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Register a new userAnisotropic Non-Gaussianity from a Two-Form Field
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We study an inflationary scenario with a two-form field to which an inflaton couples non-trivially. First, we show that anisotropic inflation can be realized as an attractor solution and that the two-form hair remains during inflation. A statistical anisotropy can be developed because of a cumulative anisotropic interaction induced by the background two-form field. The power spectrum of curvature perturbations has a prolate-type anisotropy, in contrast to the vector models having an oblate-type anisotropy. We also evaluate the bispectrum and trispectrum of curvature perturbations by employing the in-in formalism based on the interacting Hamiltonians. We find that the non-linear estimators $f_{NL}$ and $tau_{NL}$ are correlated with the amplitude $g_*$ of the statistical anisotropy in the power spectrum. Unlike the vector models, both $f_{NL}$ and $tau_{NL}$ vanish in the squeezed limit. However, the estimator $f_{NL}$ can reach the order of 10 in the equilateral and enfolded limits. These results are consistent with the latest bounds on $f_{NL}$ constrained by Planck.
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We study scalar-tensor-tensor cross correlation $langle zeta hh rangle$ generated by the dynamics of interacting axion and SU(2) gauge fields during inflation. We quantize the quadratic action and solve the linear equations by taking into account mixing terms in a non-perturbative manner. Combining that with the in-in formalism, we compute contributions from cubic interactions to the bispectrum $B_{zeta hh}$. We find that the bispectrum is peaked at the folded configuration, which is a unique feature encoded by the scalar mixing and localized production of tensor modes. With our parameter choice, the amplitude of the bispectrum is $k^6 B_{zeta hh} sim 10^{-16}$. The unique shape dependence, together with the parity-violating nature, is thus a distinguishing feature to search for in the CMB observables.
The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.
Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition - such as in the case of smooth transition or some sharp transition scenarios - the $mathcal{O}(1)$ local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.
We study the scalar-tensor-tensor non-Gaussian signal in an inflationary model comprising also an axion coupled with SU(2) gauge fields. In this set-up, metric fluctuations are sourced by the gauge fields already at the linear level providing an enhanced chiral gravitational waves spectrum. The same mechanism is at work in generating an amplitude for the three-point function that is parametrically larger than in standard single-field inflation.
We demonstrate equivalence of the in-in formalism and Greens function method for calculating the bispectrum of primordial gravitational waves generated by vacuum fluctuations of the metric. The tree-level bispectrum from the field equation, $B_h$, agrees with the results obtained previously using the in-in formalism exactly. Characterising non-Gaussianity of the fluctuations using the ratio $B_h/P^2_h$ in the equilateral configuration, where $P_h$ is the power spectrum of scale-invariant gravitational waves, we show that it is much weaker than in models with spectator gauge fields. We also calculate the tree-level bispectrum of two right-handed and one left-handed gravitational wave using Greens function, reproducing the results from in-in formalism, and show that it can be as large as the bispectrum of three right-handed gravitational waves.
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