Probing the inflationary universe and reheating with primordial black holes and induced gravitational wave background

Abstract

The direct observational test for the earliest phase of our universe comes from cosmic microwave background (CMB) radiation, which can only probe up to the recombination era. The only definitive event during the pre-recombination era is the Big Bang nucleosynthesis (BBN), which is highly sensitive to any change in the constituents of the universe. This leaves a gap in understanding the expansion history between the end of inflation and BBN, which is not accessible from any direct observations at our disposal.

Our study shall provide a unique way to connect the non-trivial expansion history with future gravitational wave (GW) observations in the context of primordial black holes (PBHs). PBHs have emerged as a promising candidate to explain the existence of cold dark matter (DM) in our universe. PBHs can form due to small-scale amplification in inflationary scalar perturbations when these perturbation modes re-enter the horizon in the post-inflationary universe. Thus, the existence of PBHs in the early universe opens up the possibility to probe our universe in the last forty $e$folds of inflation and the unknown phase between the end of inflation and the BBN. We study the PBH-forming models and different expansion histories for this intermediate phase, and we connect our results with observations; one is through the detection of second-order induced stochastic gravitational wave background (ISGWB) generated during PBH formation, other one is the GW signal coming from PBH density fluctuations in the post-inflationary universe, which can be potentially probed in different future gravitational wave observatories. Many crucial phenomena of our universe occur during this pre-BBN era, like Baryogenesis, EW phase transition, QCD phase transition, Dark matter production and freeze-out, Neutrino decoupling, etc. Thus, our study, determining the equation of the state of the pre-BBN universe, shall have enormous indirect implications for each of these events. On the other hand, the PBHs produced during this era can also directly contribute to baryogenesis, dark matter, and dark radiation production, which we can constrain and probe through future GW observatories. With the recent advances in GW detection techniques, breaking the degeneracies of GW background sources with other astrophysical sources has also become very important. The study of ISGWB, modified due to the non-trivial pre-BBN universe, is a crucial step toward identifying and classifying ISGWBs from PBH-forming models.

We study the generation of PBHs in a single field inflection point inflationary model wherein the effective potential is expanded up to the sextic order, and the inversion symmetry is imposed such that only even powers are retained in the potential. Such a potential allows an inflection point that leads to a dynamical phase of ultra-slow roll evolution, thereby causing an enhancement of the primordial perturbation spectrum at smaller scales. Working with a quasi-inflection point in the potential, we find that PBHs can be produced in our scenario in the asteroid-mass window with a nearly monochromatic mass fraction which can account for the whole dark matter in the universe. For different choices of quasi-inflection points and other parameters of our model, we can also generate PBHs in higher mass windows. Still, the primordial spectrum of curvature perturbations becomes strongly tilted at the CMB scales. Moreover, we study the effects of a reheating epoch after the end of inflation on the PBHs mass fraction and find that an epoch of a matter-dominated reheating can shift the mass fraction to a larger mass window as well as increase their fractional contribution to the total dark matter even for the case of a monochromatic mass fraction.

In all inflationary scenarios of PBH formation, amplified scalar perturbations inevitably accompany an ISGWB at smaller scales. We study the ISGWB originating from the inflection point inflationary model wherein PBHs can be produced with a nearly monochromatic mass fraction in the asteroid mass window accounting for the total dark matter in the universe. In our scenario, we numerically calculate the ISGWB for frequencies ranging from nanoHz to KHz that cover the observational scales corresponding to future space-based GW observatories such as IPTA, LISA, DECIGO, and ET. Interestingly, we find that ultralight PBHs ($M_{\rm PBH} \sim 10^{-20} M_\odot$), which shall completely evaporate by today with an exceedingly small contribution to dark matter, would still generate an ISGWB that may be detected by a future design of the ground-based Advanced LIGO detector. Using a model-independent approach, we obtain a stringent lower mass limit for ultralight PBHs, which would be valid for a large class of ultra-slow roll inflationary models. Further, we extend our formalism to study the imprints of a reheating epoch on both the ISGWB and the derived lower mass bound. We find that any non-instantaneous reheating leads to an even stronger lower bound on PBHs mass and an epoch of prolonged matter-dominated reheating shifts the ISGWB spectrum to smaller frequencies. In particular, we show that an epoch of an early matter-dominated phase leads to a secondary amplification of ISGWB at much smaller scales corresponding to the smallest comoving scale leaving the horizon during inflation or the end of inflation scale.

Ultra-low mass spinning and non-spinning PBHs, which may briefly dominate the energy density of the universe but completely evaporate before the BBN, can lead to interesting observable signatures. Here the first-order adiabatic perturbation from inflation and from the isocurvature perturbations due to PBH distribution source tensor perturbations in the second-order lead to two peaks in the induced GW background. These resonant peaks are generated at the beginning of standard radiation domination in the presence of a prior PBH-dominated era. We studied this generation of the doubly peaked spectrum of induced ISGWB for such a scenario and explored the possibility of probing PBH evaporation-induced baryogenesis, dark matter, and dark radiation. Hawking evaporation of PBHs can lead to a class of baryogenesis models wherein the emission of massive unstable particles from the PBH evaporation and their subsequent decay contributes to the matter-antimatter asymmetry. The emission of light relativistic dark sector particles can contribute to the dark radiation and massive stable dark sector particles accounting for the dark matter component of our universe. The ISGWB can probe or constrain such scenarios. For the case of dark radiation, we find a novel complementarity between the measurements of $\Delta N_{\rm eff}$ from these emitted particles and the ISGWB from PBH domination. Our results indicate that the ISGWB weakly depends on the initial PBH spin. However, for gravitons as the dark radiation particles, the initial PBH spin plays a significant role, and only above a critical value of the initial spin parameter $a_*$, which depends only on initial PBH mass, the graviton emission can be probed in the CMB-HD experiment. Upcoming CMB experiments such as CMB-HD and CMB-Bharat, together with future GW detectors like LISA and ET, open up an exciting possibility of constraining the PBHs parameter space providing deeper insights into the expansion history of the universe between the end of inflation and BBN.