Aleksander Kozak

Conformally-invariant framework for scalar-tensor theories of gravity in the metric, Palatini, and hybrid approaches

In my talk, I will summarize the research I conducted as a Ph.D. student at the Institute of Theoretical Physics. I will focus on the issue of conformal frames in modified gravity theories. Modified theories of gravity (or extended theories of gravity) introduce ambiguity in the description of gravitational phenomena related to the fact that there exists a multitude of conformal frames yielding - possibly - inequivalent predictions. In the literature, the most common frames are the Einstein and Jordan frames, and the issue of which one is correct remains a topic of debate. However, it was shown recently that it would be possible to construct a conformally-invariant framework for metric scalar-tensor (ST) theories of gravity. I will demonstrate that it is possible to extend the framework of conformal invariants to the case of Palatini ST theories of gravity. The connections between different versions of ST theories will also be explored. Some remarks on choosing the ‘right’ conformal frame will also be made. In the second part of my talk, I will move on to discussing applications of the invariant framework. It will be demonstrated that, in the minisuperspace formalism applied to the cosmological scenarios, the lapse function can be treated as a conformal factor, which will enable us to simplify the considerations and find integrals of motion for different theories. We will also revisit the connections between f(R) theories in different approaches and their ST representations. In the end, the conformally-invariant Tolman-Oppenheimer-Volkoff equation will be discussed.