Ostrogradsky in theories with multiple fields

de Rham, Claudia; Matas, Andrew

doi:10.1088/1475-7516/2016/06/041

Ostrogradsky in theories with multiple fields

Journal Article · Thu Jun 23 00:00:00 EDT 2016 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2016/06/041· OSTI ID:1434604

de Rham, Claudia ^[1]; Matas, Andrew ^[2]

Case Western Reserve Univ., Cleveland, OH (United States). CERCA, Department of Physics; CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, U.S.A.
Case Western Reserve Univ., Cleveland, OH (United States). CERCA, Department of Physics

We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.

View Accepted Manuscript (DOE)

Research Organization:: Case Western Reserve Univ., Cleveland, OH (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009946

OSTI ID:: 1434604

Alternate ID(s):: OSTI ID: 22572103

Journal Information:: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 06 Vol. 2016; ISSN 1475-7516

Publisher:: Institute of Physics (IOP)Copyright Statement

Country of Publication:: United States

Language:: English

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