On cosmological scales the gravitational metric, which is used to build the Einstein-Hilbert action, and the metric where matter play out its dynamics need not be the same but could be related in a non-trivial way. This is the case, for example, of Brans-Dicke theory, where these metrics are related by a scalar field dependent conformal transformation. What is called "observable invariance" is well known for conformal transformations. Is that the case for more general transformations involving derivatives of the scalar field, a.k.a. disformal transformations? In this talk, I will show that indeed it is the case and I will emphasise this notion of two related metrics with an example. One the other hand, two theories will not be the same if the metrics to which matter couples, which we call matter metrics, are different from each other. Using this fact, I will consider a simple power law inflation (for the gravitational metric) and show that for some matter metrics the universe seen by matter need not be inflating. That is what we call frame "dependence" of inflation. Then, I will take a curvaton as a matter field and show that in some cases this could leave interesting features in the primordial power-spectrum.

NOTES

Note unusual time