For infinitely differentiable effective potentials describing the post-inflation transition, the regularized power spectrum of primary gravitational waves exhibits exponential suppression at small scales.
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TASI Lectures on Inflation
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abstract
In a series of five lectures I review inflationary cosmology. I begin with a description of the initial conditions problems of the Friedmann-Robertson-Walker (FRW) cosmology and then explain how inflation, an early period of accelerated expansion, solves these problems. Next, I describe how inflation transforms microscopic quantum fluctuations into macroscopic seeds for cosmological structure formation. I present in full detail the famous calculation for the primordial spectra of scalar and tensor fluctuations. I then define the inverse problem of extracting information on the inflationary era from observations of cosmic microwave background fluctuations. The current observational evidence for inflation and opportunities for future tests of inflation are discussed. Finally, I review the challenge of relating inflation to fundamental physics by giving an account of inflation in string theory.
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representative citing papers
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
Computes inflationary bispectra and trispectra from tree-level unparticle exchanges using Mellin-Barnes methods and symmetry-based differential equations, revealing that full shapes are needed to distinguish unparticles from light particles.
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
A trace-anomaly-seeded infrared gap in a coherent gluonic dark sector produces the observed galactic acceleration scale g⋆ = G M_h / r_c² as its gravitational signature.
In an LQC bouncing cosmology, second-order quantum moments yield a Planck-suppressed scale-dependent correction δP_R ∝ (k ℓ_Pl)^6 to the curvature power spectrum together with post-bounce damping from gravitational moments.
The paper develops a descriptive framework in which scientific reward in physics is understood as transformations of the Polydoxon, the structured set of viable theories, with reward scaling by the transformation's scope, centrality, depth, and future leverage.
Fractional cosmology produces emergent inflation as a stable attractor from a non-singular pre-inflationary regime, with the number of e-folds related to the fractional parameter α and a subsequent radiation-dominated era.
No evidence for primordial hotspots in Planck polarization data leads to improved bounds on inflationary particle production couplings for light particles.
The stochastic noise amplitude is modified to (H/2π) * sqrt(1 + ΔP_R / P0_R) to account for one-loop corrections in interacting theories, demonstrated in a three-phase SR-USR-SR setup for PBH formation.
In USR inflation with an idealized instantaneous sharp transition to slow-roll, higher loop corrections to curvature perturbations on CMB scales grow rapidly with loop order L and may exit perturbative control.
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.
Ricci cosmology adds curvature-matter coupling terms to the stress-energy tensor, enabling analytic inflationary solutions in standard flat FLRW cosmology without Lambda or new scalar fields.
The equilateral bispectrum from massive scalar exchange in inflation is not universally negative in the full EFT of inflation; its sign depends on a critical ratio of operator coefficients.
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
The authors derive modified Friedmann equations from Kaniadakis entropy, compute inflationary observables, and find that Planck data require the deformation parameter kappa to be strongly suppressed in the standard case while allowing limited viable regions in the dual formulation.
Inflationary magnetic fields induce curvature perturbations that form ultralight PBHs, generating a stochastic GW background with model-specific features.
Adiabatic regularization combined with smoothed transitions suppresses the high-frequency oscillations in the power spectrum of primary gravitational waves about a zero mean.
A stable initial state is identified in mLQC-I that diagonalizes the Hamiltonian and minimizes particle creation, with mode functions approximated analytically by Airy or cylindrical functions whose constants are fixed by that state.
Reports f_NL = -20.5^{+19.0}_{-18.1} (68% CL) from combined Quaia quasar auto-correlation and CMB lensing cross-correlation assuming p_phi=1, or -28.7^{+26.1}_{-24.6} for p_phi=1.6.
Phase transitions in dark sectors can generate CMB B-modes with amplitudes competitive with inflation but peaking at smaller angular scales.
Einstein-Cartan pseudoscalaron inflation coupled to type-I seesaw neutrinos makes nonthermal leptogenesis a necessary mechanism for the baryon asymmetry, yielding ns ~ 0.97, r ~ 0.004 and nB/s ~ 8.7e-11 for gamma ~ -1/100 and lightest Majorana mass ~ 10^13 GeV.
