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...
We study curvature perturbations in the anisotropic inflationary model with a complex scalar field charged under a U (1) gauge field in Bianchi I universe. Due to Abelian Higgs mechanism, the gauge field receives an additional longitudinal mode. We verify that the dominant contributions into statistical anisotropies come from matter fields perturbations and one can neglect the contributions from the metric perturbations. It is shown that the contribution of longitudinal mode into the statistical anisotropy power spectrum, though exponentially small, has an opposite sign compared to the corresponding contribution from the transverse mode. We obtain an upper bound on gauge coupling in order to satisfy the observational constraints on curvature perturbations anisotropy.
We present the first Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A*), the Galactic center source associated with a supermassive black hole. These observations were conducted in 2017 using a global interferometric array of eight telescopes operating at a wavelength of λ = 1.3 mm. The EHT data resolve a compact emission region with intrahour variability. A variety of imaging and modeling analyses all support an image that is dominated by a bright, thick ring with a diameter of 51.8 ± 2.3 μas (68% credible interval). The ring has modest azimuthal brightness asymmetry and a comparatively dim interior. Using a large suite of numerical simulations, we demonstrate that the EHT images of Sgr A* are consistent with the expected appearance of a Kerr black hole with mass ∼4 × 106 M ⊙, which is inferred to exist at this location based on previous infrared observations of individual stellar orbits, as well as maser proper-motion studies. Our model comparisons disfavor scenarios where the black hole is viewed at high inclination (i > 50°), as well as nonspinning black holes and those with retrograde accretion disks. Our results provide direct evidence for the presence of a supermassive black hole at the center of the Milky Way, and for the first time we connect the predictions from dynamical measurements of stellar orbits on scales of 103–105 gravitational radii to event-horizon-scale images and variability. Furthermore, a comparison with the EHT results for the supermassive black hole M87* shows consistency with the predictions of general relativity spanning over three orders of magnitude in central mass.
We consider models of inflation with U (1) gauge fields and charged scalar fields including symmetry breaking potential, chaotic inflation and hybrid inflation. We show that there exist attractor solutions where the anisotropies produced during inflation becomes comparable to the slow-roll parameters. In the models where the inflaton field is a charged scalar field the gauge field becomes highly oscillatory at the end of inflation ending inflation quickly.Furthermore, in charged hybrid inflation the onset of waterfall phase transition at the end of inflation is affected significantly by the evolution of the background gauge field. Rapid oscillations of the gauge field and its coupling to inflaton can have interesting effects on preheating and non-Gaussianities.
Many inflation models predict that primordial density perturbations have a nonzero three-point correlation function, or bispectrum in Fourier space. Of the several possibilities for this bispectrum, the most commmon is the local-model bispectrum, which can be described as a spatial modulation of the small-scale (largewavenumber) power spectrum by long-wavelength density fluctuations. While the local model predicts this spatial modulation to be scale-independent, many variants have some scale-dependence. Here we note that this scale dependence can be probed with measurements of frequency-spectrum distortions in the cosmic microwave background (CMB), in particular highlighting Compton-y distortions. Dissipation of primordial perturbations with wavenumbers 50 Mpc −1 k 10 4 Mpc −1 give rise to chemical-potential (µ) distortions, while those with wavenumbers 1 Mpc −1 k 50 Mpc −1 give rise to Compton-y distortions. With local-model non-Gaussianity, the distortions induced by this dissipation can be distinguished from those due to other sources via their crosscorrelation with the CMB temperature T . We show that the relative strengths of the µT and yT correlations thus probe the scale-dependence of non-Gaussianity and estimate the magnitude of possible signals relative to sensitivities of future experiments. We discuss the complementarity of these measurements with other probes of squeezed-limit non-Gaussianity.
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