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Register a new userPrimordial black holes and induced gravitational waves from inflation in the Horndeski theory of gravity
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Added by
Gansukh Tumurtushaa
Publication date
2021
fields
Physics
and research's language is
English
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We investigate the production of primordial black holes (PBHs) and scalar-induced gravitational waves (GWs) for cosmological models in the Horndeski theory of gravity. The cosmological models of our interest incorporate the derivative self-interaction of the scalar field and the kinetic coupling between the scalar field and gravity. We show that the scalar power spectrum of the primordial fluctuations can be enhanced on small scales due to these additional interactions. Thus, the formation of PBHs and the production of induced GWs are feasible for our model. Parameterizing the scalar power spectrum with a local Gaussian peak, we first estimate the abundance of PBHs and the energy spectrum of GWs produced in the radiation-dominated era. Then, to explain the small-scale enhancement in the power spectrum, we reconstruct the inflaton potential and self-coupling functions from the power spectrum and their spectral tilt. Our results show that the small-scale enhancement in the power spectrum can be explained by the local feature, either a peak or dip, in the self-coupling function rather than the local feature in the inflaton potential.
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We investigate the propagation of primordial gravitational waves within the context of the Horndeski theories, for this, we present a generalized transfer function quantifying the sub-horizon evolution of gravitational waves modes after they enter the horizon. We compare the theoretical prediction of the modified primordial gravitational waves spectral density with the aLIGO, Einstein telescope, LISA, gLISA and DECIGO sensitivity curves. Assuming reasonable and different values for the free parameters of the theory (in agreement with the event GW170817 and stability conditions of the theory), we note that the gravitational waves amplitude can vary significantly in comparison with general relativity. We find that in some cases the gravitational primordial spectrum can cross the sensitivity curves for DECIGO detector with the maximum frequency sensitivity to the theoretical predictions around 0.05 - 0.30 Hz. From our results, it is clear that the future generations of space based interferometers can bring new perspectives to probing modifications in general relativity.
The possibility that in the mass range around $10^{-12} M_odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to the order of 0.01 at the scale $ksim 10^{12} text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(phi)]X$ with the function $G(phi)$ having a peak. Away from the peak, $G(phi)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(phi)$. The energy spectrum $Omega_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $Omega_{GW}(f)sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.
The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation is enhanced at $10^{12}$ Mpc$^{-1}$, $10^{8}$ Mpc$^{-1}$ and $10^{5}$ Mpc$^{-1}$, the production of PBH DM with peak masses around $10^{-13} M_{odot}$, the earths mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, $10^{-6}$ Hz and nHz, respectively. The PBHs with the mass scale $10^{-13} M_{odot}$ can make up almost all the DM and the associated SIGWs is testable by spaced based gravitational wave observatory.
Chaotic inflation is inconsistent with the observational constraint at 68% CL. Here, we show that the enhancement mechanism with a peak function in the noncanonical kinetic term not only helps the chaotic model $V(phi)=V_0phi^{1/3}$ satisfy the observational constraint at large scales but also enhances the primordial scalar power spectrum by seven orders of magnitude at small scales. The enhanced curvature perturbations can produce primordial black holes of different masses and secondary gravitational waves with different peak frequencies. We also show that the non-Gaussianities of curvature perturbations have little effect on the abundance of primordial black holes and energy density of the scalar-induced secondary gravitational waves.
A significant abundance of primordial black hole (PBH) dark matter can be produced by curvature perturbations with power spectrum $Delta_zeta^2(k_{mathrm{peak}})sim mathcal{O}(10^{-2})$ at small scales, associated with the generation of observable scalar induced gravitational waves (SIGWs). However, the primordial non-Gaussianity may play a non-negligible role, which is not usually considered. We propose two inflation models that predict double peaks of order $mathcal{O}(10^{-2})$ in the power spectrum and study the effects of primordial non-Gaussianity on PBHs and SIGWs. This model is driven by a power-law potential, and has a noncanonical kinetic term whose coupling function admits two peaks. By field-redefinition, it can be recast into a canonical inflation model with two quasi-inflection points in the potential. We find that the PBH abundance will be altered saliently if non-Gaussianity parameter satisfies $|f_{mathrm{NL}}(k_{text{peak}},k_{text{peak}},k_{text{peak}})|gtrsim Delta^2_{zeta}(k_{mathrm{peak}})/(23delta^3_c) sim mathcal{O}(10^{-2})$. Whether the PBH abundance is suppressed or enhanced depends on the $f_{mathrm{NL}}$ being positive or negative, respectively. In our model, non-Gaussianity parameter $f_{mathrm{NL}}(k_{mathrm{peak}},k_{mathrm{peak}},k_{mathrm{peak}})sim mathcal{O}(1)$ takes positive sign, thus PBH abundance is suppressed dramatically. On the contrary, SIGWs are insensitive to primordial non-Gaussianity and hardly affected, so they are still within the sensitivities of space-based GWs observatories and Square Kilometer Array.
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