GUT Scale And Leptogenesis From 5D Inflation

We discuss a five dimensional inflationary scenario based on a supersymmetric SO(10) model compactified on S/(Z2 × Z ′ 2). Inflation is implemented through scalar potentials on four dimensional branes, and a brane-localized Einstein-Hilbert term plays an essential role. The orbifold boundary conditions break the SO(10) gauge symmetry to SU(4)c×SU(2)L×SU(2)R (≡ H). The inflationary scenario yields δT/T ∝ (M/MPlanck), which fixes M , the symmetry breaking scale of H to be close to the SUSY GUT scale of 1016 GeV. The scalar spectral index n is 0.98 − 0.99, while the gravitational wave contribution to the quadrupole anisotropy is negligible ( ∼ 1%). The inflaton decay into the lightest right handed neutrinos yields the observed baryon asymmetry via leptogenesis. [email protected] [email protected] There exists a class of supersymmetric models in which a close link exists between inflation and the grand unification scale [1, 2]. In particular, the quadrupole microwave anisotropy is proportional to (M/MPlanck) , where M denotes the scale of the gauge symmetry breaking associated with inflation, and MPlanck = 1.2 × 10 GeV. Thus, M is expected to be of order 10 GeV, to within a factor of 2 or so, depending on the details of the supersymmetric model. This is tantalizingly close to the supersymmetric grand unification scale inferred from the evolution of the minimal supersymmetric standard model (MSSM) gauge couplings, and it is therefore natural to try to realize this inflationary scenario within a grand unified framework [2]. The SO(10) model is particularly attractive in view of the growing confidence in the existence of neutrino oscillations [4], which require that at least two of the three known neutrinos have a non-zero mass. Because of the presence of right handed neutrinos (MSSM singlets), non-zero masses for the known neutrinos is an automatic consequence of the see-saw mechanism [5]. Furthermore, the right handed neutrinos play an essential role in generating the observed baryon asymmetry via leptogenesis [6], which becomes especially compelling within an inflationary framework [7]. Indeed, an inflationary scenario would be incomplete without explaining the origin of the observed baryon asymmetry, and the kind of models we are interested in here automatically achieve this via leptogenesis. A realistic supersymmetric inflationary model along the lines we are after was presented in [8], based on the SO(10) subgroup SU(4)c×SU(2)L×SU(2)R (≡ H) [9]. The scalar spectral index n has a value very close to unity (typically n ≈ 0.98−0.99), while the symmetry breaking scale of H lies, as previously indicated, around 10 GeV. The vacuum energy density during inflation is of order 10 GeV, so that the gravitational contribution to the quadrupole anisotropy is essentially negligible. It is important to note here that the inflaton field in this scenario eventually decays into right handed neutrinos, whose out of equilibrium decays lead to leptogenesis. An extension to the full SO(10) model is complicated by the notorious doublet-triplet