Inflation with TeV-scale gravity needs supersymmetry

One cannot avoid the need for low-energy supersymmetry by invoking a fundamental Planck scale M ∼ TeV, because the inflaton mass during inflation then has to satisfy m/M ≪ 10. Supersymmetry should be invoked to stabilize this mass, just as it is invoked to stabilize the Higgs mass in the case that the fundamental Planck mass is MP. This observation removes the only reason for thinking that Nature might have chosen M ∼ TeV as the fundamental Planck scale. 1. There is a large hierarchy, mH/MP ∼ 10 , between the mass mH ∼ 1TeV of the Standard Model Higgs field and the Planck scale MP ≡ (8πG) −1/2 ≃ 10 GeV. This makes it difficult to understand the existence of the Higgs field, because in a generic field theory valid up to the Planck scale every elementary scalar field will have a mass of order MP. To be precise, the mass will be given by m 2 = m20 + ∑ ∆i + · · ·, where the first term is the tree-level value and the ∆i are one-loop contributions of order (λiMP) , with λi the strength of the interaction. To avoid this disaster, it is usual to invoke supersymmetry which automatically cancels the one-loop contributions to sufficient accuracy. An alternative proposal [2] is to place the fundamental Planck scale M in the TeV region. This makes the one-loop contributions of order (λiM) 2 and avoids fine-tuning. The low value of M is achieved by invoking extra space dimensions with large compactification radius. If there are n extra space dimensions with compactification radius R, and M is the fundamental Planck scale in 4 + n spacetime dimensions, the Planck scale that we observe is given by M P ∼ R M . (1) The alternatives are an accidental cancellation, perhaps to be understood anthropically [1], or a composite Higgs such as occurs in technicolor theories. It is difficult to construct composite theories that are consistent with observation.