Information Wells and the Emergence of Primordial Black Holes in a Cyclic Quantum Universe

TL;DR

This work proposes that information wells formed by gradients of imprint entropy in a cyclic bounce cosmology provide a robust mechanism to seed primordial black holes, with a PBH mass spectrum governed by two key parameters: the QMM coupling λ and the bounce temperature T_B, modulated by the imprint tilt n_S^{(S)}. The approach links PBH formation to fundamental quantum-gravitational microphysics via the Quantum Memory Matrix, predicting a dust-like QMM stress-energy that grows linearly with the scale factor and collapses upon horizon re-entry when the condition δ_QMM^{re} ≥ δ_c is met. It yields a flexible mass spectrum that can explain sub-lunar dark matter or LIGO-scale BHs depending on tilt, while making concrete observational predictions: mild ISW enhancement, μ-distortion within PIXIE reach, a nano-Hz gravitational-wave background near PTA sensitivity, and distinctive microlensing constraints. If confirmed by upcoming CMB-S4, PIXIE, and PTA measurements, this framework would offer a unified explanation for dark matter, PBH formation, and information retention in quantum gravity, rooted in the QMM program.

Abstract

Primordial black holes (PBHs) remain one of the most intriguing candidates for dark matter and a unique probe of physics at extreme curvatures. Here, we examine their formation in a bounce cosmology when the post-crunch universe inherits a highly inhomogeneous distribution of imprint entropy from the Quantum Memory Matrix (QMM). Within QMM, every Planck-scale cell stores quantum information about infalling matter; the surviving entropy field S(x) contributes an effective dust component T^QMM_{μν} = lambda * [ (nabla_mu S)(nabla_nu S) - (1/2) * g_{μν} * (nabla S)^2 + ... ] that deepens curvature wherever S is large. We show that (i) reasonable bounce temperatures and a QMM coupling lambda ~ O(1) naturally amplify these "information wells" until the density contrast exceeds the critical value delta_c ~ 0.3; (ii) the resulting PBH mass spectrum spans 10^{-16} to 10^3 solar masses, matching current microlensing and PTA windows; and (iii) the same mechanism links PBH abundance to earlier QMM explanations of dark matter and the cosmic matter-antimatter imbalance. Observable signatures include a mild blue tilt in small-scale power, characteristic mu-distortions, and an enhanced integrated Sachs-Wolfe signal - all of which will be tested by upcoming CMB, PTA, and lensing surveys.

Figures (12)

• Figure 1: Imprint-entropy power spectrum $P_{S}(k)$ for three tilts $n_{S}^{(S)}$. All curves use the fiducial amplitude $A_{S}=10^{-3}$ so their vertical placement matches the collapse-criterion plot in Figure \ref{['fig:collapse_threshold']}. The gray band marks CMB-sensitive scales ($k<0.3\;\mathrm{Mpc}^{-1}$); the dashed line illustrates a fiducial ultraviolet cutoff $k_{\max}=10^{3}\;\mathrm{Mpc}^{-1}$.
• Figure 2: Linear-scale growth factors for QMM information wells (solid) and conventional cold dark matter (dashed) in a radiation-dominated background, each normalised to its value at $a_0=10^{-6}$. The dotted line marks matter–radiation equality ($a_{\rm eq}\simeq2.9\times10^{-4}$). Because the QMM overdensity grows $\propto a$ (independent of the overall power-spectrum amplitude), it reaches the collapse threshold far earlier than CDM, enabling primordial black-hole formation well before standard structure growth becomes efficient.
• Figure 3: Collapse criterion in imprint–entropy space. The solid line shows $\sqrt{P_{S}(k)}$ for $n_{S}^{(S)}=1.2$ and $A_{S}=10^{-3}$; the dashed line is the critical threshold $\delta_{\mathrm c}k/(a_{\mathrm B}H_{\mathrm B})$ with $\delta_{\mathrm c}=0.3$ and $a_{\mathrm B}H_{\mathrm B}=1\;\mathrm{Mpc}^{-1}$. The shaded pink wedge marks modes that satisfy $\sqrt{P_{S}}\ge\delta_{\mathrm c}k/(a_{\mathrm B}H_{\mathrm B})$ and can therefore collapse into primordial black holes.
• Figure 4: Critical-collapse scaling from a 1-D toy simulation. Orange symbols are the simulated PBH masses versus excess density $\delta-\delta_{c}$. The dashed red line shows a fit with slope $\gamma_{\rm fit}\simeq0.36$, matching the theoretical critical exponent (dotted black line).
• Figure 5: Mapping between comoving wavenumber $k$ and primordial black-hole mass $M_{\rm PBH}$ from Eq. \ref{['eq:k_M_relation']} with $\gamma=0.2$. The secondary $y$-axis converts $k$ to the corresponding horizon (re-entry) temperature $T_{\rm re}$ via Eq. \ref{['eq:MHofT']}. Benchmarks for sub-lunar PBHs, the LIGO mass band, and the $30\,M_\odot$ GW150914 event are indicated.