Ghost-free, gauge invariant SVT generalizations of Horndeski theory

Abstract We analyze the generalizations of Kaluza–Klein compactifications of 5D Horndeski theory. They are Scalar–Vector–Tensor (SVT) theories with higher derivatives in the action, but with second order equations of motion. The vector field is invariant under a U(1) gauge transformation and the Scalar–Tensor sector corresponds to Horndeski theory. A subclass of these SVT theories is such that the Horndeski functions $$G_4(\pi ,X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>π</mml:mi> <mml:mo>,</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> and $$G_5(\pi )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>5</mml:mn> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>π</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> remain free, while the speed of the tensor and vector modes is exactly the same. We show a subclass where the vector sector retains freedom through new functions of $$\pi ,\, X$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> while the speed of the vector modes still tracks the speed of the tensor modes.