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We examine the effects of a stiff pre-recombination era on the present day'senergy spectrum of the primordial gravitational waves. If the background totalequation of state parameter at the pre-recombination era is described by akination era one, this directly affects the modes with characteristicwavenumbers which reenter the Hubble horizon during this stiff era. The stiffera causes a broken-power-law effect on the energy spectrum of thegravitational waves. We use two approaches, one model agnostic and a specificmodel that can realize this scenario. In all cases, the inflationary era can berealized either by some theory leading to a standard red-tilted tensor spectralindex or by some theory which has a mild tensor spectral index$n_{\mathcal{T}}=0.17-0.37$ like an Einstein-Gauss-Bonnet theory. For the modelagnostic scenario case, the NANOGrav signal can be explained by the stiffpre-recombination era combined with an inflationary era with a mild blue-tiltedtensor spectral index $n_{\mathcal{T}}=0.37$ and a low-reheating temperature$T_R\sim 0.1$GeV. In the same case, the red-tilted inflationary theory signalcan be detectable by the future LISA, BBO and DECIGO experiments. The modeldependent approach is based on a Higgs-axion model which can yield multipledeformations of the background total equation of state parameter, causingmultiple broken-power-law behaviors occurring in various eras before and afterthe recombination era. In this case, the NANOGrav signal is explained by thismodel in conjunction with an inflationary era with a really mild blue-tiltedtensor spectral index $n_{\mathcal{T}}=0.17$ and a low-reheating temperature$T_R\sim 20\,$GeV. In this case, the signal can be detectable by the futureLitebird experiment, which is a very characteristic pattern in the tail of theprimordial gravitational wave energy spectrum.

A Stiff Pre-CMB Era with a Mildly Blue-tilted Tensor Inflationary Era can Explain the 2023 NANOGrav Signal