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Soft de Sitter Effective Theory
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Soft de Sitter Effective Theory
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Calculating the quantum evolution of a de Sitter universe on superhorizon scales is notoriously difficult. To address this challenge, we introduce the Soft de Sitter Effective Theory (SdSET). This framework holds for superhorizon modes whose comoving momentum is far below the UV scale, which is set by the inverse comoving horizon. The SdSET is formulated using the same approach that yields the Heavy Quark Effective Theory. The degrees of freedom that capture the long wavelength dynamics are identified with the growing and decaying solutions to the equations of motion. The operator expansion is organized using a power counting scheme, and loops can be regulated while respecting the low energy symmetries. For massive quantum fields in a fixed de Sitter background, power counting implies that all interactions beyond the horizon are irrelevant. Alternatively, if the fields are very light, the leading interactions are at most marginal, and resumming the associated logarithms using (dynamical) renormalization group techniques yields the evolution equation for canonical stochastic inflation. The SdSET is also applicable to models where gravity is dynamical, including inflation. In this case, diffeomorphism invariance ensures that all interactions are irrelevant, trivially implying the all-orders conservation of adiabatic density fluctuations and gravitational waves. We briefly touch on the application to slow-roll eternal inflation by identifying novel relevant operators. This work serves to demystify many aspects of perturbation theory outside the horizon, and has a variety of applications to problems of cosmological interest.
Forward citations
Cited by 10 Pith papers
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Quantum correction to the diffusion term in stochastic inflation from composite-operator matching in Soft de Sitter Effective Theory
The two-loop correction to the diffusion coefficient in stochastic inflation is computed for the first time via composite-operator renormalisation and matching in SdSET.
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Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching
Constructs open EFT for stochastic inflation with stochastic RG channel, nonlocal Wilson kernels, and derived master equations matched to full theory via method-of-regions.
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Stochastic inflation from a non-equilibrium renormalization group
A generalized Fokker-Planck equation for stochastic inflation is derived from a Polchinski-type renormalization group flow on the density matrix, incorporating dissipative and diffusive corrections beyond the leading order.
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A consistent formulation of stochastic inflation I: Non-Markovian effects and issues beyond linear perturbations
The conventional truncation in stochastic inflation is inconsistent because quadratic-noise contributions are the same perturbative order as the deterministic non-Markovian corrections.
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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 th...
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Stochastic inflation as an open quantum system II: open effective field theory and stochastic matching
Develops open EFT for stochastic inflation with a distinct stochastic RG channel, derives nonlocal master equations including Fokker-Planck and Klein-Kramers forms, and demonstrates stochastic renormalization with an ...
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Nonperturbative stochastic inflation in perturbative dynamical background
Derives stochastic equations from Schwinger-Keldysh formalism that include quantum diffusion and classical metric perturbations for non-perturbative ultra-slow-roll inflation, validated on Starobinsky and critical Hig...
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Matching second-order classical and 1-loop quantum tensor power spectra in de Sitter spacetime
Classical part of 1-loop tensor power spectrum in de Sitter is IR divergent but cancels with vacuum part, enabling non-perturbative renormalization to extract unaffected physical information.
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A Compact Story of Positivity in de Sitter
Compares two methods to resolve disagreements and prove positivity of anomalous dimensions for principal series fields coupled to compact scalar operators in de Sitter space.
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From inflation to hot big bang -- a tutorial on cosmological perturbations
A tutorial deriving cosmological perturbation equations from inflation through reheating, with explicit gauge-invariant computations and Python scripts.
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