Different dimensional regularization schemes agree with each other and with unitarity; new analytic eta regulators simplify the work and fix the imaginary part of one-loop coefficients by the logarithmic running of the real part under scale invariance and Bunch-Davies conditions.
On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation
5 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Studying loop corrections to inflationary perturbations, with particular emphasis on infrared factors, is important to understand the consistency of the inflationary theory, its predictivity and to establish the existence of the slow-roll eternal inflation phenomena and its recently found volume bound. In this paper we prove that the zeta correlation function is time-independent at one-loop level in single clock inflation. While many of the one-loop diagrams lead to a time-dependence when considered individually, the time-dependence beautifully cancels out in the overall sum. We identify two subsets of diagrams that cancel separately due to different physical reasons. The first cancellation is related to the change of the background cosmology due to the renormalization of the stress tensor. It results in a cancellation between the non-1PI diagrams and some of the diagrams made with quartic vertices. The second subset of diagrams that cancel is made up of cubic operators, plus the remaining quartic ones. We are able to write the sum of these diagrams as the integral over a specific three-point function between two very short wavelengths and one very long one. We then apply the consistency condition for this three-point function in the squeezed limit to show that the sum of these diagrams cannot give rise to a time dependence. This second cancellation is thus a consequence of the fact that in single clock inflation the attractor nature of the solution implies that a long wavelength zeta perturbation is indistinguishable from a trivial rescaling of the background, and so results in no physical effect on short wavelength modes.
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background 2representative citing papers
The authors define a locality condition for hard-mode states during inflation that unifies local effective dynamics for soft modes, suppression of loop corrections, generalized soft theorems, and absence of infrared divergences in observable correlators.
A new UV in-in algorithm for inflationary loops identifies renormalization difficulties and distinguishable finite corrections to the one-loop bispectrum in EFT inflation.
Tree-level multi-soft theorems for scalar and graviton correlation functions are derived at leading soft order via background-wave coordinate rescaling, including tensor exchanges in scalars and scalar exchanges in tensors.
Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.
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Unitary and Analytic Renormalisation of Cosmological Correlators
Different dimensional regularization schemes agree with each other and with unitarity; new analytic eta regulators simplify the work and fix the imaginary part of one-loop coefficients by the logarithmic running of the real part under scale invariance and Bunch-Davies conditions.
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Locality in effective field theory for inflationary soft modes
The authors define a locality condition for hard-mode states during inflation that unifies local effective dynamics for soft modes, suppression of loop corrections, generalized soft theorems, and absence of infrared divergences in observable correlators.
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Finite parts of inflationary loops II: A streamlined UV in-in algorithm and distinguishable signatures
A new UV in-in algorithm for inflationary loops identifies renormalization difficulties and distinguishable finite corrections to the one-loop bispectrum in EFT inflation.
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Multi-soft theorems for cosmological correlators: Background wave method for scalars & gravitons
Tree-level multi-soft theorems for scalar and graviton correlation functions are derived at leading soft order via background-wave coordinate rescaling, including tensor exchanges in scalars and scalar exchanges in tensors.
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Fixing the Renormalization of Inflationary Loops via Ward Identities
Ward identities from large gauge symmetry impose model-independent constraints on renormalizing inflationary loops and non-perturbatively govern the infrared power spectrum evolution.