An inverse-scattering method reconstructs inflationary potentials from primordial power spectra using Jost functions derived from the Mukhanov-Sasaki equation.
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Encyclopaedia Inflationaris
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abstract
The current flow of high accuracy astrophysical data, among which are the Cosmic Microwave Background (CMB) measurements by the Planck satellite, offers an unprecedented opportunity to constrain the inflationary theory. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. Given that there is currently no observational evidence for primordial non-Gaussianities, isocurvature perturbations or any other non-minimal extension of the inflationary paradigm, a reasonable approach is to consider the simplest models first, namely the slow-roll single field models with minimal kinetic terms. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. It has been customary to tackle this problem by means of approximate model independent methods while a more ambitious alternative is to study the inflationary scenarios one by one. We have developed the publicly available runtime library ASPIC to implement this last approach. The ASPIC code provides all routines needed to quickly derive reheating-consistent observable predictions within this class of scenarios. ASPIC has been designed as an evolutive code which presently supports 118 different models. In this paper, for each of the ASPIC models, we present and collect new results in a systematic manner, thereby constituting the first Encyclopaedia Inflationaris.
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representative citing papers
Exact solution of time-reversed stochastic inflation in the quantum well yields curvature perturbation distributions with faster-decaying exponential tails than forward stochastic inflation.
For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.
Out-of-equilibrium superfluids in Bjorken, Gubser and FLRW flows reach hydrodynamic attractors after an initial-condition-dependent attractor time, with a novel nonlinear constant-anisotropy regime in Gubser evolution.
A one-parameter family of α-attractor potentials interpolates between exponential and polynomial attractor predictions, letting n_s scan the range preferred by CMB+DESI.
Starobinsky supergravity coupled to the MSSM links the CMB inflationary scale to the Higgs boson mass (~125 GeV) and predicts thermal wino dark matter at ~3 TeV, testable at future colliders and direct detection experiments.
Bumblebee gravity enhances primordial black hole abundance through three mechanisms, but the model harbors a ghost instability and a tachyonic instability that make it cosmologically unviable.
In warm inflation with Υ∝T³, a residual inflaton condensate after rapid drop in Q evolves as cold dark matter with mass fixed at m≈0.02 MeV by the observed abundance.
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
BOSS + eBOSS galaxy clustering favors a featureless, quasi-scale-invariant primordial spectrum, with a reconstructed spectral index n_s = 0.976 ± 0.021.
The paper introduces new exponential and polynomial supergravity ξ-attractor models in the Jordan frame with non-minimal coupling and shows that Palatini gravity with independent affine connection has no supergravity embedding.
A vacuum-decay model generates primordial curvature perturbations from spatially correlated stochastic noise rather than inflaton fluctuations, solving horizon and flatness problems with zero tensor-to-scalar ratio.
Physics equation corpora exhibit exponential decay in mathematical operator frequencies, proposed as a meta-law that narrows the space of plausible expressions for symbolic regression.
Improved end-of-inflation dynamics shift the Starobinsky model's predicted spectral index n_s by up to 1.2×10^{-3} within the allowed reheating range.
α-attractor quintessence models approximate axion-like potentials and fit DESI dynamical dark energy data, preferring α of order 1 via a simple fa-α relation.
An effective constrained scalar-Gauss-Bonnet inflation model yields n_s ≃ 0.958 and r ≃ 2.7×10^{-4} while the exact theory has no propagating scalar degree of freedom.
New ξ-attractors with non-minimal coupling and non-canonical kinetics yield Einstein-frame exponential and polynomial potentials whose ns spans 1-2/N to 1-1/N and r can reach zero as ξ grows, fitting Planck, BICEP/Keck, ACT, SPT, and DESI data, plus a supergravity realization.
Single-field inflation with ε(N) approaching a constant in (0,1) at early times forms an asymptotic universality class with a Weyl-flat null origin while producing ns and r values compatible with Planck data.
Genetic algorithm reconstructs single-field inflationary models with features in the scalar power spectrum that fit Planck 2018 CMB data better by Δχ² ≲ -10 and suggest alternative background parameters.
A Palatini-supergravity Higgs-inflation model with induced gravity predicts a scalar spectral index ns≈0.972-0.974, consistent with ACT DR6, and favors split supersymmetry with gravitino mass 40-60 PeV.
