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arxiv: 2604.24011 · v1 · submitted 2026-04-27 · 🌀 gr-qc

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Primordial black hole production in scalar field inflation within f(T) gravity

Daniel Villalobos-Silva, Giovanni Otalora, Yerko V\'asquez

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Pith reviewed 2026-05-08 02:25 UTC · model grok-4.3

classification 🌀 gr-qc
keywords inflationgravityteleparallelmodifiedframeworkprimordialbackgroundblack
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The pith

In f(T) gravity with power-law and exponential models, a fiber inflation potential with ultra slow-roll phase amplifies the primordial curvature power spectrum on small scales to enable primordial black hole formation consistent with CMB constraints.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard inflation uses a scalar field to drive rapid early expansion and create tiny density ripples that grow into galaxies. This work replaces Einstein gravity with f(T) gravity, where the key quantity is torsion rather than curvature. Two simple extensions (power-law and exponential) add a small correction controlled by a parameter alpha. The scalar field follows a fiber inflation potential from string theory that naturally includes a brief ultra slow-roll interval where the field moves extremely slowly. The authors solve the background expansion equations numerically and track how ripples in spacetime evolve. During the ultra slow-roll stretch the ripples on tiny scales grow much larger than usual. These large ripples can collapse into primordial black holes after inflation ends. On the much larger scales probed by the cosmic microwave background the models stay within observed limits. The torsion corrections also shift the predicted strength of gravitational waves and the tilt of the spectrum in ways that differ from ordinary inflation.

Core claim

Both models generate an amplification of the primordial curvature power spectrum on small scales due to the USR phase, while remaining compatible with cosmic microwave background constraints at large scales.

Load-bearing premise

That the chosen fiber inflation potential produces a transient ultra slow-roll phase whose perturbation amplification survives the modified teleparallel background equations and yields PBH abundances without violating other constraints.

read the original abstract

We investigate inflation in modified teleparallel gravity within a scalar-tensor framework. We focus on two viable extensions of the Teleparallel Equivalent of General Relativity: a power-law model and an exponential model, which introduce controlled deviations from standard teleparallel gravity through a correction parameter $\alpha$. Inflation is driven by a string-inspired fiber inflation potential that naturally realizes a transient ultra slow-roll (USR) phase. We solve the background equations numerically and compute the evolution of cosmological perturbations within the modified teleparallel framework. We show that both models generate an amplification of the primordial curvature power spectrum on small scales due to the USR phase, while remaining compatible with cosmic microwave background constraints at large scales. The modified gravity sector introduces corrections to the slow-roll parameters, tensor spectral index, and tensor-to-scalar ratio through derivatives of the torsion function, leading to potentially observable signatures distinct from canonical inflation. We further analyze the implications of enhanced scalar perturbations for primordial black hole (PBH) formation and demonstrate that modified teleparallel gravity provides a theoretically consistent and phenomenologically rich framework for producing PBHs during inflation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The framework rests on standard teleparallel equivalence, scalar-tensor inflation dynamics, and numerical solution of perturbation equations; free parameters are the correction alpha and the fiber potential coefficients.

free parameters (2)
  • alpha
    Dimensionless correction parameter controlling deviation from teleparallel equivalent of GR in both power-law and exponential models.
  • fiber potential parameters
    Coefficients in the string-inspired fiber inflation potential that set the ultra slow-roll duration and amplitude.
axioms (2)
  • standard math Teleparallel Equivalent of General Relativity as the base theory
    f(T) extensions are defined as modifications around the torsion scalar T of the teleparallel formulation.
  • domain assumption Scalar field drives inflation with standard kinetic term
    The action is written in scalar-tensor form within the modified teleparallel framework.

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Reference graph

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