MG15 - Talk detail

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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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Session

Accepted

Yes

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Time

Talk

Title

Abstract

We consider a particular scalar-tensor Horndeski gravity in Palatini formalism as a theory with two disformally related metrics. The first metric couples to matter, while the second one gives rise to an independent connection. This theory admits an alternative interpretation as Einstein gravity with minimally coupled scalar field. This proves the absence of ghosts in the considered variant of the Palatini-Hordeski model and also gives rise to generating technique for Horndeski theory. We construct the Horndeski counterpart to Fisher-Janis-Newman-Winicour (FJNW) singular solution of the standard theory for some partiucular mass to scalar charge ratio. Surprisingly, we find that in the Horndeski setting this solution becomes fully regular. The disformal transformation turns the former singular FJNW horizon to the product space of the two-dimensional Minkowski space $M_{-1,1}$ and a two sphere. This sphere is spatial section of the null hypersurface, which is neither a horizon nor an infinite redshift surface, though radial geodesics take infinite coordinate time to approach it.

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