Towards general patterns of features in multi-field inflation

We investigate the consequences of general curved trajectories in multi-field inflation. After setting up a completely general formalism using the mass basis, which naturally accommodates the notion of light and heavy modes, we study in detail the simple case of two successive turns in two-field system. We find the power spectrum of the curvature perturbation receives corrections that exhibit oscillatory features sinusoidal in the logarithm of the comoving wavenumber without slow-roll suppression. We show that this is because of the resonance of the heavy modes inside and outside the mass horizon.Comment: (v1) 16 pages, 2 figures; (v2) 17 pages, minor updates, to appear in Journal of High Energy Physic

Exact Analytic Solution for Non-Linear Density Fluctuation in a LCDM Universe

We derive the exact third-order analytic solution of the matter density fluctuation in the proper-time hypersurface in a $\Lambda$CDM universe, accounting for the explicit time-dependence and clarifying the relation to the initial condition. Furthermore, we compare our analytic solution to the previous calculation in the comoving gauge, and to the standard Newtonian perturbation theory by providing Fourier kernels for the relativistic effects. Our results provide an essential ingredient for a complete description of galaxy bias in the relativistic context.Comment: 20 pages, no figures, published in JCA

Waterfall field in hybrid inflation and curvature perturbation

We study carefully the contribution of the waterfall field to the curvature perturbation at the end of hybrid inflation. In particular we clarify the parameter dependence analytically under reasonable assumptions on the model parameters. After calculating the mode function of the waterfall field, we use the delta N formalism and confirm the previously obtained result that the power spectrum is very blue with the index 4 and is absolutely negligible on large scales. However, we also find that the resulting curvature perturbation is highly non-Gaussian and hence we calculate the bispectrum. We find that the bispectrum is at leading order independent of momentum and exhibits its peak at the equilateral limit, though it is unobservably small on large scales. We also present the one-point probability distribution function of the curvature perturbation.Comment: (v1) 23 pages, 1 figure; (v2) 26 pages, discussions expanded including a new appendix section and references added; (v3) minor updates, to appear in Journal of Cosmology and Astroparticle Physic

Running of scalar spectral index in multi-field inflation

We compute the running of the scalar spectral index in general multi-field slow-roll inflation. By incorporating explicit momentum dependence at the moment of horizon crossing, we can find the running straightforwardly. At the same time, we can distinguish the contributions from the quasi de Sitter background and the super-horizon evolution of the field fluctuations.Comment: (v1) 7 pages; (v2) 8 pages, 1 figure, discussions expanded especially regarding the initial conditions, to appear in Journal of Cosmology and Astroparticle Physic