AT1 - Extended Theories of Gravity and Quantum Cosmology |
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Speaker |
Zhidkova, Sofia |
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| Talk Title |
Non-minimal derivative coupling and disformal transformations in Palatini formalism |
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Abstract |
We discuss some special cases of Horndeski theory with non-minimal coupling of the curvature tensor to derivatives of the scalar field in Palatini formalism. We show that torsion in this theory can be eliminated by means of the gauge transformation. Further we show that the Palatini connection can be presented as the Levi-Civita one of a second metric, that is related to the initial metric by some disformal transformation. Due to this fact the equations of motion are modified considerably with respect to those in the metric Horndeski theory. Still we show that the two theories coincide up to the linear order in the weak coupling regime. On the contrary, in the strong coupling limit the system of equations becomes rather complicated and at first glance contains the Ostrogradsky ghosts. Nevertheless the equations of motion in the Palatini version remain of the second order in terms of some new disformally related metric. Also we observe that applying certain disformal transformations to Horndeski-type action we can reduce the action to the Einstein-Hilbert one plus some non-standard kinetic term of the scalar field. |
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