As we have already seen before, there are several inflation models which discuss the possibility of the production of primordial black holes in inflation process of the early universe. But, the production of PBHs requires the violation of slow-roll condition. For this reason, slow-roll violating models become an interesting alternative, including ultra-slow-roll (USR) inflation, inflation with inflection points or bumps and others. In this scenario, the inflaton field experiences a very flat potential in the inflection point region of the potential. Such a flat region results in a so-called ultra slow-roll phase in which the inflaton velocity decreases with a faster rate than the slow-roll phase and inflaton has a friction dominated phase. Consequently, the curvature perturbation grows rapidly due to the great decrease of the Hubble slow-roll parameter.
Now, Zeinab Teimoori and colleagues proposed a novel mechanism yo achieve the ultra-roll inflation. In particular, they carried out study on the process of the Primordial Black Holes (PBHs) production in the novel framework, namely α-attractor Galileon inflation (G-inflation) model.
“The most important motivation for choosing the Galileon scalar field theory is that, the field equations driven from this theory include derivatives only up to second order.”— they said.
In their framework, they take the Galileon function as G(ϕ)=GI(ϕ)(1+GII(ϕ)), where the part GI(ϕ) is motivated from the α-attractor inflationary scenario in its original non-canonical frame, and it ensures for the model to be consistent with the Planck 2018 observations at the CMB scales. The part GII(ϕ) is invoked to enhance the curvature perturbations at some smaller scales which in turn gives rise to PBHs formation.
By fine tuning of the model parameters φc, ω, and σ, they found 3 parameters sets which successfully produced a sufficiently large peak in the curvature power spectrum. They showed that, these parameter sets produce PBHs with masses 12.99 M (for set 3), 1.76 × 10¯5 M (for set 2), and 8.6 × 10¯12 M (for set 1) which can explain the LIGO events, the ultrashort-timescale microlensing events in OGLE data, and around 0.98% of the current Dark Matter (DM) content of the universe, respectively.
Additionally, they studied the induction of the secondary gravitational waves (GWs) accompanied by the PBHs formation in their α-attractor G-inflation setup, and in particular they computed the present fractional energy density (ΩGW0) for the three parameter sets of their model. The spectrum of ΩGW0 exhibits a peak in its shape, and the peaks height for all the three cases is of order 10¯8, but their frequencies are different. The frequencies of the peaks for Cases 1, 2, and 3 are 2.953 × 10¯3 Hz, 8.017 × 10¯7 Hz, and 5.848 × 10¯10 Hz, respectively. The spectrum of ΩGW0 for Case 1 can be placed within the sensitivity region of detectors like LISA, TaiJi, and TianQin, and for Case 3 within the sensitivity regions of EPTA and SKA, while for Case 2, the spectrum is located completely outside of the sensitivity curves.
“Since the predictions of our α-attractor G-inflation model can lie inside the sensitivity regions of some GWs detectors, therefore the viability of our model can be tested in light of the forthcoming observational data.”— they added
Finally, they estimated the tilt of the spectrum of secondary GWs in their setting for different regions of the frequency band. Their findings confirmed that the power spectrum of ΩGW0 can be parameterized in terms of frequency as the power-law function Ω_GW0 ∼ f^n. They calculated the values of the constant ‘n’ for different frequency bands for each case of their model, and showed that the results in the infrared regime f ≪ fc satisfy properly the analytical expression ΩGW0 ∼ f^[3–2/ln(fc/f).
Reference: Zeinab Teimoori, Kazem Rezazadeh, Mariwan Ahmed Rasheed, Kayoomars Karami, “Mechanism of primordial black holes production and secondary gravitational waves in α-attractor Galileon inflationary scenario”, Arxiv, pp. 1-31, 2021. https://arxiv.org/abs/2107.07620
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