scholarly journals Stochastic Inflation at NNLO

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Timothy Cohen ◽  
Daniel Green ◽  
Akhil Premkumar ◽  
Alexander Ridgway
Keyword(s):  
Renormalization Group ◽  
Initial Conditions ◽  
Planck Equation ◽  
Effective Theory ◽  
Tree Level ◽  
Order Effects ◽  
De Sitter ◽  
Light Scalar ◽  
Non Gaussian ◽  
Group Flow

Abstract Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the probability distribution for a light scalar field as a function of time. Despite its successes, the quantum field theoretic origins and the range of validity for this equation have remained elusive, and establishing a formalism to systematically incorporate higher order effects has been an area of active study. In this paper, we calculate the next-to-next-to-leading order (NNLO) corrections to Stochastic Inflation using Soft de Sitter Effective Theory (SdSET). In this effective description, Stochastic Inflation manifests as the renormalization group evolution of composite operators. The leading impact of non-Gaussian quantum fluctuations appears at NNLO, which is presented here for the first time; we derive the coefficient of this term from a two-loop anomalous dimension calculation within SdSET. We solve the resulting equation to determine the NNLO equilibrium distribution and the low-lying relaxation eigenvalues. In the process, we must match the UV theory onto SdSET at one-loop order, which provides a non-trivial confirmation that the separation into Wilson-coefficient corrections and contributions to initial conditions persists beyond tree level. Furthermore, these results illustrate how the naive factorization of time and momentum integrals in SdSET no longer holds in the presence of logarithmic divergences. It is these effects that ultimately give rise to the renormalization group flow that yields Stochastic Inflation.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

scholarly journals Systematizing the effective theory of self-interacting dark matter

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Prateek Agrawal ◽  
Aditya Parikh ◽  
Matthew Reece
Keyword(s):  
Dark Matter ◽  
Cross Section ◽  
Axial Vector ◽  
Effective Theory ◽  
Tree Level ◽  
Low Velocity ◽  
Scattering Rate ◽  
Light Scalar ◽  
Sommerfeld Enhancement ◽  
Particle Nature

Abstract If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter scattering rate. To interpret such data, we should understand what predictions for this quantity are made by various models of the underlying particle nature of dark matter. In this paper, we systematically compute this function for fermionic dark matter with light bosonic mediators of vector, scalar, axial vector, and pseudoscalar type. We do this by matching to the nonrelativistic effective theory of self-interacting dark matter and then computing the spin-averaged viscosity cross section nonperturbatively by solving the Schrödinger equation, thus accounting for any possible Sommerfeld enhancement of the low-velocity cross section. In the pseudoscalar case, this requires a coupled-channel analysis of different angular momentum modes. We find, contrary to some earlier analyses, that nonrelativistic effects only provide a significant enhancement for the cases of light scalar and vector mediators. Scattering from light pseudoscalar and axial vector mediators is well described by tree-level quantum field theory.

RENORMALIZATION GROUP AND STRING LOOPS

1990 ◽  
Vol 05 (04) ◽  
pp. 589-658 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
Renormalization Group ◽  
Moduli Spaces ◽  
Tree Level ◽  
Generating Functional ◽  
String Loop ◽  
Schottky Type ◽  
String Amplitudes ◽  
Group Flow ◽  
Model Approach

The fixed points of the 2-d renormalization group flow are known to correspond to the tree level string vacua. We analyze how the “renormalization group” (or “sigma model”) approach can be extended to the string loop level. The central role of the condition of renormalizability of the generating functional for string amplitudes with respect to both “local” and “modular” infinities is emphasized. Several one- and two-loop examples of renormalization are discussed. It is found that in order to ensure the renormalizability of the generating functional one is to use “extended” (e.g. Schottky-type) parametrizations of moduli spaces. An approach to a resummation of the string perturbative expansion based on operators of insertion of topological fixtures is suggested.

scholarly journals Towards the Structure of Black Holes in Asymptotically Safe Gravity

2018 ◽  
Author(s):  
Adémólá Adéìféoba
Keyword(s):  
Black Holes ◽  
Fixed Point ◽  
Renormalization Group ◽  
Cosmological Constant ◽  
Critical Exponents ◽  
De Sitter ◽  
Renormalization Group Flow ◽  
Spacetime Singularity ◽  
Singularity Resolution ◽  
Group Flow

