$\delta T/T$ and Neutrino Masses in SU(5)

Abstract

We implement inflation in a supersymmetric SU(5) model with U(1) R-symmetry such that the cosmic microwave anisotropy $\delta T/T$ is proportional to $(M/M_{\rm Planck})^2$, where $M\sim M_{GUT}=2-3\times 10^{16}$ GeV, the SU(5) breaking scale, and $M_{\rm Planck}=2.4\times 10^{19}$ GeV. The presence of a global $U(1)_X$ symmetry, spontaneously broken also at scale $M_{GUT}$, provides an upper bound $M_{GUT}^2/M_{\rm Planck}\sim 10^{14}$ GeV on the masses of SU(5) singlet right handed neutrinos, which explains the mass scale associated with atmospheric neutrino oscillations. The SU(5) monopoles and $U(1)_X$ cosmic strings are inflated away. Although the doublet-triplet splitting requires fine-tuning, the MSSM $\mu$ problem is resolved and dimension five proton decay is strongly suppressed.