Dominance of gauge artifact in the consistency relation for the primordial bispectrum

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observable fluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in single field models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistency relation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.Comment: 12 pages; v2: accepted version in JCA

The Trispectrum in the Multi-brid Inflation

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters $\tau_{NL}$ and $g_{NL}$. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that $\tau_{NL}$ is always positive and roughly equals to $({6\over 5}f_{NL})^2$ for the low scale inflation, but $g_{NL}$ can be negative or positive and its order of magnitude can be the same as that of $\tau_{NL}$ or even largerComment: 12 pages; minor correction, refs added; further refs added, version for publication in JCA

Quadra-Spectrum and Quint-Spectrum from Inflation and Curvaton Models

We calculate the quadra-spectrum and quint-spectrum, corresponding to five and six point correlation functions of the curvature perturbation. For single field inflation with standard kinetic term, the quadra-spectrum and quint-spectrum are small, which are suppressed by slow roll parameters. The calculation can be generalized to multiple fields. When there is no entropy perturbation, the quadra-spectrum and quint-spectrum are suppressed as well. With the presence of entropy perturbation, the quadra-spectrum and quint-spectrum can get boosted. We illustrate this boost in the multi-brid inflation model. For the curvaton scenario, the quadra-spectrum and quint-spectrum are also large in the small r limit. We also calculate representative terms of quadra-spectrum and quint-spectrum for inflation with generalized kinetic terms, and estimate their order of magnitude for quasi-single field inflation.Comment: 16 pages; v2: references added

The trispectrum in ghost inflation

We calculate the trispectrum in ghost inflation where both the contact diagram and scale-exchange diagram are taken into account. The shape of trispectrum is discussed carefully and we find that the local form is absent in ghost inflation. In general, for the non-local shape trispectrum there are not analogous parameters to $\tau_{NL}^{loc.}$ and $g_{NL}^{loc.}$ which can completely characterize the size of local form trispectrum.Comment: 19 pages, 8 figures; clarifications and corrections added, version accepted for publication in JCA

Large non-Gaussianity from two-component hybrid inflation

We study the generation of non-Gaussianity in models of hybrid inflation with two inflaton fields, (2-brid inflation). We analyse the region in the parameter and the initial condition space where a large non-Gaussianity may be generated during slow-roll inflation which is generally characterised by a large f_NL, tau_NL and a small g_NL. For certain parameter values we can satisfy tau_NL>>f_NL^2. The bispectrum is of the local type but may have a significant scale dependence. We show that the loop corrections to the power spectrum and bispectrum are suppressed during inflation, if one assume that the fields follow a classical background trajectory. We also include the effect of the waterfall field, which can lead to a significant change in the observables after the waterfall field is destabilised, depending on the couplings between the waterfall and inflaton fields.Comment: 16 pages, 6 figures; v2: comments and references added, typos corrected, matches published versio

Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model

We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures showed that we can easily distinguish the two different momenta configurations.Comment: 17pages, 7 figures, version to appear in JCA

Affleck-Dine baryogenesis with modulated reheating

Modulated reheating scenario is one of the most attractive models that predict possible detections of not only the primordial non-Gaussianity but also the tensor fluctuation through future CMB observations such as the Planck satellite, the PolarBeaR and the LiteBIRD satellite experiments. We study the baryonic-isocurvature fluctuations in the Affleck-Dine baryogenesis with the modulated reheating scenario. We show that the Affleck-Dine baryogenesis can be consistent with the modulated reheating scenario with respect to the current observational constraint on the baryonic-isocurvature fluctuations.Comment: 7 page

Loop Corrections to Cosmological Perturbations in Multi-field Inflationary Models

We investigate one-loop quantum corrections to the power spectrum of adiabatic perturbation from entropy modes/adiabatic mode cross-interactions in multiple DBI inflationary models. We find that due to the non-canonical kinetic term in DBI models, the loop corrections are enhanced by slow-varying parameter $\epsilon$ and small sound speed $c_s$. Thus, in general the loop-corrections in multi-DBI models can be large. Moreover, we find that the loop-corrections from adiabatic/entropy cross-interaction vertices are IR finite.Comment: 21 pages, 7 figures; v2, typos corrected, ref added; v3 typos corrected, version for publishing in jca

Non-Gaussianity from Lifshitz Scalar

A Lifshitz scalar with the dynamical critical exponent z = 3 obtains scale-invariant, super-horizon field fluctuations without the need of an inflationary era. Since this mechanism is due to the special scaling of the Lifshitz scalar and persists in the presence of unsuppressed self-couplings, the resulting fluctuation spectrum can deviate from a Gaussian distribution. We study the non-Gaussian nature of the Lifshitz scalar's intrinsic field fluctuations, and show that primordial curvature perturbations sourced from such field fluctuations can have large non-Gaussianity of order f_NL = O(100), which will be detected by upcoming CMB observations. We compute the bispectrum and trispectrum of the fluctuations, and discuss their configurations in momentum space. In particular, the bispectrum is found to take various shapes, including the local, equilateral, and orthogonal shapes. Intriguingly, all integrals in the in-in formalism can be performed analytically.Comment: 17 pages, 15 figures, v2: published in JCA

Trispectrum from Ghost Inflation

Ghost inflation predicts almost scale-invariant primordial cosmological perturbations with relatively large non-Gaussianity. The bispectrum is known to have a large contribution at the wavenumbers forming an equilateral triangle and the corresponding nonlinear parameter $f_{NL}^{equil}$ is typically of order $O(10^2)$. In this paper we calculate trispectrum from ghost inflation and show that the corresponding nonlinear parameter $\tau_{NL}$ is typically of order $O(10^4)$. We investigate the shape dependence of the trispectrum and see that it has some features different from DBI inflation. Therefore, our result may be useful as a template to distinguish ghost inflation from other models of inflation by future experiments.Comment: 25 pages, 10 figure