NANOGrav data favors a blue-tilted tensor spectrum with nt ≈ 2.2, radiation-dominated reheating, and alpha-vacuum states over standard Bunch-Davies, with a frequency-dependent alpha suggested to resolve the blue-tilt tension.
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.
citing papers explorer
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Primary gravitational waves at high frequencies II: Emergence of the exponential cut-off in the power spectrum
For infinitely differentiable effective potentials describing the post-inflation transition, the regularized power spectrum of primary gravitational waves exhibits exponential suppression at small scales.
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Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
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Strongly Coupled Sectors in Inflation: Gapless Theories and Unparticles
Computes inflationary bispectra and trispectra from tree-level unparticle exchanges using Mellin-Barnes methods and symmetry-based differential equations, revealing that full shapes are needed to distinguish unparticles from light particles.
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Fine-Tuning Small Reasoning Models for Quantum Field Theory
Small 7B reasoning models were fine-tuned on synthetic and curated QFT problems using RL and SFT, yielding performance gains, error analysis, and public release of data and traces.
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Infrared Spectral Gap in a Gluonic Dark Sector as the Origin of the Galactic Acceleration Scale
A trace-anomaly-seeded infrared gap in a coherent gluonic dark sector produces the observed galactic acceleration scale g⋆ = G M_h / r_c² as its gravitational signature.
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Quantum corrections to cosmic perturbations for a bouncing background
In an LQC bouncing cosmology, second-order quantum moments yield a Planck-suppressed scale-dependent correction δP_R ∝ (k ℓ_Pl)^6 to the curvature power spectrum together with post-bounce damping from gravitational moments.
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Polydoxon Transformations and Scientific Reward in Physics
The paper develops a descriptive framework in which scientific reward in physics is understood as transformations of the Polydoxon, the structured set of viable theories, with reward scaling by the transformation's scope, centrality, depth, and future leverage.
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Emergent inflation in fractional cosmology
Fractional cosmology produces emergent inflation as a stable attractor from a non-singular pre-inflationary regime, with the number of e-folds related to the fractional parameter α and a subsequent radiation-dominated era.
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Constraining Inflationary Particle Production with CMB Polarization
No evidence for primordial hotspots in Planck polarization data leads to improved bounds on inflationary particle production couplings for light particles.
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Stochastic Inflation with Interacting Noises
The stochastic noise amplitude is modified to (H/2π) * sqrt(1 + ΔP_R / P0_R) to account for one-loop corrections in interacting theories, demonstrated in a three-phase SR-USR-SR setup for PBH formation.
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Non-Perturbative Hamiltonian and Higher Loop Corrections in USR Inflation
In USR inflation with an idealized instantaneous sharp transition to slow-roll, higher loop corrections to curvature perturbations on CMB scales grow rapidly with loop order L and may exit perturbative control.
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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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Ricci cosmology
Ricci cosmology adds curvature-matter coupling terms to the stress-energy tensor, enabling analytic inflationary solutions in standard flat FLRW cosmology without Lambda or new scalar fields.
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Massive Exchange and the Sign of the Equilateral Bispectrum
The equilateral bispectrum from massive scalar exchange in inflation is not universally negative in the full EFT of inflation; its sign depends on a critical ratio of operator coefficients.
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Inflaton Accretion onto Primordial Black Holes During Reheating
Inflaton accretion during reheating drives non-linear PBH mass growth that extends lifetimes and amplifies emitted SGWB by multiple orders of magnitude.
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Slow-roll inflation in (dual) Kaniadakis cosmology
The authors derive modified Friedmann equations from Kaniadakis entropy, compute inflationary observables, and find that Planck data require the deformation parameter kappa to be strongly suppressed in the standard case while allowing limited viable regions in the dual formulation.
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The Magnetic Origin of Primordial Black Holes: Ultralight PBHs and Secondary GWs
Inflationary magnetic fields induce curvature perturbations that form ultralight PBHs, generating a stochastic GW background with model-specific features.
