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

TL;DR

This paper explores how modified teleparallel gravity with scalar fields can produce primordial black holes during inflation, showing amplified small-scale perturbations while fitting large-scale observations.

Contribution

It introduces two viable $f(T)$ gravity models with controlled deviations that naturally generate primordial black holes through an ultra slow-roll phase during inflation.

Findings

Both models amplify small-scale curvature perturbations due to USR phase.

The models remain compatible with CMB constraints at large scales.

Modified gravity affects inflationary parameters, leading to observable signatures.

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.