  We propose a minimal gauged $U(1)_{B-L}$ extension of the minimal
supersymmetric Standard Model (MSSM) which resolves the cosmological moduli
problem via thermal inflation, and realizes late-time Affleck-Dine leptogensis
so as to generate the right amount of baryon asymmetry at the end of thermal
inflation. The present relic density of dark matter can be explained by
sneutrinos, MSSM neutralinos, axinos, or axions. Cosmic strings from
$U(1)_{B-L}$ breaking are very thick, and so the expected stochastic
gravitational wave background from cosmic string loops has a spectrum different
from the one in the conventional Abelian-Higgs model, as would be
distinguishable at least at LISA and DECIGO. The characteristic spectrum is due
to a flat potential, and may be regarded as a hint of supersymmetry. Combined
with the resolution of moduli problem, the expected signal of gravitational
waves constrains the $U(1)_{B-L}$ breaking scale to be
$\mathcal{O}(10^{12-13})\,{\rm GeV}$. Interestingly, our model provides a
natural possibility for explaining the observed ultra-high-energy cosmic rays
thanks to the fact that the core width of strings in our scenario is very
large, allowing a large enhancement of particle emissions from the cusps of
string loops. Condensation of $LH_u$ flat-direction inside of string cores
arises inevitably and can also be the main source of the ultra-high-energy
cosmic rays accompanied by ultra-high-energy lightest supersymmetric particles.
