Primordial Black Holes from $α$-attractors (1805.09483v2)

Abstract: We consider primordial black hole (PBH) production in inflationary $\alpha$-attractors. We discuss two classes of models, namely models with a minimal polynomial superpotential as well as modulated chaotic ones that admit PBHs. We find that a significant amplification of the curvature power spectrum ${\cal P_R}$ can be realized in this class of models with a moderate tuning of the potential parameters. We consistently examine the PBH formation during radiation and additionally during reheating eras where the background pressure is negligible. It is shown that basic features of the curvature power spectrum are explicitly related with the postinflationary cosmic evolution and that the PBH mass and abundance expressions are accordingly modified. PBHs in the mass range $10^{-16}-10^{-14} \, M_{\odot}$ can form with a cosmologically relevant abundance for a power spectrum peak ${\cal P_R} \sim 10^{-2}$ and large reheating temperature and, furthermore, for a moderate peak ${\cal P_R} \sim 10^{-5}$ and reheating temperature $T_\text{rh}\sim 10^7$ GeV, characteristic of the position of the power spectrum peak. Regarding the CMB observables, the $\alpha$-attractor models utilized here to generate PBH in the low-mass region predict in general a smaller $n_s$ and larger $r$ and $\alpha_s$ parameter values compared to the conventional inflationary $\alpha$-attractor models.

• The paper shows that α-attractor models significantly amplify the curvature power spectrum, a key condition for primordial black hole formation.
• The paper demonstrates that tuning model parameters can yield PBHs with masses between 10⁻¹⁶ and 10⁻¹⁴ solar masses, aligning with dark matter scenarios.
• The paper predicts distinct spectral indices and tensor-to-scalar ratios, offering testable implications for early-universe reheating and cosmic evolution.

Primordial Black Holes from $\alpha$-Attractors: Exploring Formation and Implications

This paper addresses the formation of primordial black holes (PBHs) within the framework of inflationary $\alpha$-attractors. It posits that these PBHs can form with an abundance sufficient to contribute significantly to the dark matter content of the universe. The authors explore two models under the $\alpha$-attractors family—those with minimal polynomial superpotentials and those with modulated chaotic potentials—and examine how each potentially allows for PBH production.

Key Findings

1. Curvature Power Spectrum Amplification: The paper demonstrates that $\alpha$-attractor models can achieve a significant amplification of the curvature power spectrum, ${\cal P_R}$, a necessary condition for PBH formation. This can result from moderate tuning of the potential parameters, fundamentally tied to the post-inflationary cosmic evolution.
2. PBH Mass and Abundance: For specific parameter configurations, PBHs could form within the mass range $10^{-16}-10^{-14} \, M_{\odot}$, aligning with cosmologically relevant scenarios where ${\cal P_R} \sim 10^{-2}$. The paper outlines that even for a moderate spectrum peak, such as ${\cal P_R} \sim 10^{-5}$, PBHs could form if the reheating temperature $T_\text{rh}$ is around $10^7$ GeV.
3. Cosmological Observables: The paper asserts that the models predict specific values for the spectral index $n_s$, and the tensor-to-scalar ratio $r$. These predictions can diverge from conventional inflationary models, providing a testing ground for future observational data.
4. Reheating and Matter-Domination Epochs: The researchers discuss PBH formation during the reheating stage and even during a subsequent matter-dominated epoch. They highlight that the lack of radiation pressure in such epochs modifies the expression for PBH mass and abundance, leading to differences in expected PBH characteristics.
5. Non-Spherical Effects: The modulated chaotic models consider the influence of quantum diffusion and non-Gaussianities, acknowledging their impact on PBH abundance predictions.

Implications and Future Research Directions

The work has significant implications for our understanding of dark matter and quantum cosmology. If PBHs formed during the early universe can indeed be attributed to these inflationary processes, their paper could provide insights into the primordial conditions that governed inflation.

This research suggests areas for further inquiry, particularly around:

• The Role of Reheating: A precise understanding of the reheating phase is vital, as it plays a crucial role in dictating the PBH formation conditions. Delving deeper into this epoch could help refine estimates of PBH abundance.
• Model Parameterization: Exploring different inflationary scenarios within the broader context of $\alpha$-attractors and beyond can help reveal more about the diversity of potential early universe events that could lead to PBH formation.
• CMB Measurements: As the authors note differences in $n_s$ and $r$, ongoing CMB studies could serve as a critical testing ground for the validity of $\alpha$-attractor models in explaining cosmic inflation.

Overall, the paper makes strides in linking sophisticated theoretical models with observable cosmic phenomena, opening pathways for integrated approaches combining theoretical physics and astrophysical observation to unlock the secrets of our universe's infancy.