A general proof of the equivalence between the \delta N and covariant formalisms

Recently, the equivalence between the \delta N and covariant formalisms has been shown (Suyama et al. 2012), but they essentially assumed Einstein gravity in their proof. They showed that the evolution equation of the curvature covector in the covariant formalism on uniform energy density slicings coincides with that of the curvature perturbation in the \delta N formalism assuming the coincidence of uniform energy and uniform expansion (Hubble) slicings, which is the case on superhorizon scales in Einstein gravity. In this short note, we explicitly show the equivalence between the \delta N and covariant formalisms without specifying the slicing condition and the associated slicing coincidence, in other words, regardless of the gravity theory.Comment: 7 pages,a reference added, to be published in EP

Conservation of the nonlinear curvature perturbation in generic single-field inflation

It is known that the curvature perturbation on uniform energy density (or comoving or uniform Hubble) slices on superhorizon scales is conserved to full nonlinear order if the pressure is only a function of the energy density (ie, if the perturbation is purely adiabatic), independent of the gravitational theory. Here we explicitly show that the same conservation holds for a universe dominated by a single scalar field provided that the field is in an attractor regime, for a very general class of scalar field theories. However, we also show that if the scalar field equation contains a second time derivative of the metric, as in the case of the Galileon theory, one has to invoke the gravitational field equations to show the conservation.Comment: 6 pages, minor revisions made but conclusion unchanged, references added, to be published in CQG as a fast track communicatio

Conditions for large non-Gaussianity in two-field slow-roll inflation

We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_nl in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bound of |f_nl|<100.Comment: 16 pages, 6 figures, 1 table, v2: typos corrected and references added, matches version accepted by JCA

Spectral Index and Non-Gaussianity in Supersymmetric Hybrid Inflation

We consider a supersymmetric hybrid inflation model with two inflaton fields. The superpotential during inflation is dominated by W=(\kappa S+\kappa' S')M^2, where S, S' are inflatons carrying the same U(1)_R charge, \kappa, \kappa' are dimensionless couplings, and M (\sim 10^{15-16} GeV) is a dimensionful parameter associated with a symmetry breaking scale. One light mass eigenstate drives inflation, while the other heavier mass eigenstate is stuck to the origin. The smallness of the lighter inflaton mass for the scalar spectral index n_s\approx 0.96, which is the center value of WMAP7, can be controlled by the ratio \kappa'/\kappa through the supergravity corrections. We also discuss the possibility of the two field inflation and large non-Gaussianity in this setup.Comment: 17 pages, 2 figures, version published in Eur. Phys. J.

Planck 2015 results. XX. Constraints on inflation

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 ± 0.006 and tightly constrain its scale dependence to dn s /dlnk = −0.003 ± 0.007 when combined with the Planck lensing likelihood. When the high-ℓ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 <0.11 (95% CL), consistent with the B-mode polarization constraint r<0.12 (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that V(ϕ)∝ϕ 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data

Beyond δN formalism

International audienc