The consortium NANOGrav discovered the isotropic gravitational wave background (GWB) with an amplitude of $h\sim 10^{-15}$ and a frequency of $f\sim 10^{-8}\mathrm{Hz}$ using observations of millisecond pulsars. We hypothesize that the GWB is relic radiation left over from the merging stellar mass black holes (SBHs) during Big Crunch at $z\sim 10^{10}$. The relic gravitational waves are similar to the gravitational waves with $f\sim 10^2\mathrm{Hz}$ discovered by LIGO in 2015, taking into account a decrease in frequency by a factor $\sim 10^{10}$ due to the expansion of the Universe. We take as a basis the observed spectrum of 139 SBHs, discovered by the LIGO observatory. Our model explains well all the observed features of the GWB. Unlike all other GWB models, our model predicts a sharp decrease in the GWB amplitude at frequencies $f>3.5\ast 10^{-8}\mathrm{Hz}$, reflecting the deficit of SBHs with masses $<4M_{\odot }$. The SBMH mergers at Big Crunch should generate yet undiscovered GWB with a frequency of $f\sim 10^{-(14-17)}\mathrm{Hz}$.

NANOGrav 财团发现了振幅为 $H～10^{-15}$ 和频率 $F～10^{-8}\mathrm{赫兹}$使用毫秒脉冲星的观测。我们假设 GWB 是在 Big Crunch 期间合并恒星质量黑洞 (SBHs) 留下的残余辐射$z～10^{10}$. 遗迹引力波类似于引力波$F～10^2\mathrm{赫兹}$ LIGO 在 2015 年发现的，考虑到频率下降了一个因素 $～10^{10}$由于宇宙的膨胀。我们以 LIGO 天文台发现的 139 个 SBH 的观测光谱为基础。我们的模型很好地解释了 GWB 的所有观察到的特征。与所有其他 GWB 模型不同，我们的模型预测 GWB 幅度在频率处急剧下降$F>3.5＊10^{-8}\mathrm{赫兹}$, 反映了 SBHs 与群众的赤字 $<4{米}_{\odot }$. Big Crunch 的 SBMH 合并应该会产生尚未发现的 GWB，频率为$F～10^{-(14-17)}\mathrm{赫兹}$.