A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
$\delta N$ formalism from superpotential and holography
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abstract
We consider the superpotential formalism to describe the evolution of scalar fields during inflation, generalizing it to include the case with non-canonical kinetic terms. We provide a characterization of the attractor behaviour of the background evolution in terms of first and second slow-roll parameters (which need not be small). We find that the superpotential is useful in justifying the separate universe approximation from the gradient expansion, and also in computing the spectra of primordial perturbations around attractor solutions in the $\delta N$ formalism. As an application, we consider a class of models where the background trajectories for the inflaton fields are derived from a product separable superpotential. In the perspective of the holographic inflation scenario, such models are dual to a deformed CFT boundary theory, with $D$ mutually uncorrelated deformation operators. We compute the bulk power spectra of primordial adiabatic and entropy cosmological perturbations, and show that the results agree with the ones obtained by using conformal perturbation theory in the dual picture.
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Orbital Inflation reconstructs two-field actions with an angular isometry yielding single-field-like predictions that violate consistency relations and allow f_NL from slow-roll suppressed to O(few) depending on entropy mass and self-interactions.
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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
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Orbital Inflation: inflating along an angular isometry of field space
Orbital Inflation reconstructs two-field actions with an angular isometry yielding single-field-like predictions that violate consistency relations and allow f_NL from slow-roll suppressed to O(few) depending on entropy mass and self-interactions.