Impact of memory-burdened black holes on primordial gravitational waves in light of Pulsar Timing Array

Blue-tilted Gravitational Waves (BGWs) have been proposed as a potential candidate for the cosmic gravitational waves detected by Pulsar Timing Arrays (PTA). In the standard cosmological framework, BGWs are constrained in their frequency range by the Big Bang Nucleosynthesis (BBN) limit on GW amplitude, which precludes their detection at interferometer scales. However, introducing a phase of early matter domination dilutes BGWs at higher frequencies, ensuring compatibility with both the BBN and LIGO constraints on stochastic GWs. This mechanism allows BGWs to align with PTA data while producing a distinct and testable GW signal across a broad frequency spectrum. Ultralight Primordial Black Holes (PBHs) could provide the required early matter-dominated phase to support this process. Interpreted through the lens of BGWs, the PTA results offer a way to constrain the parameter space of a new scenario involving modified Hawking radiation, known as the ``memory burden" effect, associated with ultralight PBHs. This interpretation can be further probed by high-frequency GW detectors. Specifically, we demonstrate that PBHs as light as $10^{2-3}~{\rm g}$ can leave detectable imprints on BGWs at higher frequencies while remaining consistent with PTA observations.