Cosmological ${\alpha }^{\prime }$-corrections from the functional renormalization group

Abstract

We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale ${\alpha }^{\prime }$. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimension $D$, which is however incompatible with Einstein gravity at low energies. Within an $\epsilon$-expansion about $D=2$, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution in $D=4$. Finally, we comment on potential cosmological implications of our findings.

arXiv comment31 pages, 9 figures. V2: References added and minor modifications. Matches published version

References in corpus (51)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Loop Quantum Cosmology: A Status Report
• Nonperturbative Evolution Equation for Quantum Gravity
• The Exact Renormalisation Group and Approximate Solutions
• The Swampland: Introduction and Review
• Double Field Theory
• Optimised Renormalisation Group Flows
• Distance and de Sitter Conjectures on the Swampland
• Generalized metric formulation of double field theory
• The nonperturbative functional renormalization group and its applications
• Renormalization group improved black hole spacetimes
• De Sitter Space and the Swampland
• Bounds on Slow Roll and the de Sitter Swampland
• Nonperturbative Quantum Gravity
• Double Field Theory: A Pedagogical Review
• Quantum Gravity from Causal Dynamical Triangulations: A Review
• Approaches to Quantum Cosmology
• Symmetries of higher-order string gravity actions
• Quantum cosmology: a review
• Scaling Exponents in Quantum Gravity near Two Dimensions
• Ultraviolet Stable Fixed Point and Scaling Relations in 2+$\epsilon$ Dimensional Quantum Gravity
• Convergence of Non-Perturbative Approximations to the Renormalization Group
• A second-order phase transition in CDT
• Background Field Equations for the Duality Symmetric String
• de Sitter Space in Non-Critical String Theory
• Duality Invariant Cosmology to all Orders in ${\alpha }^{\prime }$
• Evidence for Asymptotic Safety from Lattice Quantum Gravity
• Non-perturbative unitarity and fictitious ghosts in quantum gravity
• Lattice Quantum Gravity and Asymptotic Safety
• Renormalizability of Quantum Gravity near Two Dimensions
• Two-loop Prediction for Scaling Exponents in (2 + ε)-dimensional Quantum Gravity
• Towards reconstructing the quantum effective action of gravity
• A Double Sigma Model for Double Field Theory
• O$(d,d)$ covariant String Cosmology to all orders in ${\alpha }^{\prime }$
• Asymptotic safety, string theory and the weak gravity conjecture
• Non-perturbative de Sitter vacua via ${\alpha }^{\prime }$ corrections
• $AdS$ Vacua from Dilaton Tadpoles and Form Fluxes
• T-duality Constraints on Higher Derivatives Revisited
• O(D,D) and the string ${\alpha }^{\prime }$ expansion: An obstruction
• String Dualities at Order ${\alpha }^{\prime 3}$
• String Tension between de Sitter vacua and Curvature Corrections
• Functional Renormalization Group flows on Friedman-Lema\^ıtre-Robertson-Walker backgrounds
• ${\alpha }^{\prime }$-Cosmology: solutions and stability analysis
• New non-perturbative de Sitter vacua in ${\alpha }^{\prime }$-complete cosmology
• The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
• Universal critical behavior in tensor models for four-dimensional quantum gravity
• Construct ${\alpha }^{\prime }$ corrected or loop corrected solutions without curvature singularities
• A Lorentz invariant doubled worldsheet theory
• Searching for a continuum limit in causal dynamical triangulation quantum gravity
• de Sitter, ${\alpha }^{\prime }$-Corrections & Duality Invariant Cosmology

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• Cosmology at the top of the ${\alpha }^{\prime }$ tower
• No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology
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• Flowing in discrete gravity models and Ward identities: A review
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Configuration space for quantum gravity in a locally regularized path integral
• Kalb-Ramond backgrounds in ${\alpha }^{\prime }$-complete cosmology
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Lectures in Quantum Gravity
• Stability of the non-perturbative $O(D,D)$ de-Sitter spacetime. The isotropic case
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