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The no-scale flipped SU(5) superstring framework constitutes a very promisingparadigm for physics below the Planck scale providing us with a very richcosmological phenomenology in accordance with observations. In particular, itcan accommodate Starobinsky-like inflation, followed by a reheating phase,which is driven by a light "flaton" field, and during which the GUT phasetransition occurs. In this Letter, we extract for the first time agravitational-wave (GW) signal which naturally arises in the context of theflipped SU(5) cosmological phenomenology and is related to the existence of anearly matter era (eMD) driven by the flaton field. Specifically, we study GWsnon-linearly induced by inflationary perturbations and which are abundantlyproduced during a sudden transition from the flaton-driven eMD era to thelate-time radiation-dominated era. Remarkably, we find a GW signal with acharacteristic peak frequency $f_\mathrm{GW,peak}$ depending only on the stringslope $\alpha'$ and reading as $f_\mathrm{GW,peak} \propto 10^{-9}\left(\frac{\alpha'}{\alpha'_*}\right)^4 \mathrm{Hz}$, where $\alpha'_*$ is thefiducial string slope being related directly to the reduced Planck scale$M_\mathrm{Pl}$ as $\alpha'_* = 8/M^2_\mathrm{Pl}$. Interestingly enough,$f_\mathrm{GW,peak}$ lies within the $\mathrm{nHz}$ frequency range; hencerendering this primordial GW signal potentially detectable by SKA, NANOGrav andPTA probes at their very low frequency region of their detection bands.

Induced gravitational waves from flipped SU(5) superstring theory at $\mathrm{nHz}$