Improvement of energy-momentum tensor and non-Gaussianities in holographic cosmology

In holographic models of cosmology based on the (A)dS/CFT correspondence, conformal symmetry is implicit in the dual description of the Universe. Generically, however, one cannot expect the (broken) conformal invariance in the cosmic fluctuations as only the scale invariance is manifest in experiments. Also, in order for the prediction of the holographic models to make sense, the conformal symmetry needs to be broken as the scalar mode of the metric fluctuations becomes pure gauge in the conformal limit. We discuss the improvement ambiguity of the energy-momentum tensor in this context and construct a holographic model of the Universe that preserves the scale invariance but not necessarily the full conformal invariance. Our sample computation using a weakly coupled dual field theory shows that the orthogonal type of non-Gaussianity is present over and above the equilateral type. The improvement ambiguity corresponds to the choice of the energy momentum tensor that will couple to our particle physics sector after inflation. Our results show that the holographic prediction of the cosmological parameters crucially depends on such a choice.