分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: Since the gravitational waves were detected by LIGO and Virgo, it has been promising that lots of information about the primordial Universe could be learned by further observations on stochastic gravitational waves background. The studies on gravitational waves induced by primordial curvature perturbations are of great interest. The aim of this paper is to investigate the third order induced gravitational waves. Based on the theory of cosmological perturbations, the first order scalar induces the second order scalar, vector and tensor perturbations. At the next iteration, the first order scalar, the second order scalar, vector and tensor perturbations all induce the third order tensor perturbations. We present the energy density spectrum of the third order gravitational waves for a monochromatic primordial power spectrum. The shape of the energy density spectrum of the third order gravitational waves is different from that of the second order scalar induced gravitational waves. And it is found that the third order gravitational waves sourced by the second order scalar perturbations dominate the energy density spectrum.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The damping effect of the free-streaming neutrinos on the second order
gravitational waves is investigated in detail. We solve the Boltzmann equation
and give the anisotropic stress induced by neutrinos to second order. The first
order tensor and its coupling with scalar perturbations induced gravitational
waves are considered. We give the analytic equations of the damping kernel
functions and finally obtain the energy density spectrum. The results show that
the free-streaming neutrinos suppress the density spectrum significantly for
low frequency gravitational waves and enlarge the logarithmic slope $n$ in the
infrared region ($k \ll k_*$) of the spectrum. For the spectrum of $k_*\sim
10^{-7}$Hz, the damping effect in the range of $k
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The process of \acp{PBH} formation would be inevitably accompanied by \acp{SIGW}. This strong correlation between \acp{PBH} and \acp{SIGW} signals could be a promising approach to detecting \acp{PBH} in the upcoming \ac{GW} experiments, such as \ac{LISA}. We investigate the third order \acp{SIGW} during a \ac{RD} era in the case of a monochromatic primordial power spectrum $\mathcal{P}_{\zeta}=A_{\zeta}k_*\delta\left(k-k_*\right)$. For \ac{LISA} observations, the relations between \ac{SNR} and monochromatic primordial power spectrum are studied systematically. It shows that the effects of third order \acp{SIGW} extend the cutoff frequency from $2f_*$ to $3f_*$ and lead to about $200\%$ increase of the \ac{SNR} for frequency band from $10^{-5}$Hz to $1.6\times 10^{-3}$Hz corresponding to \acp{PBH} with mass range $4\times 10^{-12}M_{\odot} \sim 10^{-7}M_{\odot}$. We find that there exists a critical value $A_*=1.76\times 10^{-2}$ for the amplitude of the monochromatic primordial power spectra, such that when $A_{\zeta}>A_*$, the energy density of third order \acp{SIGW} will be larger than the energy density of second order \acp{SIGW}.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The process of \acp{PBH} formation would be inevitably accompanied by \acp{SIGW}. This strong correlation between \acp{PBH} and \acp{SIGW} signals could be a promising approach to detecting \acp{PBH} in the upcoming \ac{GW} experiments, such as \ac{LISA}. We investigate the third order \acp{SIGW} during a \ac{RD} era in the case of a monochromatic primordial power spectrum $\mathcal{P}_{\zeta}=A_{\zeta}k_*\delta\left(k-k_*\right)$. For \ac{LISA} observations, the relations between \ac{SNR} and monochromatic primordial power spectrum are studied systematically. It shows that the effects of third order \acp{SIGW} extend the cutoff frequency from $2f_*$ to $3f_*$ and lead to about $200\%$ increase of the \ac{SNR} for frequency band from $10^{-5}$Hz to $1.6\times 10^{-3}$Hz corresponding to \acp{PBH} with mass range $4\times 10^{-12}M_{\odot} \sim 10^{-7}M_{\odot}$. We find that there exists a critical value $A_*=1.76\times 10^{-2}$ for the amplitude of the monochromatic primordial power spectra, such that when $A_{\zeta}>A_*$, the energy density of third order \acp{SIGW} will be larger than the energy density of second order \acp{SIGW}.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The primordial perturbations will inevitably generate higher order perturbations. We study the second order scalar perturbations generated by the primordial curvature and tensor perturbations in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second order scalar perturbations. The contributions from the initial second-order perturbations are considered. We calculate the power spectra of second order scalar perturbations for different tensor-to-scalar ratio $r$.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The cosmological background of higher order vector modes can be generated by the first order scalar perturbations. We investigate the second order and the third order vector modes systematically. The explicit expressions of two point functions $\langle V^{(n),\lambda}V^{(n),\lambda'} \rangle$$\left(n=2,3\right)$ and power spectra corresponded are presented. In the case of a monochromatic primordial power spectrum, the second order vector modes do not exist. However, the third order vector modes can be generated by a monochromatic primordial power spectrum. And it is found that the third order vector modes sourced by the second order scalar perturbations dominate the two point function $\langle V^{(3),\lambda}V^{(3),\lambda'} \rangle$ and power spectrum corresponded.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: The primordial perturbations will inevitably generate higher order perturbations. We study the second order scalar perturbations generated by the primordial curvature and tensor perturbations in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second order scalar perturbations. The contributions from the initial second-order perturbations are considered. We calculate the power spectra of second order scalar perturbations for different tensor-to-scalar ratio $r$.
分类: 天文学 >> 天文学 提交时间: 2023-02-19
摘要: We investigate the second order gravitational waves induced by the primordial scalar and tensor perturbations during radiation-dominated era. The explicit expressions of the power spectra of the second order GWs are presented. We calculate the energy density spectra of the second order GWs for a monochromatic primordial power spectra. For large $k$ $\left( k>k_* \right)$, the effects of the primordial tensor perturbation with tensor-to-scalar ratio $r=A_{h}/A_{\zeta}=0.2$ lead to an around $50\% $ increase of the signal-to-noise ratio (SNR) for LISA observations.