Non - minimal quartic inflation in supersymmetric SO ( 10 )

Article history: Received 4 December 2016 Accepted 12 December 2016 Available online 16 December 2016 Editor: M. Cvetič We describe how quartic (λφ4) inflation with non-minimal coupling to gravity is realized in realistic supersymmetric SO (10) models. In a well-motivated example the 16 − 16 Higgs multiplets, which break SO (10) to SU (5) and yield masses for the right-handed neutrinos, provide the inflaton field φ. Thus, leptogenesis is a natural outcome in this class of SO (10) models. Moreover, the adjoint (45-plet) Higgs also acquires a GUT scale value during inflation so that the monopole problem is evaded. The scalar spectral index ns is in good agreement with the observations and r, the tensor to scalar ratio, is predicted for realistic values of GUT parameters to be of order 10−3–10−2. © 2016 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. By incorporating a single right-handed neutrino per generation to cancel new anomalies from gauging the accidental global U(1)B−L symmetry of the Standard Model (SM), both SU (4) × SU (2)L × SU (2)R [1] and SO (10) [2] provide particularly compelling examples of unifying the strong and electroweak forces. A non-supersymmetric model of SO(10) inflation [3], based on an earlier SU (5) model [4], was proposed a longtime ago. In this class of SO (10) inflation models, driven by a gauge singlet field with minimal coupling to gravity and utilizing the Coleman–Weinberg potential [5], the scalar to tensor ratio r, a canonical measure of gravity waves generated during inflation, is estimated to be 0.02, for ns = 0.96–0.97 [6]. Depending on the SO (10) symmetry breaking pattern, an observable number density of intermediate mass magnetic monopoles may be present in our galaxy [7]. In this letter we propose to implement primordial inflation in realistic supersymmetric SO (10) models [8]. We do this with a supergravity generalization of non-minimal λφ4 inflation [9]. Recall that λφ4 inflation with a minimal coupling to gravity predicts an r value close to 0.25–0.3, depending on the number of e-foldings (N0 = 60–50). This prediction for r lies well outside the 2-σ range allowed by Planck [10] and WMAP 9 [11]. In contrast, λφ4 inflation with a suitable non-minimal coupling to gravity is in good agreement with the data regarding the key parameters ns and r. The quantity r, in particular, can be as low as 0.003 or * Corresponding author. E-mail addresses: [email protected] (G.K. Leontaris), [email protected] (N. Okada), [email protected] (Q. Shafi). http://dx.doi.org/10.1016/j.physletb.2016.12.038 0370-2693/© 2016 Published by Elsevier B.V. This is an open access article under the CC so, for ns = 0.96–0.97. The discussion closely follows a previous model [12] based on supersymmetric SU (5). In order to retain perturbative unification of the MSSM gauge couplings in supersymmetric SO (10) we prefer to work with lower dimensional SO (10) representations. We employ 16 − 16 Higgs to break SO (10) to SU (5) while keeping supersymmetry unbroken. The 16 vacuum expectation value (VEV) also provides large masses ( 1014 GeV), via higher dimensional operators, to the right-handed neutrinos. In addition, the adjoint 45-plet, in conjunction either with a 54-plet or using higher dimensional operators, is employed to complete the breaking of SO (10) to the MSSM gauge symmetry. Finally, following [13], we can employ two Higgs 10-plets to implement electroweak symmetry breaking and accommodate the charged fermion masses and mixings as well as neutrino oscillation data. This summarizes the basic structure of a realistic supersymmetric SO (10) model. Recall that a non-minimal λφ4 inflation scenario is defined by the following action in the Jordan frame: S J = ∫ d4x √−g [ − 2 (1+ ξφ2)R+ 1 2 g∂μφ∂νφ − λ 16 φ4 ]