Dynamical Constraints on RG Flows and Cosmology

Abstract

Sum rules connecting low-energy observables to high-energy physics are an interesting way to probe the mechanism of inflation and its ultraviolet origin. Unfortunately, such sum rules have proven difficult to study in a cosmological setting. Motivated by this problem, we investigate a precise analogue of inflation in anti-de Sitter spacetime, where it becomes dual to a slow renormalization group flow in the boundary quantum field theory. This dual description provides a firm footing for exploring the constraints of unitarity, analyticity, and causality on the bulk effective field theory. We derive a sum rule that constrains the bulk coupling constants in this theory. In the bulk, the sum rule is related to the speed of radial propagation, while on the boundary, it governs the spreading of nonlocal operators. When the spreading speed approaches the speed of light, the sum rule is saturated, suggesting that the theory becomes free in this limit. We also discuss whether similar results apply to inflation, where an analogous sum rule exists for the propagation speed of inflationary fluctuations.

37 pages, 6 figures

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Cited by in corpus (29)

• The Cosmological Optical Theorem
• Building a Boostless Bootstrap for the Bispectrum
• Cutting Cosmological Correlators
• The Inflationary Wavefunction from Analyticity and Factorization
• Quantum loop effects on the power spectrum and constraints on primordial black holes
• The Boostless Bootstrap: Amplitudes without Lorentz boosts
• The Speed of Gravity
• On the time evolution of cosmological correlators
• No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
• Causality in Curved Spacetimes: The Speed of Light & Gravity
• On the Symmetries of Cosmological Perturbations
• From Amplitudes to Contact Cosmological Correlators
• Causal Effective Field Theories
• Gravitational Regge bounds
• Positivity Bounds without Boosts
• Dispersion Formulas in QFTs, CFTs, and Holography
• Evading no-go for PBH formation and production of SIGWs using Multiple Sharp Transitions in EFT of single field inflation
• Large fluctuations and Primordial Black Holes
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Spinning Sum Rules for the Dimension-Six SMEFT
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Inflationary Adler Conditions
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Multipositivity Bounds for Scattering Amplitudes
• Microcausality without Lorentz invariance
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• RG flows in de Sitter: c-functions and sum rules
• A Tail of Eternal Inflation