We consider a supersymmetric hybrid inflation scenario in which the U (1) R-symmetry is explicitly broken by Planck scale suppressed operators in the superpotential. We provide an example with minimal Kähler potential, with the R-symmetry breaking term relevant during inflation being αS 4 , where S denotes the well-known gauge singlet inflaton superfield. The inflationary potential takes into account the radiative and supergravity corrections, as well as the soft supersymmetry breaking terms. For successful inflation, with the scalar spectral index in the currently preferred range, n s ≈ 0.97 ± 0.010, |α| 10 −7 . The tensor to scalar ratio r 10 −4 , while |dn s /d ln k| ∼ O(10 −3 ) − O(10 −4 ).PACS numbers: 98.80.Cq
INTRODUCTIONModern cosmology has seen rapid developments due to experiments such as COBE and WMAP. Augmenting their unprecedented successes will be Planck, which may for the first time yield direct evidence of inflation. At the same time, there are enormous strides being made in particle physics, with the LHC having made perhaps the greatest single discovery in the field in decades, while the testing of supersymmetry (SUSY) is highly anticipated. For the first time particle and cosmological models can be tested with precision, and the deep connections between these two fields motivate us to consider the effects that particle physics considerations have on inflationary models. This has led to models such as, among others, SUSY hybrid inflation.The standard version of SUSY hybrid inflation [1-3] remains one of the most successful and well-motivated inflationary models. It is the most general non-trivial model one can write with a gauge singlet field S and supermultiplets Φ andΦ that respects U (1) R , such that the latter two fields belong to non-trivial representations of the gauge group G. It has a connection to particle physics in that within it grand unified theories (GUTs) are naturally incorporated. In this model the gauge group G is broken to a subgroup H at the end of inflation, and the energy scale at which this occurs is related to local temperature anisotropies in the cosmic microwave background radiation [1]; this scale happens to be close to the GUT scale, indicating that G may be related to a GUT. In addition, supergravity (SUGRA) corrections remain under control [4] because this model can yield solutions within the WMAP nine-year 2σ bounds without trans-Planckian inflaton field values. In this model, where only (minimal) SUGRA and radiative corrections are added to the global potential, a numerical lower bound on the scalar spectral index, n s ≈ 0.985, develops. This is somewhat disfavored, although it is within the 2σ bounds, n s = 0.971 ± 0.010 [5]. However, the addition of a linear soft-SUSY breaking term [6] reduces n s significantly [7]; this term is also important in explaining the MSSM µ-problem [8][9][10]. It has been shown that small gravity waves (tensor-to-scalar ratio r) are produced with minimal Kähler (retaining the lowest-order SUGRA term), radiative corrections, and positi...
