Abstract
We investigate the production of primordial black holes and their contribution to the presently observed dark matter in a dilaton two-field extension of Starobinsky's quadratic $f(R)$ model of inflation. The model features a multi-field amplification mechanism which leads to the generation of a sharp peak in the inflationary power spectrum at small wavelengths responsible for the production of primordial black holes. This mechanism is significantly different from single-field models and requires a stochastic treatment during an intermediate phase of the inflationary dynamics. We find that the model leads to a successful phase of effective single-field Starobinsky inflation for wavelengths probed by the cosmic microwave background radiation and explains the observed cold dark matter content in the Universe by the formation of primordial black holes.
Highlights
Primordial black holes (PBHs) could provide an explanation of the origin of cold dark matter (CDM) without assuming new particles, generate the seeds of large scale structure, and probe very high energy physics including quantum gravity; see, e.g., [1,2,3,4,5] for a review, cosmological and astrophysical constraints on PBHs, and references therein to original papers.The phenomenologically most relevant PBH formation scenario is due to large density fluctuations generated during inflation
We find that the model leads to a successful phase of effective single-field Starobinsky inflation for wavelengths probed by the cosmic microwave background radiation and explains the observed cold dark matter content in the Universe by the formation of primordial black holes
We present our numerical results for the PBH mass distribution (A23) in the three mass windows (101)–(103)
Summary
Primordial black holes (PBHs) could provide an explanation of the origin of cold dark matter (CDM) without assuming new particles, generate the seeds of large scale structure, and probe very high energy physics including quantum gravity; see, e.g., [1,2,3,4,5] for a review, cosmological and astrophysical constraints on PBHs, and references therein to original papers. In this paper we investigate the formation of PBHs in a two-field dilaton extension of Starobinsky’s model. The nonminimal coupling to the linear Einstein-Hilbert term leads to an effective dilaton-dependent Planck mass, while the coupling to the quadratic R2-term leads to an effective dilaton-dependent scalaron mass The latter is a key element in the successful realization of the multi-field amplification mechanism that leads to an enhancement of the power spectrum of scalar perturbations crucial for the formation of PBHs. Our paper is organized as follows. An approximate analytical estimate for the power spectrum peak amplitude required for a significant PBH production is provided in Appendix B
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