Breaking diffeomorphism invariance to transverse diffeomorphisms in the inflaton sector yields modified slow-roll parameters and power spectra with novel post-inflationary regimes for quadratic potentials.
Non-Bunch-Davies initial conditions substantially improve the fit of various single-field slow-roll inflation models to updated n_s-r constraints from ACT DR6 combined with Planck, DESI, and BICEP/Keck data.
Deriving Hubble slow-roll parameters from an analytic approximate Hubble parameter in Starobinsky inflation provides better accuracy than the potential slow-roll approximation, reducing the inferred e-foldings by more than one for ns=0.9649.
Expanded Simons Observatory could measure reheating temperature and inflaton-gluon coupling to a few percent in QCD-driven warm inflation if r=0.01 primordial gravitational waves are found.
citing papers explorer
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Inverse-Scattering Reconstruction of Inflation from Scalar and Tensor Primordial Spectra
An inverse-scattering method reconstructs inflationary potentials from primordial power spectra using Jost functions derived from the Mukhanov-Sasaki equation.
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Time-reversed stochastic inflation in the quantum well
Exact solution of time-reversed stochastic inflation in the quantum well yields curvature perturbation distributions with faster-decaying exponential tails than forward stochastic inflation.
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Inflaton Regeneration via Scalar Couplings: Generic Models and the Higgs Portal
For monomial inflationary potentials with k≥4, the inflaton regenerates from the thermal bath after reheating because its amplitude-dependent mass vanishes asymptotically.
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Superfluids in expanding backgrounds and attractor times
Out-of-equilibrium superfluids in Bjorken, Gubser and FLRW flows reach hydrodynamic attractors after an initial-condition-dependent attractor time, with a novel nonlinear constant-anisotropy regime in Gubser evolution.
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Unification of polynomial and exponential cosmological attractors
A one-parameter family of α-attractor potentials interpolates between exponential and polynomial attractor predictions, letting n_s scan the range preferred by CMB+DESI.
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Higgs boson mass and thermal wino dark matter from Starobinsky supergravity with the MSSM
Starobinsky supergravity coupled to the MSSM links the CMB inflationary scale to the Higgs boson mass (~125 GeV) and predicts thermal wino dark matter at ~3 TeV, testable at future colliders and direct detection experiments.
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Primordial black hole in Lorentz-violating theories: Insights from Bumblebee gravity
Bumblebee gravity enhances primordial black hole abundance through three mechanisms, but the model harbors a ghost instability and a tachyonic instability that make it cosmologically unviable.
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Dark Matter as an Inflationary Relic in Warm Inflation
In warm inflation with Υ∝T³, a residual inflaton condensate after rapid drop in Q evolves as cold dark matter with mass fixed at m≈0.02 MeV by the observed abundance.
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The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories
The Coherence Principle supplies a falsifiable prior for Bayesian model selection by converting compatibility with a theory's validated grammar into prior weights via a maximum-entropy exponential controlled by one parameter.
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Primordial power spectrum reconstructions from BOSS + eBOSS
BOSS + eBOSS galaxy clustering favors a featureless, quasi-scale-invariant primordial spectrum, with a reconstructed spectral index n_s = 0.976 ± 0.021.
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Jordan Frame in Supergravity and Cosmology
The paper introduces new exponential and polynomial supergravity ξ-attractor models in the Jordan frame with non-minimal coupling and shows that Palatini gravity with independent affine connection has no supergravity embedding.
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The Noise of Vacuum
A vacuum-decay model generates primordial curvature perturbations from spatially correlated stochastic noise rather than inflaton fluctuations, solving horizon and flatness problems with zero tensor-to-scalar ratio.
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Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature
Physics equation corpora exhibit exponential decay in mathematical operator frequencies, proposed as a meta-law that narrows the space of plausible expressions for symbolic regression.
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Precision Inflationary Predictions: Impact of Accurate End-of-Inflation Dynamics
Improved end-of-inflation dynamics shift the Starobinsky model's predicted spectral index n_s by up to 1.2×10^{-3} within the allowed reheating range.
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Quintessential $\alpha$-attractors fit DESI
α-attractor quintessence models approximate axion-like potentials and fit DESI dynamical dark energy data, preferring α of order 1 via a simple fa-α relation.
