The stochastic gravitational-wave background from primordial black holes and observable proton decay in R-symmetric SU(5) Inflation

Abstract This study explores the realization of nonminimally coupled Higgs inflation in the context of no-scale supergravity, investigates the formation of primordial black holes, and examines the potential for observable proton decay within the framework of the R-symmetric SU (5) model. For inflation, both single and multifield scenarios are investigated. The prediction of the single-field model for the tensor-to-scalar ratio, r , is approximately $$10^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> </mml:math> , and the scalar spectral index falls within Planck’s 1 $$\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> range. The running of the scalar spectral index, $$-{dn_{s}}/{d\ln {k}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>-</mml:mo> <mml:mrow> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>ln</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , is approximately $$10^{-4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> . A realistic scenario of reheating and non-thermal leptogenesis is employed with reheat temperature $$T_r\sim 10^9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> </mml:mrow> </mml:math> GeV. In the multifield case, we mainly focus on Primordial Black Holes (PBHs) and Gravitational Waves (GWs). In this inflationary framework, we demonstrate how a suitable choice of parameters can result in an enhanced scalar power spectrum, leading to the production of primordial black holes (PBHs) capable of fully accounting for dark matter. We also show that this scenario leads to Scalar Induced Gravitational Waves (SIGW) which can be detected in current and future GW detectors. We explore different proton decay channels to look for observable predictions for the next-generation proton decay experiments Hyper-K and DUNE consistent with gauge coupling unification and cosmological bounds.