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Register a new userNumerically evaluating the bispectrum in curved field-space - with PyTransport 2.0
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We extend the transport framework for numerically evaluating the power spectrum and bispectrum in multi-field inflation to the case of a curved field-space metric. This method naturally accounts for all sub- and super-horizon tree level effects, including those induced by the curvature of the field-space. We present an open source implementation of our equations in an extension of the publicly available PyTransport code. Finally we illustrate how our technique is applied to examples of inflationary models with a non-trivial field-space metric.
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We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or delta-N expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.
We evaluate the dimensionless non-Gaussianity parameter $h_{_{rm NL}}$, that characterizes the amplitude of the tensor bispectrum, numerically for a class of two field inflationary models such as double inflation, hybrid inflation and aligned natural inflation. We compare the numerical results with the slow roll results which can be obtained analytically. In the context of double inflation, we also investigate the effects on $h_{_{rm NL}}$ due to curved trajectories in the field space. We explicitly examine the validity of the consistency relation governing the tensor bispectrum in the squeezed limit. Lastly, we discuss the contribution to $h_{_{rm NL}}$ due to the epoch of preheating in two field models.
Massive fields during inflation provide an interesting opportunity to test new physics at very high energy scales. Meanwhile in fundamental realizations, the inflationary field space typically has a curved geometry, which may leave detectable imprints in primordial observables. In this paper we study an extension of quasi-single field inflation where the inflaton and the massive field belong to a curved field manifold. Because of the nontrivial field space curvature, the massive field here can get significant mass corrections of order the Hubble scale, thus the quasi-single field predictions on primordial non-Gaussianity are affected. We derive the same result in an equivalent approach by using the background effective field theory of inflation, where a dimension-6 operator is identified to play an important role and its cutoff scale is associated with the curvature scale of the field space. In addition, due to the slow-roll evolution of the inflaton, this type of mass correction has intrinsic time-dependence. Consequently, the running mass modifies the scaling behaviour in the squeezed limit of the scalar bispectrum, while the resulting running index measures the curvature of the internal field space. Therefore the minimal setup of a massive field within curved field space during inflation may naturally lead to new observational signatures of the field space geometry.
We study the angular bispectrum of local type arising from the (possibly correlated) combination of a primordial adiabatic mode with an isocurvature one. Generically, this bispectrum can be decomposed into six elementary bispectra. We estimate how precisely CMB data, including polarization, can enable us to measure or constrain the six corresponding amplitudes, considering separately the four types of isocurvature modes (CDM, baryon, neutrino density, neutrino velocity). Finally, we discuss how the model-independent constraints on the bispectrum can be combined to get constraints on the parameters of multiple-field inflation models.
One of the most pressing questions in modified gravity is how deviations from general relativity can manifest in upcoming galaxy surveys. This is especially relevant for theories exhibiting Vainshtein screening, where such deviations are efficiently suppressed within a (typically large) Vainshtein radius. However, Vainshtein screening is known to be shape dependent: it is most effective around spherical sources, weaker around cylindrical objects and completely absent for planar sources. The Cosmic Web therefore offers a testing ground, as it displays many shapes in the form of clusters, filaments and walls. In this work, we explicitly derive the signature of the shape dependence of Vainshtein screening on the matter bispectrum, by considering a cubic Galileon model with a conformal coupling to matter and a cosmological constant. We perform a second order perturbative analysis, deriving analytic, integral expressions for the bispectrum, which we integrate using hi_class. We find that the shape dependence of Vainshtein screening enters the bispectrum with a unique scale-factor dependence of $propto a^{3/2}$. The magnitude of the effect today is up to 2 % for a model whose linear growth rate deviates up to 5 % from $Lambda$CDM.
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