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Effective Constrained Scalar--Gauss--Bonnet Inflation Motivated by $f(R,\mathcal{G})$ Gravity
An effective constrained scalar-Gauss-Bonnet inflation model yields n_s ≃ 0.958 and r ≃ 2.7×10^{-4} while the exact theory has no propagating scalar degree of freedom.
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New Exponential and Polynomial $\xi$-attractors
New ξ-attractors with non-minimal coupling and non-canonical kinetics yield Einstein-frame exponential and polynomial potentials whose ns spans 1-2/N to 1-1/N and r can reach zero as ξ grows, fitting Planck, BICEP/Keck, ACT, SPT, and DESI data, plus a supergravity realization.
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Inflation from a Weyl-flat null origin
Single-field inflation with ε(N) approaching a constant in (0,1) at early times forms an asymptotic universality class with a Weyl-flat null origin while producing ns and r values compatible with Planck data.
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Reconstructing inflationary features on large scales using genetic algorithm
Genetic algorithm reconstructs single-field inflationary models with features in the scalar power spectrum that fit Planck 2018 CMB data better by Δχ² ≲ -10 and suggest alternative background parameters.
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Induced-Gravity Palatini-Like Higgs Inflation in Supergravity Confronts ACT DR6
A Palatini-supergravity Higgs-inflation model with induced gravity predicts a scalar spectral index ns≈0.972-0.974, consistent with ACT DR6, and favors split supersymmetry with gravitino mass 40-60 PeV.
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Inflation in theories with broken diffeomorphisms
Breaking diffeomorphism invariance to transverse diffeomorphisms in the inflaton sector yields modified slow-roll parameters and power spectra with novel post-inflationary regimes for quadratic potentials.
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ACT-ing on inflation: Implications of non Bunch-Davies initial condition and reheating on single-field slow roll models
Non-Bunch-Davies initial conditions substantially improve the fit of various single-field slow-roll inflation models to updated n_s-r constraints from ACT DR6 combined with Planck, DESI, and BICEP/Keck data.
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Improving Slow-Roll Estimates in Starobinsky Inflation Using Analytic Hubble Parameter
Deriving Hubble slow-roll parameters from an analytic approximate Hubble parameter in Starobinsky inflation provides better accuracy than the potential slow-roll approximation, reducing the inferred e-foldings by more than one for ns=0.9649.
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Observing Cosmic Reheating with the expanded Simons Observatory
Expanded Simons Observatory could measure reheating temperature and inflaton-gluon coupling to a few percent in QCD-driven warm inflation if r=0.01 primordial gravitational waves are found.
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F-Term Hybrid Inflation with T-Model K\"ahler Geometry and Beyond
F-term hybrid inflation with SU(1,1)/U(1) or SU(2)/U(1) Kähler geometry in GUTs can be realized without inflationary extrema for broad parameters, matching ACT/SPT data via curvature and tadpole adjustments while predicting cosmic string gravitational waves.
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Thermal effects on Dark Matter production during cosmic reheating
Thermal corrections to reheating and freeze-in DM production rates are generally small in the computable regime but can be large in constructed counter-examples.
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ACT DR6+Planck impact on inflation with non-zero vacuum expectation value and the post-inflationary behavior
Updated constraints on non-zero VEV parameter M from ACT+Planck data, plus lattice simulations showing oscillon formation and reheating implications.
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Inflationary models in a minimally coupled $f(R,T)$ gravity: Constraints from $Planck$, BICEP/$Keck$, and ACT
Three standard inflationary potentials remain compatible with Planck, BICEP/Keck, DESI DR2, and ACT DR6 data when placed in minimally coupled f(R,T)=R+16πGλT gravity for suitable ranges of the model parameters and coupling λ.
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Noncanonical Approaches To Inflation
A review thesis covering Mukhanov parametrization, general scalar-tensor theories, and new slow-roll techniques for canonical and noncanonical inflation observables.
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Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
Modified gravity theories supply viable mathematical frameworks for inflation, bounces, and dark energy eras that match observational data.
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Lectures on Reheating after Inflation
Lecture notes providing a generic introduction to reheating after inflation, covering its theoretical, phenomenological, and observational aspects.