The large-N running of the spectral index of inflation

Abstract

We extend previous classifications of inflationary models by means of their behaviour at large-N, where N is the number of e-foldings. In addition to the perturbative 1/N case, whose slow-roll parameters fall off as powers of 1/N, we introduce the constant, non-perturbative and logarithmic classes. This covers the large majority of inflationary models. Furthermore, we calculate the running of the spectral tilt for all these classes. Remarkably, we find that the tilt's runnings essentially cluster around the permil level. We comment on the implications for future experiments.

8 pages, 4 figures. v2: minor clarifications and refs added

References in corpus (2)

• The Best Inflationary Models After Planck
• Planck Data Reconsidered

Cited by in corpus (66)

• Primordial black holes from single field models of inflation
• The Unity of Cosmological Attractors
• Single Field Double Inflation and Primordial Black Holes
• Gravitational waves at interferometer scales and primordial black holes in axion inflation
• Investigating Cosmic Discordance
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• Exploring Cosmic Origins with CORE: Inflation
• Cosmological constraints in extended parameter space from the Planck 2018 Legacy release
• Updated Cosmological Constraints in Extended Parameter Space with Planck PR4, DESI Baryon Acoustic Oscillations, and Supernovae: Dynamical Dark Energy, Neutrino Masses, Lensing Anomaly, and the Hubble Tension
• The Observational Status of Cosmic Inflation after Planck
• Cosmological Attractors from $\alpha$-Scale Supergravity
• Cosmology in Extended Parameter Space with DESI Data Release 2 Baryon Acoustic Oscillations: A 2$\sigma$+ Detection of Nonzero Neutrino Masses with an Update on Dynamical Dark Energy and Lensing Anomaly
• Universality classes for models of inflation
• Towards a measurement of the spectral runnings
• Generalized Pole Inflation: Hilltop, Natural, and Chaotic Inflationary Attractors
• Maximal Supersymmetry and B-Mode Targets
• Implications of the scalar tilt for the tensor-to-scalar ratio
• The Lyth Bound of Inflation with a Tilt
• Constant-roll tachyon inflation and observational constraints
• New perspectives on constant-roll inflation
• The reconstruction of inflationary potentials
• $\mu$-Distortions or Running: A Guaranteed Discovery from CMB Spectrometry
• Reconstructing a $f(R)$ theory from the $\alpha$-Attractors
• Nonminimal coupling and inflationary attractors
• Reconstructing inflation in scalar-torsion $f(T,\varphi )$ gravity
• Reconstruction of constant slow-roll inflation
• Shortcomings of New Parametrizations of Inflation
• Reconstructing the inflaton potential from the spectral index
• Reconstructing warm inflation
• The present and future of the most favoured inflationary models after $Planck$ 2015
• The reconstruction of tachyon inflationary potentials
• Trans-Planckian censorship and single-field inflaton potential
• Reconstruction of extended inflationary potentials for attractors
• Cosmological constraints on nonphantom dynamical dark energy with DESI Data Release 2 Baryon Acoustic Oscillations: A 3$\sigma$+ lensing anomaly
• Can CMB data constrain the inflationary field range?
• Running and running of the running of the scalar spectral index in warm inflation
• Running of the Running and Entropy Perturbations During Inflation
• Exploring extensions to the standard cosmological model and the impact of baryons on small scales
• Phenomenological approaches of inflation and their equivalence
• Reconstructing G-inflation: From the attractors $n_S(N)$ and $r(N)$
• Tachyon inflation in the Large-$N$ formalism
• Approximate reconstruction of inflationary potential with ACT observations
• Reconstructing k-essence: Unifying the attractor $n_S(N)$ and the swampland criteria
• Theoretical and observational constraints on Tachyon Inflation
• On the Three Primordial Numbers
• The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials
• Probing the BSM physics with CMB precision cosmology: an application to supersymmetry
• The impact of theoretical assumptions in the determination of the neutrino effective number from future CMB measurements
• Large tensor-to-scalar ratio from Composite Inflation
• Effects of the speed of sound at large-N
• Swampland Constraints on No-Boundary Quantum Cosmology
• The Quest for the Inflationary Spectral Runnings in the Presence of Systematic Errors
• Non-standard hierarchies of the runnings of the spectral index in inflation
• Inflationary field excursion in broad classes of scalar field models
• The fate of Quasi-Exponential inflation in the light of ACT-DR6
• An Inflationary Equation of State
• Inflationary attractors from nonminimal coupling
• Inflationary attractors from a non-canonical kinetic term
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Non-perpetual Eternal Inflation and the Emergent de Sitter Swampland Conjecture
• Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential
• Scaling behavior of observables as a model characteristic in multifield inflation
• Confronting Mukhanov Parametrization of Inflationary Equation-of-State with ACT-DR6
• The (relative) size does not matter in inflation
• Logarithmic Extensions to Inflation Universality Classes
• Returning Back to Mukhanov Parametrization of Inflationary Equation of State