3 research outputs found
Analytical approximations for curved primordial power spectra
We extend the work of Contaldi et al. and derive analytical approximations
for primordial power spectra arising from models of inflation which include
primordial spatial curvature. These analytical templates are independent of any
specific inflationary potential and therefore illustrate and provide insight
into the generic effects and predictions of primordial curvature, manifesting
as cut-offs and oscillations at low multipoles and agreeing with numerical
calculations. We identify through our analytical approximation that the effects
of curvature can be mathematically attributed to shifts in the wavevectors
participating dynamically.Comment: 11 pages, 2 figures, supplementary material available at
https://doi.org/10.5281/zenodo.4024321. v1: As submitted to PRD. v2: As
published in PRD (with only minor additions between v1 and v2
On Graviton non-Gaussianities in the Effective Field Theory of Inflation
We derive parity-even graviton bispectra in the Effective Field Theory of
Inflation (EFToI) to all orders in derivatives. Working in perturbation theory,
we construct all cubic interactions that can contribute to tree-level graviton
bispectra, showing that they all come from EFToI operators containing two or
three powers of the extrinsic curvature and its covariant derivatives: all
other operators can be removed by field redefinitions or start at higher-order
in perturbations. For operators cubic in the extrinsic curvature, where the
single-clock consistency relations are satisfied without a correction to the
graviton two-point function, we use the Manifestly Local Test (MLT) to
efficiently extract the effects of evolving graviton fluctuations to the end of
inflation. Despite the somewhat complicated nature of the bulk interactions,
the final boundary correlators take a very compact form. For operators
quadratic in the extrinsic curvature, the leading order bispectra are a sum of
contact and single exchange diagrams, which are tied together by spatial
diffeomorphisms, and to all orders in derivatives we derive these bispectra by
computing the necessary bulk time integrals. For single exchange diagrams we
exploit factorisation properties of the bulk-bulk propagator for massless
gravitons and write the result as a finite sum over residues. Perhaps
surprisingly, we show these single exchange contributions have only
total-energy poles and also satisfy the MLT
On graviton non-Gaussianities in the Effective Field Theory of Inflation
Abstract
We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT.</jats:p