BICEP2, the curvature perturbation and supersymmetry

The tensor fraction $r\simeq 0.16$ found by BICEP2 corresponds to a Hubble parameter $H\simeq 1.0\times 10^{14}\GeV$ during inflation. This has two implications for the (single-field) slow-roll inflation hypothesis. First, the inflaton perturbation must account for much more than $10\%$ of the curvature perturbation $ζ$, which barring fine-tuning means that it accounts for practically all of it. It follows that a curvaton-like mechanism for generating $ζ$ requires an alternative to slow roll such as k-inflation. Second, accepting slow-roll inflation, the excursion of the inflaton field is at least of order Planck scale. As a result, the flatness of the inflaton presumably requires a shift symmetry. I point out that if such is the case, the resulting potential is likely to have at least approximately the quadratic form suggested in 1983 by Linde, which is known to be compatible with the observed $r$ as well as the observed spectral index $\ns$. The shift symmetry does not require supersymmetry. Also, the big $H$ may rule out a GUT by restoring the symmetry and producing fatal cosmic strings. The absence of a GUT would correspond to the absence of superpartners for the Standard Model particles, which indeed have yet to be found at the LHC. It therefore seems quite possible that the quantum field theory chosen by Nature is not supersymmetric.

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