Primordial Black Holes from Polynomial Potentials in Single Field Inflation

Abstract

Within canonical single field inflation models, we provide a method to reverse engineer and reconstruct the inflaton potential from a given power spectrum. This is not only a useful tool to find a potential from observational constraints, but also gives insight into how to generate a large amplitude spike in density perturbations, especially those that may lead to primordial black holes (PBHs). In accord with other works, we find that the usual slow-roll conditions need to be violated in order to generate a significant spike in the spectrum. We find that a way to achieve a very large amplitude spike in single field models is for the classical roll of the inflaton to over-shoot a local minimum during inflation. We provide an example of a quintic polynomial potential that implements this idea and leads to the observed spectral index, observed amplitude of fluctuations on large scales, significant PBH formation on small scales, and is compatible with other observational constraints. We quantify how much fine-tuning is required to achieve this in a family of random polynomial potentials, which may be useful to estimate the probability of PBH formation in the string landscape.

arXiv comment13 pages in double column format, 5 figures. V2: Added references and small clarifications

References in corpus (61)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• The Cosmic Microwave Background Spectrum from the Full COBE/FIRAS Data Set
• Did LIGO detect dark matter?
• New cosmological constraints on primordial black holes
• Primordial Black Holes as Dark Matter
• Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
• Primordial Black Hole Scenario for the Gravitational-Wave Event GW150914
• Density Perturbations and Black Hole Formation in Hybrid Inflation
• The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO
• European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background
• Primordial black holes from single field models of inflation
• Gravitational waves from binary supermassive black holes missing in pulsar observations
• Primordial black hole constraints for extended mass functions
• Gravitational wave background as a probe of the primordial black hole abundance
• Effect of Primordial Black Holes on the Cosmic Microwave Background and Cosmological Parameter Estimates
• Primordial black hole dark matter from single field inflation
• The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravitational Wave Background
• Primordial Black Holes and Slow-Roll Violation
• Probing the inflaton: Small-scale power spectrum constraints from measurements of the CMB energy spectrum
• Single Field Double Inflation and Primordial Black Holes
• Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments
• Dark Matter Triggers of Supernovae
• Inflationary Primordial Black Holes as All Dark Matter
• Primordial Black Holes as All Dark Matter
• Calculating the mass spectrum of primordial black holes
• Could supermassive black holes be quintessential primordial black holes?
• Improved constraints on the primordial power spectrum at small scales from ultracompact minihalos
• The Formation of Primary Galactic Nuclei during Phase Transitions in the Early Universe
• Primordial Black Hole Formation in a Double Inflation Model in Supergravity
• Chaotic new inflation and formation of primordial black holes
• Towards an Explicit Model of D-brane Inflation
• New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts
• Reconstructing the Inflaton Potential---in Principle and in Practice
• Experimental Limits on Primordial Black Hole Dark Matter from the First Two Years of Kepler Data
• Gravitational-Wave Constraints on the Abundance of Primordial Black Holes
• Minimally Parametric Power Spectrum Reconstruction from the Lyman-alpha Forest
• Primordial Black Holes as Dark Matter: Almost All or Almost Nothing
• Black hole formation and slow-roll inflation
• Running Spectral Index and Formation of Primordial Black Hole in Single Field Inflation Models
• Supermassive black holes from primordial black hole seeds
• On the inflationary flow equations
• Accidental Inflation in String Theory
• Hidden universality in the merger rate distribution in the primordial black hole scenario
• Formation of intermediate-mass black holes as primordial black holes in the inflationary cosmology with running spectral index
• Reconstruction of the Primordial Power Spectrum using Temperature and Polarisation Data from Multiple Experiments
• Probing Dark Matter Substructure with Pulsar Timing
• Pulsar timing can constrain primordial black holes in the LIGO mass window
• Investigating dark matter substructure with pulsar timing: I. Constraints on ultracompact minihalos
• Primordial Black Holes, Eternal Inflation, and the Inflationary Parameter Space after WMAP5
• Microlensing towards the SMC: a new analysis of OGLE and EROS results
• Reconstruction of the Primordial Power Spectrum by Direct Inversion
• Exact Superstring Motivated Cosmological Models
• Ultracompact minihalos as probes of inflationary cosmology
• Constraints on small-scale primordial power by annihilation signals from extragalactic dark matter minihalos
• Observational Constraints on the Primordial Curvature Power Spectrum
• Inflation in random Gaussian landscapes
• A Density Spike on Astrophysical Scales from an N-Field Waterfall Transition
• $\mathcal{O}(10)M_{\odot }$ primordial black holes and string axion dark matter

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• Primordial Black Holes as a dark matter candidate
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• Constraints on Dark Matter from Dynamical Heating of Stars in Ultrafaint Dwarfs. Part 2: Substructure and the Primordial Power Spectrum
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• CMB spectral distortions from black holes formed by vacuum bubbles
• Large fluctuations and Primordial Black Holes
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• Primordial black holes from a curvaton scenario with strongly non-Gaussian perturbations
• Pinning down the primordial black hole formation mechanism with gamma-rays and gravitational waves
• Primordial black hole compaction function from stochastic fluctuations in ultra-slow-roll inflation
• Numerically modeling stochastic inflation in slow-roll and beyond
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• Primordial black holes and gravitational waves in teleparallel Gravity
• Primordial black holes from an inflationary potential valley
• Double peaks of gravitational wave spectrum induced from inflection point inflation
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Fitting power spectrum of scalar perturbations for primordial black hole production during inflation
• Detecting Axion-Like Particles with Primordial Black Holes
• CMB $\mu T$ cross-correlations as a probe of PBH scenarios
• Do we need fine-tuning to create primordial black holes?
• Rogue worlds meet the dark side: revealing terrestrial-mass primordial black holes with the Nancy Grace Roman Space Telescope
• Spectral Distortion Anisotropy from Inflation for Primordial Black Holes
• Exploring Critical Overdensity Thresholds in Inflationary Models of Primordial Black Holes Formation
• Constraints on ultra-slow-roll inflation from the third LIGO-Virgo observing run
• The primordial black hole from running curvaton
• Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics
• $\mu$-distortion around stupendously large primordial black holes
• Primordial Black Hole Formation in Non-Standard Post-Inflationary Epochs
• On the primordial black hole formation in hybrid inflation
• Primordial Black Holes and Scalar-induced Gravitational Waves in Radiative Hybrid Inflation
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• PBH assisted search for QCD axion dark matter
• Gauging Fine-Tuning
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• Primordial tensor bispectra in $\mu$-CMB cross-correlations
• Large fluctuations in the Sky
• Constraining the history of reheating with the NANOGrav 15-year data
• Mechanisms for producing Primordial Black Holes from Inflationary Models Beyond Fine-Tuning
• Reconstruction of potentials of the hybrid inflation in the light of primordial black hole formation
• The History of Primordial Black Holes
• Primordial black holes and induced gravitational waves from inflation in the Horndeski theory of gravity
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
• Unifying attractor and non-attractor models of inflation under a single soft theorem
• Gravitational Waves From No-Scale Supergravity
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• Earth-mass primordial black hole mergers as sources for non-repeating FRBs
• Generating large primordial fluctuations in single-field inflation for PBH formation
• Primordial black hole formation in $\alpha$-attractor models: an analysis using optimized peaks theory
• Loops in inflation with strongly non-geodesic motion
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• Primordial blackholes from Gauss-Bonnet-corrected single field inflation
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• Updated constraints on the primordial power spectrum at sub-Mpc scales
• Exploring the CMB Power Suppression in Canonical Inflation Models
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