Asymptotically safe quantum gravity suggests a resolution to the classical spacetime singularity of Schwarzschild-(A)dS black holes. In particular, this is realizable only for a vanishing microscopic value of the dimensionless cosmological constant at the asymptotically safe fixed point. To accommodate a nonzero infrared value of the cosmological constant, we consider the linearized Renormalization Group flow away from the fixed point, which is characterized by two critical exponents in the Einstein-Hilbert truncation. In this study, we show that the realization of a regular de-Sitter core places a bound on the universal gravitational critical exponents. Accordingly, our study hints at the possibility of singularity resolution in black holes, as explicit estimates of the critical exponents in the literature point towards a realization of our bound.

EXTENDED CHAMSEDDINE–FRÖHLICH APPROACH TO NONCOMMUTATIVE GEOMETRY AND THE TWO-DOUBLETS HIGGS MODEL

2007 ◽  
Vol 22 (32) ◽  
pp. 6279-6305 ◽  
Author(s):  
N. MEBARKI ◽  
M. HARRAT ◽  
M. BOUSSAHEL
Keyword(s):  
Renormalization Group ◽  
Noncommutative Geometry ◽  
Scalar Product ◽  
Higgs Model ◽  
Tree Level ◽  
Quantization Method ◽  
Renormalization Group Flow ◽  
New Approach ◽  
Mixing Angles ◽  
Group Flow

The Chamseddine–Fröhlich approach to noncommutative geometry is extended by the introduction of the strong interaction sector in the mathematical formalism, and generalization of the Dirac operator and scalar product. This new approach is applied to the reformulation of the two-doublets Higgs model where the fuzzy mass, coupling and unitarity relations as well as mixing angles are derived. These tree level relations are no more preserved under the renormalization group flow in the context of the standard quantization method.

scholarly journals Ruppeiner curvature along a renormalization group flow

2021 ◽  
pp. 136450
Author(s):  
Pavan Kumar Yerra ◽  
Chandrasekhar Bhamidipati
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Group Flow

scholarly journals The scalar chemical potential in cosmological collider physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Arushi Bodas ◽  
Soubhik Kumar ◽  
Raman Sundrum
Keyword(s):  
Particle Production ◽  
Chemical Potential ◽  
Direct Detection ◽  
Heavy Particle ◽  
Scalar Particle ◽  
Energy Scale ◽  
Fine Tuning ◽  
Tree Level ◽  
Heavy Particles ◽  
Non Gaussian

Abstract Non-analyticity in co-moving momenta within the non-Gaussian bispectrum is a distinctive sign of on-shell particle production during inflation, presenting a unique opportunity for the “direct detection” of particles with masses as large as the inflationary Hubble scale (H). However, the strength of such non-analyticity ordinarily drops exponentially by a Boltzmann-like factor as masses exceed H. In this paper, we study an exception provided by a dimension-5 derivative coupling of the inflaton to heavy-particle currents, applying it specifically to the case of two real scalars. The operator has a “chemical potential” form, which harnesses the large kinetic energy scale of the inflaton, $$ {\overset{\cdot }{\phi}}_0^{1/2}\approx 60H $$ ϕ ⋅ 0 1 / 2 ≈ 60 H , to act as an efficient source of scalar particle production. Derivative couplings of inflaton ensure radiative stability of the slow-roll potential, which in turn maintains (approximate) scale-invariance of the inflationary correlations. We show that a signal not suffering Boltzmann suppression can be obtained in the bispectrum with strength fNL ∼ $$ \mathcal{O} $$ O (0.01–10) for an extended range of scalar masses $$ \lesssim {\overset{\cdot }{\phi}}_0^{1/2} $$ ≲ ϕ ⋅ 0 1 / 2 , potentially as high as 1015 GeV, within the sensitivity of upcoming LSS and more futuristic 21-cm experiments. The mechanism does not invoke any particular fine-tuning of parameters or breakdown of perturbation-theoretic control. The leading contribution appears at tree-level, which makes the calculation analytically tractable and removes the loop-suppression as compared to earlier chemical potential studies of non-zero spins. The steady particle production allows us to infer the effective mass of the heavy particles and the chemical potential from the variation in bispectrum oscillations as a function of co-moving momenta. Our analysis sets the stage for generalization to heavy bosons with non-zero spin.

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