We present a consistent δN formalism for curvature perturbations in anisotropic cosmological backgrounds. We employ our δN formalism to calculate the power spectrum, the bispectrum and the trispectrum in models of anisotropic inflation with the background gauge fields in Bianchi I universe. Our results coincide exactly with the recent results obtained from in-in formalism. To satisfy the observational constraints the anisotropies generated on power spectrum are kept small but large orientation-dependent non-Gaussianities can be generated. We study the Suyama-Yamaguchi inequality for the amplitudes of the bispectrum and the trispectrum in the presence of anisotropic shapes. * Electronic address: abolhasani-AT-ipm.ir † Electronic address: emami-AT-ipm.ir ‡ Electronic address: j.taghizadeh.f-AT-ipm.ir § Electronic address: firouz-AT-mail.ipm.ir or gauge fields but the effects of anisotropic background were not taken into account, i.e. the gauge field is treated on the same footing as the scalar fields in an FRW background. In this work we present a consistent δN formalism for anisotropic backgrounds such as in [16] in which the background metric is in the form of Bianchi I. After presenting our δN formalism we calculate the power spectrum and reproduce exactly the results in [45,48]. We also calculate the bispectrum which coincides exactly with the results of [48].Planck is expected to release its data soon. Any detection or otherwise of primordial non-Gaussianities from Planck will have significant implications for inflationary model buildings. Simple models of inflation predict almost scale-invariant and almost Gaussian perturbations. Therefore, any detection of primordial non-Gaussianity will go a long way to rule out or classify different inflationary scenarios. Non-Gaussianity may take different shapes in different models, for a review see [60,61]. In models of inflation based on scalar fields the shapes of Bispectrum and Trispectrum are statistically isotropic. However, in models of anisotropic inflation, one obtains new shapes which are anisotropic.As an important consistency condition for single field inflation, a detection of local form bispectrum in the squeezed limit can rule out all single field models of inflation provided the system reaches the attractor solution [62,63] so one can neglect the evolution of curvature perturbations on super-horizon scales and the curvature perturbations have the initial Bunch-Davies vacuum state [64,65]. As a different consistency condition, the Suyama-Yamaguchi (SY) inequality [66], [67], [68, 69] between the amplitude of the Bispectrum in the squeezed limit, f N L , and the amplitude of the trispectrum in the collapsed limit, τ N L , are expected to hold generally in models of inflation based on scalar fields. It is an interesting question to see if the SY inequality holds when the primordial perturbations are not statistically isotropic. We will study this question in the context of anisotropic inflation.The rest of the paper is organized as follows. In Section II we...

International audienceNumerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples

Application of concepts like black hole and event horizon in cosmological context are not trivial, as has been shown in the last decade. We introduce special solutions of the LTB family representing collapsing over-dense regions extending to an expanding closed, open, or flat FRW model asymptotically. We study the dynamics of the collapsing region, and its density profile. The question of the strength of the central singularity and its nakedness, as well as the existence of an apparent horizon and an event horizon is dealt with in detail. Differences to the Schwarzschild black hole are addressed.Comment: 9 pages, 6 figure

Most of the inflationary scenarios that try to explain the origin of Primordial Black Holes (PBHs) from the enhancements of the power spectrum to values of order one, at the relevant scales, run into clashes with the Effective Field Theory (EFT) criteria or fail to enhance the power spectrum to such large amplitudes. In this paper, we unravel a mechanism for enhancing the power spectrum during inflation that does not use the flattening of the potential or reduction of the sound speed of scalar perturbations. The mechanism is based on this observation in the formalism of Extended EFT of inflation (EEFToI) with the sixth order polynomial dispersion relation for scalar perturbations that if the quartic coefficient in the dispersion relation is negative and smaller than a certain threshold, the amplitude of the power spectrum is enhanced substantially. The instability mechanism must arrange to kick in at the scales of interest related to the mass of the PBHs one would like to produce, which can be ten(s) of solar mass PBHs, suitable for LIGO events, or 10−17− 10−13 solar mass PBHs, which can comprise the whole dark matter energy density. We argue that the strong coupling is avoided for the range of parameters that the mechanisms enhance the power spectrum to the required amount.