Constraining <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> bouncing cosmologies through primordial black holes

The phenomenology of primordial black hole (PBH) physics and the associated PBH abundance constraints can be used to probe early universe. In this work, we investigate formation during standard radiation-dominated era by studying effect an $F(R)$ modified gravity phase with a bouncing behavior which is introduced avoid initial spacetime singularity problem. particular, calculate energy density power spectrum at horizon crossing time, then extract in context peak theory as function parameter $\ensuremath{\alpha}$ our model hand. Interestingly, find that gravitational-wave overproduction from dominated before big bang nucleosynthesis, should lie within range $\ensuremath{\alpha}\ensuremath{\le}{10}^{\ensuremath{-}19}{M}_{\mathrm{Pl}}^{2}$. This constraint translated on scale onset hot phase, ${H}_{\mathrm{RD}}\ensuremath{\sim}\sqrt{\ensuremath{\alpha}}/2$, recast ${H}_{\mathrm{RD}}&lt;{10}^{\ensuremath{-}10}{M}_{\mathrm{Pl}}$.