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Non-Minimal M-flation

We show how in a matrix inflationary model in which there is a non-minimal coupling between the matrix inflatons and gravity --hence dubbed Non-$\MM$-flation-- some of the disadvantages of the minimal model can be avoided. In particular, the number of D3 branes can be reduced substantially to $\lesssim \mathcal{O}(100)$, which can alleviate the ``potential'' backreaction problem of large number of D3 branes on the background geometry. This is achieved by values of non-minimal coupling of order few hundred, which is much smaller than that of Higgs Inflation. The prediction of the model in the symmetry breaking part of the potential, which is a local attractor and can support eternal inflation, is compatible with the latest PLANCK results. In contrast to the minimal model, the spectator fields can partially or completely reheat the universe, depending on the symmetry-breaking vacuum expectation value and the non-minimal coupling parameter. We also comment on how the presence of gauge species keep the UV cutoff at around the Planck scale in the Einstein frame and, in contrast to the Higgs inflation, the problem of field displacements beyond the cutoff does not occur.