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arXiv · 1810.07434

Higher derivative scalar-tensor theory through a non-dynamical scalar field

Xian Gao·Masahide Yamaguchi·Daisuke Yoshida
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Abstract

We propose a new class of higher derivative scalar-tensor theories without the Ostrogradsky's ghost instabilities. The construction of our theory is originally motivated by a scalar field with spacelike gradient, which enables us to fix a gauge in which the scalar field appears to be non-dynamical. We dub such a gauge as the spatial gauge. Though the scalar field loses its dynamics, the spatial gauge fixing breaks the time diffeomorphism invariance and thus excites a scalar mode in the gravity sector. We generalize this idea and construct a general class of scalar-tensor theories through a non-dynamical scalar field, which preserves only spatial covariance. We perform a Hamiltonian analysis and confirm that there are at most three (two tensors and one scalar) dynamical degrees of freedom, which ensures the absence of a degree of freedom due to higher derivatives. Our construction opens a new branch of scalar-tensor theories with higher derivatives.

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Xian Gao, Masahide Yamaguchi, Daisuke Yoshida. 2018-10-17. Higher derivative scalar-tensor theory through a non-dynamical scalar field. https://doi.org/10.1088/1475-7516%2F2019%2F03%2F006

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