Abstract
We study an inevitable cosmological consequence in PeV scale SUSY-breaking scenarios. We focus on the SUSY-breaking scale corresponding to the gravitino mass $m_{3/2}=100{\rm eV}-1{\rm keV}$. We argue that the presence of an early matter-dominated era and the resulting entropy production are requisite for the Universe with this gravitino mass. We infer the model-independent minimum amount of the entropy production $\Delta$ by requiring that the number of dwarf satellite galaxies $N_{\rm sat}$ in the Milky Way exceed the currently observed value, i.e. $N_{\rm sat}\gtrsim63$. This entropy production is inevitably imprinted on the primordial gravitational waves (pGWs) produced during the inflationary era. We study how the information on the value of $\Delta$ and the time of entropy production are encoded in the pGW spectrum $\Omega_{\rm GW}$. If the future GW surveys observe a suppression feature in the pGW spectrum for the frequency range $\mathcal{O}(10^{-10}){\rm Hz}\lesssim f_{\rm GW}\lesssim\mathcal{O}(10^{-5}){\rm Hz}$, it works as a smoking gun for PeV SUSY-breaking scenarios. Even if they do not, our study can be used to rule out all such scenarios.
Highlights
One of the advantages of studying gravitino cosmology lies in the fact that the gravitino mass m3=2 is directplyffiffirffielated to a superpsyffimffi metry (SUSY)-breaking scale F, i.e., m3=2 ≃ F=ð 3MPÞ, where MP ≃ 2.4 × 1018 GeV
We study the deviation of the primordial gravitational waves (PGWs) spectrum from its usual, almost scale-invariant form induced by the presence of an early matter-dominated (EMD) era followed by the entropy production via the decay of a heavy degree of freedom
We demonstrated the necessity of the late time entropy production prior to big bang nucleosynthesis (BBN) era for the Universe
Summary
One of the advantages of studying gravitino cosmology lies in the fact that the gravitino mass m3=2 is directplyffiffirffielated to a superpsyffimffi metry (SUSY)-breaking scale F, i.e., m3=2 ≃ F=ð 3MPÞ, where MP ≃ 2.4 × 1018 GeV. We derive the necessary amount of entropy production for each m3=2 and argue that this entropy production is inevitably imprinted on the primordial (inflationary) gravitational wave (PGW) spectrum [8,9,10,11,12] This means that the feature in the PGW spectrum works as a smoking gun for PeV-scale SUSY-breaking scenarios. Since the entropy production must occur after gravitino decoupling, the corresponding frequency of the PGW falls in the best frequency band explored by future experiments Even if they detect only the PGW spectrum without any suppression feature in the frequency range Oð10−10Þ Hz≲ fPGW ≲ Oð10−5Þ Hz, our study contributes to ruling out all the PeV-scale SUSY-breaking scenarios.
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