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Primary gravitational waves at high frequencies I: Origin of suppression in the power spectrum
Adiabatic regularization combined with smoothed transitions suppresses the high-frequency oscillations in the power spectrum of primary gravitational waves about a zero mean.
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Stable initial conditions and analytical investigations of cosmological perturbations in a modified loop quantum cosmology
A stable initial state is identified in mLQC-I that diagonalizes the Hamiltonian and minimizes particle creation, with mode functions approximated analytically by Airy or cylindrical functions whose constants are fixed by that state.
-
Constraints on primordial non-Gaussianity from Quaia
Reports f_NL = -20.5^{+19.0}_{-18.1} (68% CL) from combined Quaia quasar auto-correlation and CMB lensing cross-correlation assuming p_phi=1, or -28.7^{+26.1}_{-24.6} for p_phi=1.6.
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Observable CMB B-modes from Cosmological Phase Transitions
Phase transitions in dark sectors can generate CMB B-modes with amplitudes competitive with inflation but peaking at smaller angular scales.
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Einstein-Cartan pseudoscalaron inflation, reheating and nonthermal leptogenesis
Einstein-Cartan pseudoscalaron inflation coupled to type-I seesaw neutrinos makes nonthermal leptogenesis a necessary mechanism for the baryon asymmetry, yielding ns ~ 0.97, r ~ 0.004 and nB/s ~ 8.7e-11 for gamma ~ -1/100 and lightest Majorana mass ~ 10^13 GeV.
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Constraints on the inflationary vacuum and reheating era from NANOGrav
NANOGrav data favors a blue-tilted tensor spectrum with nt ≈ 2.2, radiation-dominated reheating, and alpha-vacuum states over standard Bunch-Davies, with a frequency-dependent alpha suggested to resolve the blue-tilt tension.
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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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Gravitational Waves from Matter Perturbations of Spectator Scalar Fields
A spectator scalar field with strong portal coupling to the inflaton sources a stochastic gravitational wave background reaching Ω_GW h² ∼ 10^{-11} at frequencies 10^7-10^8 Hz for benchmark parameters σ/λ ≃ 10^4 and T_reh = 2×10^{14} GeV.
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Accretion Effects on Primordial Black Hole Reheating Constraints
Accretion on primordial black holes prolongs matter domination and shifts reheating constraints from isocurvature gravitational waves and mergers toward smaller formation masses and initial abundances.
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Single field matter bounce with dark energy era: comparison with CMB Planck 2018 data and best fit parameters
A matter bounce model driven by a scalar field with exponential potential fits Planck 2018 CMB data comparably to inflationary ΛCDM, with the potential slope λ directly setting the scalar spectral index ns.
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Reconstructing slow-roll Scalar-Tensor Gauss-Bonnet single field inflation from running spectral data
Derives slow-roll observables and consistency relations for scalar-tensor Gauss-Bonnet inflation and fits a specific model to Planck data.
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Precision Analysis for $\boldsymbol{H_0}$ Using Upcoming Multi-band Gravitational Wave Observations
Multi-band GW observations of PBHs can reduce H0 uncertainty to ≲2 km/s/Mpc (conservative) or O(0.1) km/s/Mpc (optimistic) via Fisher forecasts on M_PBH and f_PBH.
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Explaining Neural Networks on the Sky: Machine Learning Interpretability for Cosmic Microwave Background Maps
Hybrid PCA-neural network classifiers trained on full CMB maps, interpreted via SHAP to identify spatial signatures distinguishing LambdaCDM from primordial feature models.
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Inflation with Gauss-Bonnet Correction and Higgs Potential
A Higgs-potential inflation model with a Gauss-Bonnet correction yields r and n_s values compatible with ACT DR6 data after numerical integration of the e-folding integral.
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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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Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
Lecture notes that build the BMS group from prerequisites to applications in soft theorems, memory effects, and new material on asymptotic conformal Killing horizons.
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Scalar induced gravitational waves review
A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.
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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.