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Disformal transformation of cosmological perturbations

Masato Minamitsuji

CMB observations are in very good agreements with inflationary models with non-minimal coupling between the scalar field and gravity. In such a model, the well-known conformal invariance is a powerful tool to analyze predictions in such a model. In this talk, we show how the notion of the conformal invariance can be extended to inflationary models in more general scalar-tensor theories motivated by the high energy theories.
First, we study multi-field inflation models with nonminimal coupling. In the multi-field case, we find that curvature perturbations in the Jordan and Einstein frames indeed evolve differently during inflation, but by the end of inflation they converge to the unique final observables. With nonminimal coupling, observables can easily be brought into agreement with the Planck data. On the other hand, more recently it has been known that realistic inflationary models can be recast into the Horndeski theory known as the most general scalar-tensor theory. While the conformal transformation generated by the scalar field can frame the classic scalar-tensor theories, the disformal transformation generated by the scalar field and its first order derivative can frame the Horndeski theory. We investigate how the gauge-invariant cosmological perturbation variables defined in two different frames are related under the disformal transformation and show that the comoving curvature perturbation is disformally invariant as well as conformally invariant. In case that the disformally coupled matter is the main source of curvature perturbations, we show how the evolution of curvature perturbation in both frames is interpreted differently. Finally, we argue how these results can further be generalized and useful for analyzing predictions from the unknown inflationary models.

2015 May 18, 11:00

Faculdade de Ciências da Universidade de Lisboa (C6.2.51)
Campo Grande, 1749-016 Lisboa

Faculdade de Ciências da Universidade de Lisboa Universidade do Porto Faculdade de Ciências e Tecnologia da Universidade de Coimbra
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia