δT/T and Neutrino Masses in SU(5)

We implement inflation in a supersymmetric SU(5) model with U(1)R symmetry such that the cosmic microwave anisotropy δT/T is proportional to (M/MPlanck) 2, where M ∼ MGUT = 2 − 3 × 1016 GeV, the SU(5) breaking scale, and MPlanck = 1.2 × 1019 GeV. The presence of a global U(1)X symmetry, spontaneously broken also at scale MGUT , provides an upper bound M2 GUT /MPlanck ∼ 1014 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 breaking of an accidental U(1)PQ axion symmetry generates the MSSM μ term. Dimension five proton decay mediated by the color triplet Higgsinos is strongly suppressed. [email protected] [email protected] In a class of supersymmetric models of inflation associated with some symmetry breaking G → H , the cosmic microwave anisotropy δT/T turns out to be proportional to (M/MPlanck) , where M denotes the symmetry breaking scale of G, and MPlanck = 1.2 × 10 GeV [1, 2]. Comparison with the determination of δT/T by WMAP and several other experiments [3] leads to the conclusion [1, 4] that M is comparable to MGUT ∼ 2 − 3 × 10 GeV, the scale at which the three gauge couplings of the minimal supersymmetric standard model (MSSM) unify. In such models, the scalar spectral index of density fluctuations including supergravity (SUGRA) corrections is ns ≈ 0.98−1.00 [4, 5], in excellent agreement with observations [3]. An essential role in the discussion is played by a global U(1)R symmetry which helps determine the form of the tree level superpotential and has other important phenomenological implications. For instance, the Z2 subgroup of U(1)R can be identified with the “matter parity” in the MSSM. This ensures the absence of rapid proton decay and stability of the LSP. Examples of G include the groups SU(3)c × SU(2)L × SU(2)R × U(1)B−L and SU(4)c × SU(2)L × SU(2)R [6], discussed in the context of inflation in Refs. [7] and [8], respectively. Among supersymmetric grand unified theories SU(5) [9] certainly has the simplest with the most direct connection to MGUT given above. It is therefore natural to try to realize this type of inflationary scenario in an SU(5) framework [10]. The minimal SU(5) model does not incorporate inflation and it also fails to provide an understanding of neutrino masses inferred from neutrino oscillations [11] and from cosmological considerations [3]. Our goal in this paper is to provide a suitable extension which can overcome both these shortcomings. We have already indicated the important role to be played by the U(1)R symmetry. Next we consider another symmetry, namely U(1)X , which also will be important for our analysis. This is a global symmetry of the minimal model [12] and its presence prevents the appearance of tree level superheavy masses ( > ∼ MGUT ) for the SU(5) singlet right handed neutrinos. In our extended model, the breaking of U(1)X trig-