Memory burden effect on gravitational waves in the presence of primordial black holes

We present the spectrum of primordial gravitational wave (GW) expected from the presence of primordial black holes (PBHs) and inflaton in the early Universe. For the first time, to our knowledge, we combine the waves produced by the PBH decay with their density fluctuation counterpart, as well as their effects on the GW produced by the inflaton (high-frequency modes) and (low-frequency modes) the end of inflation. We generalize our study for a potential <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>V</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>ϕ</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>∝</a:mo> <a:msup> <a:mi>ϕ</a:mi> <a:mi>k</a:mi> </a:msup> </a:math> during reheating. We also extend our study, taking into account a possible memory burden effect to see how it can affect the shape of the spectrum.