Escher in the Sky

Abstract

The cosmological models called $\alpha$-attractors provide an excellent fit to the latest observational data. Their predictions $n_s=1-2/N$ and $r=12\alpha /N^2$ are very robust with respect to the modifications of the inflaton potential. An intriguing interpretation of $\alpha$-attractors is based on a geometric moduli space with a boundary: a Poincare disk model of a hyperbolic geometry with the radius $\sqrt{3\alpha }$, beautifully represented by the Escher's picture Circle Limit IV. In such models, the amplitude of the gravitational waves is proportional to the square of the radius of the Poincare disk.

11 pages, 12 figures, Introductory part is extended, references added

References in corpus (11)

• The Standard Model Higgs boson as the inflaton
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Monodromy in the CMB: Gravity Waves and String Inflation
• The Anthropic Landscape of String Theory
• The Unity of Cosmological Attractors
• Simple de Sitter Solutions
• Planck, LHC, and $\alpha$-attractors
• Single-field $\alpha$-attractors
• Cosmological Attractors from $\alpha$-Scale Supergravity
• Does the first chaotic inflation model in supergravity provide the best fit to the Planck data?
• Planck 2015 results. XX. Constraints on inflation

Cited by in corpus (78)

• Cosmological Attractors and Initial Conditions for Inflation
• Planck, LHC, and $\alpha$-attractors
• The Hyperbolic Geometry of Cosmological Attractors
• Dark energy, $\alpha$-attractors, and large-scale structure surveys
• Single-field $\alpha$-attractors
• Primordial Black Holes from String Inflation
• Hyperinflation
• Primordial fluctuations and non-Gaussianities in sidetracked inflation
• Robust Inflation from Fibrous Strings
• Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds
• A Geometrical Upper Bound on the Inflaton Range
• BICEP/Keck Constraints on Attractor Models of Inflation and Reheating
• Implications of Planck2015 for inflationary, ekpyrotic and anamorphic bouncing cosmologies
• Universality of multi-field $\alpha$-attractors
• Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation
• Generalized Pole Inflation: Hilltop, Natural, and Chaotic Inflationary Attractors
• Hybrid cosmological attractors
• Maximal Supersymmetry and B-Mode Targets
• Cosmological Attractors and Asymptotic Freedom of the Inflaton Field
• Hypernatural inflation
• Inflation from Nilpotent Kähler Corrections
• On the problem of initial conditions for inflation
• Inflatino-less Cosmology
• CMB targets after the latest Planck data release
• BICEP/Keck and Cosmological Attractors
• Polynomial $\alpha$-attractors
• On hilltop and brane inflation after Planck
• Inflationary quasi-scale invariant attractors
• On the inflationary massive field with a curved field manifold
• Position-dependent mass, finite-gap systems, and supersymmetry
• On Primordial Black Holes from Rapid Turns in Two-field Models
• Starobinsky-Type Inflation from ${\alpha }^{\prime }$-Corrections
• Sneutrino Inflation with $\alpha$-attractors
• Random Potentials and Cosmological Attractors
• A Tip for Landscape Riders: Multi-Field Inflation Can Fulfill the Swampland Distance Conjecture
• Dilaton-Axion Inflation with PBHs and GWs
• B-mode Targets
• Primordial black holes and inflation from double-well potentials
• Gravitational waves and large field inflation
• One residue to rule them all: Electroweak symmetry breaking, inflation and field-space geometry
• Pole N-flation
• $\alpha$-attractor inflation: Models and predictions
• On inflation, cosmological constant, and SUSY breaking
• Dark Energy from Inspiraling in Field Space
• Generalized two-field $\alpha$-attractor models from geometrically finite hyperbolic surfaces
• Two-field Cosmological $\alpha$-attractors with Noether Symmetry
• Pole-Induced Higgs Inflation With Hyperbolic Kaehler Geometries
• Hidden symmetries of two-field cosmological models
• M-theory Cosmology, Octonions, Error Correcting Codes
• U(1) symmetric $\alpha$-attractors
• Generalized two-field $\alpha$-attractors from the hyperbolic triply-punctured sphere
• Primordial Black Holes from non-Gaussian tails
• Multipoint correlators in multifield cosmology
• Gravity-Mediated SUSY Breaking, R Symmetry and Hyperbolic Kaehler Geometry
• Scale Factor Duality for Conformal Cyclic Cosmologies
• Generalized $\alpha$-attractor models from elementary hyperbolic surfaces
• Noether symmetry approach in the cosmological alpha-attractors
• Realising Mutated Hilltop Inflation in Supergravity
• Large and small field inflation from hyperbolic sigma models
• Supergravity, $\alpha$-attractors and primordial non-Gaussianity
• Introduction to the number of $e$-folds in slow-roll inflation
• An Alternative Framework for E-Model Inflation in Supergravity
• Cosmological flows on hyperbolic surfaces
• Coupling the Inflationary Sector to Matter
• Pole inflation in Jordan frame supergravity
• Constraining the quintessential $\alpha$-attractor inflation through dynamical horizon exit method
• Constraint percolation on hyperbolic lattices
• Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime
• Two-field cosmological models and the uniformization theorem
• An alternative attractor in gauged NJL inflation
• A New Class of Non-canonical Conformal Attractors for Multifield Inflation
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves
• Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential $\alpha$-attractor
• On solving dynamical equations in general homogeneous isotropic cosmologies with scalaron
• Are latest detected events of gravitational waves in favor of some models of inflation based on string theory?
• Ultra slow-turn inflation
• Adaptive asymptotic solutions of inflationary models in the Hamilton-Jacobi formalism: Application to T-models
• A novel way of constraining the $\alpha$-attractor chaotic inflation through Planck data