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

Gao, Xian; Yamaguchi, Masahide; Yoshida, Daisuke

doi:10.1088/1475-7516/2019/03/006

Cited by 24 publications

(19 citation statements)

References 96 publications

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“…Spatially covariant theories of gravity have been proposed and studied previously with different motivations and forms, such as in the effective field theory of inflation [19,20], in the Hořava gravity [21,22], etc. Spatially covariant gravity theories with at most three degrees of freedom were extensively studied in [23][24][25][26][27][28][29][30].…”

Section: The Formalismmentioning

confidence: 99%

Higher derivative scalar-tensor monomials and their classification

Gao

2020

Preprint

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We make a full classification of scalar monomials built of the Riemann curvature tensor up to the quadratic order and of the covariant derivatives of the scalar field up to the third order. From the point of view of the effective field theory, the third or even higher order covariant derivatives of the scalar field are of the same order as the higher curvature terms, and thus should be taken into account. Moreover, higher curvature terms and higher order derivatives of the scalar field are complementary to each other, of which novel ghost-free combinations may exist. We make a systematic classification of all the possible monomials, according to the numbers of Riemann tensor and higher derivatives of the scalar field in each monomial. Complete basis of monomials at each order are derived, of which linear combinations may yield novel ghost-free Lagrangians. We also develop a diagrammatic representation of the monomials, which may help to simplify the analysis.

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Section: The Formalismmentioning

confidence: 99%

Higher derivative scalar-tensor monomials and their classification

Gao

2020

Preprint

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“…[65,66], in which a general framework for the spatially covariant gravity theories was proposed. This framework was further generalized by including a dynamical lapse function [67,68], and by including an additional nondynamical scalar field [69]. The virtue of the spatially covariant gravity theories is that they can be related to the scalar-tensor theories that are healthy in the unitary gauge (a gauge in which φ = φ(t)) [70], which are much broader than the healthy covariant scalar-tensor theories and have much more applications in cosmology.…”

Section: Introductionmentioning

confidence: 99%

Propagation of gravitational waves in a cosmological background

Gao

Hong

2020

Phys. Rev. D

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We investigate the propagation of the gravitational waves in a cosmological background. Based on the framework of spatially covariant gravity, we derive the general quadratic action for the gravitational waves. The spatial derivatives of the extrinsic curvature and the parity-violating terms are systematically introduced. Special attention is paid to the propagation speed of the gravitational waves. We find that it is possible to make the two polarization modes propagate in the same speed, which may differ from that of the light, in the presence of parity-violating terms in the action. In particular, we identify a large class of spatially covariant gravity theories with parity violation, in which both the polarization modes propagate in the speed of light. Our results imply that there are more possibilities in the framework of spatially covariant gravity in light of the propagation speed of the gravitational waves. *

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“…The SCG can be traced back to the ghost condensation [26] and was developed in the effective field theory of inflation [27,28] as well as in the Hořava gravity [29,30]. It was further generalized in [31] in which a large class of SCG theories was proposed and was extended in [32] by including the dynamical lapse function and in [33] with an auxiliary scalar field.…”

Section: Introductionmentioning

confidence: 99%

Spatially covariant gravity with two degrees of freedom: perturbative analysis

Hu,

Gao

2021

Preprint

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We revisit the problem of building the Lagrangian of a large class of metric theories that respect spatial covariance, which propagate at most two degrees of freedom and in particular no scalar mode. The Lagrangians are polynomials built of the spatially covariant geometric quantities. By expanding the Lagrangian around a cosmological background and focusing on the scalar modes only, we find the conditions for the coefficients of the monomials in order to eliminate the scalar mode at the linear order in perturbations. We find the conditions up to d = 4 with d the total number of derivatives in the monomials and determine the explicit Lagrangians for the cases of d = 2, d = 3 as well as the combination of d = 2 and d = 3. We also expand the Lagrangian of d = 2 to the cubic order in perturbations, and find additional conditions for the coefficients such that the scalar mode is eliminated up to the cubic order. This perturbative analysis can be performed order by order, and one expects to determine the final Lagrangian at some finite order such that the scalar mode is fully eliminated. Our analysis provides an alternative and complimentary approach to building spatially covariant gravity with only tensorial degrees of freedom. The resulting theories can be used as alternatives to the general relativity to describe the tensorial gravitational waves in a cosmological setting.

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

Cited by 24 publications

References 96 publications

Higher derivative scalar-tensor monomials and their classification

Higher derivative scalar-tensor monomials and their classification

Propagation of gravitational waves in a cosmological background

Spatially covariant gravity with two degrees of freedom: perturbative analysis

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