Quantum loop effects on the power spectrum and constraints on primordial black holes

TL;DR

This paper investigates the formation of primordial black holes during inflation, showing that quantum loop effects and power spectrum renormalization severely limit the mass range and abundance of PBHs in single-field inflation models.

Contribution

It provides a model-independent EFT analysis demonstrating that quantum loop corrections constrain PBH formation, ruling out large PBH masses in single-field inflation.

Findings

Quantum loop effects restrict PBH mass range to 10^2-10^3 grams.

One-loop corrected power spectrum limits the total e-foldings to 54-59.

Adding a slow-roll regime after ultra slow-roll does not change the constraints.

Abstract

We present a detailed exposition on the prospects of the formation of Primordial Black Holes (PBHs) during Slow Roll (SR) to Ultra Slow Roll (USR) sharp transitions in the framework of single-field inflation. We use an effective field theory (EFT) approach in order to keep the analysis model-independent and applicable to both the canonical and non-canonical cases. We show in detail how renormalizing the power spectrum to one loop order in $P(X,\phi)$ theories severely limits the prospects for PBH formation in a single-field inflationary framework. We demonstrate that for the allowed range of effective sound speed, $1<c_s<1.17$, the consistency of one-loop corrected power spectrum leaves a small window for black hole masses, $M_{\rm PBH}\sim \mathcal{O}(10^2-10^3)$gm to have sufficient e-foldings, $\Delta {\cal N}_{\rm Total}\sim {\cal O}(54-59)$ for inflation. We confirm that adding an SR regime after USR before the end of inflation does not significantly alter our conclusions. Our findings for sharp transition strictly rule out the possibility of generating large masses of PBHs from all possible models of single-field inflation (canonical and non-canonical). Our results are at least valid for the situation where constraints from the loop effects are computed using either Late-Time (LT) or Adiabatic-Wave function (AF) scheme followed by Power Spectrum (PS) renormalization schemes.