial gradient expansion approach, characterised by O(ǫ m ), where ǫ = 1/(HL) is a small parameter representing the ratio of the Hubble radius to the characteristic length scale L of perturbations. We obtain the general solution for a full nonlinear version of the curvature perturbation valid up through second-order in ǫ (m = 2). We find the solution satisfies a nonlinear second-order differential equation as an extension of the equation for the linear curvature perturbation on the comoving hypersurface. Then we formulate a general method to match a perturbative solution accurate to n-th-order in perturbation inside the horizon to our nonlinear solution accurate to second-order (m = 2) in the gradient expansion on scales slightly greater than the Hubble radius. The formalism developed in this paper allows us to calculate the superhorizon evolution of a primordial non-Gaussianity beyond the so-called δN formalism or separate universe approach which is equivalent to leading order (m = 0) in the gradient expansion. In particular, it can deal with the case when there is a temporary violation of slow-roll conditions. As an application of our formalism, we consider Starobinsky's model, which is a single field model having a temporary non-slow-roll stage due to a sharp change in the potential slope. We find that a large non-Gaussianity can be generated even on superhorizon scales due to this temporary suspension of slow-roll inflation.PACS numbers: 98.80.-k, 98.90.Cq

We investigate the possibility that a heavy scalar field, whose mass exceeds the Hubble scale during inflation, could leave non-negligible signatures in the Cosmic Microwave Background (CMB) temperature anisotropy power spectrum through the parametric resonance between its background oscillations and the inflaton fluctuations. By assuming the heavy scalar field couples with the inflaton derivatively, we show that the resonance can be efficient without spoiling the slow-roll inflation. The primordial power spectrum modulated by the resonance has a sharp peak at a specific scale and could be an origin of the anomalies observed in the angular power spectrum of the CMB. In some values of parameters, the modulated spectrum can fit the observed data better than the simple power-law power spectrum, though the resultant improvement of the fit is not large enough and hence other observations such as non-Gaussianity are necessary to confirm that the CMB anomalies are originated from the resonant effect of the heavy scalar field. The resonant signatures can provide an opportunity to observe heavy degrees of freedom during inflation and improve our understanding of physics behind inflation.

We discuss the possibility that we could obtain some hints of the heavy physics during inflation by analyzing local features of the primordial bispectrum. A heavy scalar field could leave large signatures in the primordial spectra through the parametric resonance between its background oscillation and the fluctuations. Since the duration of the heavymode oscillations is finite, the effect of the resonance is localized in momentum space. In this paper, we show that the bispectrum is amplified when such a resonance occurs, and that the peak amplitude of the feature can be O(10 1−2 ), or as large as O(10 5 ) depending on the type of interactions. In particular, the resonance can give large contributions in finitely squeezed configurations, while the bispectrum cannot be large in the exact squeezed limit. We also find that there is a relation between the scales at which the features appear in the bispectrum and the power spectrum, and that the feature in the bispectrum can be much larger than that in the power spectrum. If correlated features are observed at characteristic scales in the primordial spectra, it will indicate the presence of heavy degrees of freedom. By analyzing these features, we may be able to obtain some information on the physics behind inflation.

We study the effects of sudden change in the sound velocity on primordial curvature perturbation spectrum in inflationary cosmology, assuming that the background evolution satisfies the slow-roll condition throughout. It is found that the power spectrum acquires oscillating features which are determined by the ratio of the sound speed before and after the transition and the wavenumeber which crosses the sound horizon at the transition, and their analytic expression is given. In some values of those parameters, the oscillating primordial power spectrum can better fit the observed Cosmic Microwave Background temperature anisotropy power spectrum than the simple power-law power spectrum, although introduction of such a new degree of freedom is not justified in the context of Akaike's Information Criterion.Subject Index: 400, 436, 440, 442 * ) As discussed in Appendix A, this is not the case in the curvaton scenario.

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for generic single-field inflation. Our inflaton is described by the Lagrangian of the form W (X, φ) − G(X, φ)✷φ with X = −∂ µ φ∂µφ/2, which is no longer equivalent to a perfect fluid. This model is more general than k-inflation, and is called G-inflation. A general nonlinear solution for the metric and the scalar field is obtained at second order in gradient expansion. We derive a simple master equation governing the large-scale evolution of the nonlinear curvature perturbation. It turns out that the nonlinear evolution equation is deduced as a straightforward extension of the corresponding linear equation for the curvature perturbation on uniform φ hypersurfaces. PACS numbers: 98.80.-k, 98.90.Cqwhere the prime represents differentiation with respect to the conformal time, ǫ is the small expansion parameter, and the other quantities will be defined in the rest of the paper. This equation is to be compared with its linear counterpart: