2018/10/31 by Xian Gao, Masahide Yamaguchi, Daisuke Yoshida
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical field theory #Classical mechanics #Cosmology and Gravitation Theories #Diffeomorphism #Exact solutions in general relativity #Gauge theory #General relativity #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Scalar field #Scalar field theory #Scalar theories of gravitation #Tensor field #Theoretical physics #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2019/03/006
published as JCAP 03 (2019) 006 · 19 pages, 1 figure; v2 matching the JCAP version
arxiv created 2019/03/04 · openalex publication_date 2019/03/04 · arxiv updated 2019/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.