Inflationary $\alpha$-Attractor Models with Singular Derivative of Potential

Abstract

A generalization of inflationary $\alpha$-attractor models (``polynomial $\alpha$-attractor'') was recently proposed by Kallosh and Linde, in which the potential involves logarithmic functions of the inflaton so that the derivative of the potential but not potential itself has a singularity. We find that the models can lead to viable inflationary observables even without the pole in the kinetic term. Also, the generalization with a pole order other than two does not significantly change the functional form of the potential. This allows a systematic analysis of the predictions of this class of models. Our models predict larger spectral index $n_s$ and tensor-to-scalar ratio $r$ than in the polynomial $\alpha$-attractor: typically, $n_s$ around 0.97--0.98 and $r$ observable by LiteBIRD. Taking advantage of the relatively large $n_s$, we discuss the modification of the potential to produce primordial black holes as the whole dark matter and gravitational waves induced by curvature perturbations detectable by LISA and BBO/DECIGO, while keeping $n_s$ in agreement with the Planck/BICEP/Keck data.

25 pages, 9 figures, 1 table. Published version; references and table added

References in corpus (37)

• The Standard Model Higgs boson as the inflaton
• BICEP / Keck XIII: Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season
• Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
• Primordial Black Holes as Dark Matter: Recent Developments
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• The Unity of Cosmological Attractors
• Constraints on Earth-mass primordial black holes from OGLE 5-year microlensing events
• Primordial black hole dark matter from single field inflation
• Primordial Black Holes and Slow-Roll Violation
• Gravitational Wave signatures of inflationary models from Primordial Black Hole Dark Matter
• Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse
• Understanding caustic crossings in giant arcs: characteristic scales, event rates, and constraints on compact dark matter
• Stochastic gravitational waves associated with the formation of primordial black holes
• Large Field Inflation and Double $\alpha$-Attractors
• The end of the MACHO era- revisited: new limits on MACHO masses from halo wide binaries
• Curvature profiles as initial conditions for primordial black hole formation
• LiteBIRD: JAXA's new strategic L-class mission for all-sky surveys of cosmic microwave background polarization
• Single-field $\alpha$-attractors
• Gauge Independence of Induced Gravitational Waves
• Logarithmic Duality of the Curvature Perturbation
• Questions on calculation of primordial power spectrum with large spikes: the resonance model case
• Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds
• Approximate gauge independence of the induced gravitational wave spectrum
• Towards early dark energy and $n_s$=1 with Planck, ACT and SPT
• Universality classes for models of inflation
• Hybrid cosmological attractors
• Primordial black holes from stochastic tunnelling
• The Primordial Black Hole Formation from Single-Field Inflation is Not Ruled Out
• Polynomial $\alpha$-attractors
• A grounded perspective on New Early Dark Energy using ACT, SPT, and BICEP/Keck
• Primordial black holes and third order scalar induced gravitational waves
• $\alpha$-attractor inflation: Models and predictions
• Gauge Invariant Second Order Gravitational Waves
• On the Gauge Invariance of Scalar Induced Gravitational Waves: Gauge Fixings Considered
• Primordial black holes from Volkov-Akulov-Starobinsky supergravity
• Energy spectrum of gravitational waves

Cited by in corpus (1)

• Primordial black holes and scalar-induced gravitational waves from the polynomial attractor model