Primordial black holes in loop quantum cosmology: the effect on the threshold

Abstract Primordial black holes form in the early Universe and constitute one of the most viable candidates for dark matter. The study of their formation process requires the determination of a critical energy density perturbation threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> , which in general depends on the underlying gravity theory. Up to now, the majority of analytic and numerical techniques calculate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> within the framework of general relativity. In this work, using simple physical arguments we estimate semi-analytically the PBH formation threshold within the framework of quantum gravity, working for concreteness within loop quantum cosmology (LQC). In particular, for low mass PBHs formed close to the quantum bounce, we find a reduction in the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>50</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> compared to the general relativistic regime quantifying for the first time to the best of our knowledge how quantum effects can influence PBH formation within a quantum gravity framework. Finally, by varying the Barbero–Immirzi parameter γ of loop quantum gravity (LQG) we show its effect on the value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>δ</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> while using the observational/phenomenological signatures associated to ultra-light PBHs, namely the ones affected by LQG effects, we propose the PBH portal as a novel probe to constrain the potential quantum nature of gravity.

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