The paper discusses the cosmological constraints on supersymmetric theories with a new, stable particle, focusing on the neutral gauge/Higgs fermion as the best candidate. The authors derive bounds on the parameters governing the mass and couplings of this particle. They consider two favored possibilities: a photino with a mass above 0.5 GeV, or a Higgs fermion with a mass above 5 GeV or below 0.1 eV. The paper also highlights that a gravitino mass of 10 to 100 GeV implies a limit on the temperature after inflation, which affects mechanisms for generating the baryon number of the universe. The authors analyze the annihilation rates of these particles to provide constraints on the Lagrangian parameters and conclude that the lightest supersymmetric particle is likely a mixture of neutral gauge and Higgs fermions. They present numerical results showing the cosmologically allowed domains in the parameter space and discuss the implications for different sfermion masses.The paper discusses the cosmological constraints on supersymmetric theories with a new, stable particle, focusing on the neutral gauge/Higgs fermion as the best candidate. The authors derive bounds on the parameters governing the mass and couplings of this particle. They consider two favored possibilities: a photino with a mass above 0.5 GeV, or a Higgs fermion with a mass above 5 GeV or below 0.1 eV. The paper also highlights that a gravitino mass of 10 to 100 GeV implies a limit on the temperature after inflation, which affects mechanisms for generating the baryon number of the universe. The authors analyze the annihilation rates of these particles to provide constraints on the Lagrangian parameters and conclude that the lightest supersymmetric particle is likely a mixture of neutral gauge and Higgs fermions. They present numerical results showing the cosmologically allowed domains in the parameter space and discuss the implications for different sfermion masses.