[Paper Review] Gravitational wave signatures of no-scale Supergravity in NANOGrav and beyond

Spyros Basilakos, Dimitri V. Nanopoulos+3 more|arXiv (Cornell University)|Jul 17, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a three-peaked gravitational wave (GW) signal—spanning nHz, Hz, and kHz frequencies—arising from no-scale Supergravity models with inflection-point inflation and primordial black hole (PBH)-induced early matter-dominated eras. The signal emerges from second-order GW production via curvature and isocurvature perturbations, with all three peaks in strong agreement with NANOGrav PTA data and offering a potential observational signature for no-scale Supergravity.

ABSTRACT

In this Letter, we derive for the first time a characteristic three-peaked GW signal within the framework of no-scale Supergravity, being the low-energy limit of Superstring theory. We concentrate on the primordial gravitational wave (GW) spectrum induced due to second-order gravitational interactions by inflationary curvature perturbations as well as by isocurvature energy density perturbations of primordial black holes (PBHs) both amplified due to the presence of an early matter-dominated era (eMD) era before Big Bang Nucleosythesis (BBN). In particular, we work with inflection-point inflationary potentials naturally-realised within Wess-Zumino type no-scale Supergravity and giving rise to the formation of microscopic PBHs triggering an eMD era and evaporating before BBN. Remarkably, we obtain an abundant production of gravitational waves at the frequency ranges of $\mathrm{nHz}$, $\mathrm{Hz}$ and $\mathrm{kHz}$ and in strong agreement with Pulsar Time Array (PTA) GW data. Interestingly enough, a simultaneous detection of all three $\mathrm{nHz}$, $\mathrm{Hz}$ and $\mathrm{kHz}$ GW peaks can constitute a potential observational signature for no-scale Supergravity.

Motivation & Objective

• To identify a distinctive gravitational wave (GW) signature within no-scale Supergravity, the low-energy limit of Superstring theory.
• To explore how primordial black holes (PBHs) with masses <10⁹ g can trigger an early matter-dominated (eMD) era before Big Bang Nucleosynthesis (BBN).
• To derive the induced stochastic GW background from second-order gravitational interactions of inflationary adiabatic and PBH isocurvature perturbations.
• To test whether the simultaneous detection of nHz, Hz, and kHz GW peaks can serve as a unique observational signature for no-scale Supergravity.

Proposed method

• Employing Wess-Zumino type no-scale Supergravity with a deformed Kähler potential to realize inflection-point inflationary potentials.
• Modeling the formation of microscopic PBHs with masses <10⁹ g that trigger an early matter-dominated (eMD) era prior to BBN.
• Calculating the induced GW spectrum via second-order gravitational interactions of curvature perturbations and isocurvature energy density fluctuations from PBH number density Poisson fluctuations.
• Applying resonant amplification of GWs due to the sudden transition from eMD to radiation-dominated (RD) era.
• Comparing the predicted GW power spectra with NANOGrav 15-year PTA data and sensitivities of future detectors (SKA, LISA, BBO, ET).
• Using the constraint Ω_GW,0 h² ≤ 6.9×10⁻⁶ from CMB and BBN to bound the total GW energy density.

Experimental results

Research questions

• RQ1 Can no-scale Supergravity with inflection-point inflation produce a three-peaked gravitational wave signal across nHz, Hz, and kHz frequencies?
• RQ2 How do PBH-induced early matter-dominated eras amplify GWs through second-order gravitational interactions?
• RQ3 To what extent does the predicted GW spectrum match the 15-year NANOGrav pulsar timing array data?
• RQ4 Can the simultaneous detection of nHz, Hz, and kHz GW peaks serve as a unique observational signature for no-scale Supergravity?
• RQ5 Is the three-peaked GW signal a generic feature of SU(2,1)/SU(2)×U(1) no-scale Supergravity models with inflection-point potentials?

Key findings

• The model produces a three-peaked induced GW spectrum at nHz, Hz, and kHz frequencies, with the nHz peak in agreement with the 15-year NANOGrav pulsar timing array data.
• The nHz peak arises from resonantly amplified inflationary adiabatic perturbations due to the eMD-to-RD transition, matching PTA observations within error bars.
• The Hz peak originates from isocurvature energy density perturbations of PBHs, lying within the sensitivity bands of future detectors like ET and BBO.
• The kHz peak is associated with the formation process of microscopic PBHs, providing a high-frequency GW component.
• The simultaneous detection of all three peaks would constitute a unique observational signature for no-scale Supergravity.
• The three-peaked signal is a direct consequence of the no-scale Wess-Zumino inflection-point potential and is not generic to all PBH models, distinguishing it from oscillatory signals in broader mass function scenarios.