Journal ArticleDOI
Second-order scalar-tensor field equations in a four-dimensional space
TLDR
In this article, the second-order Euler-Lagrange tensors are derived from a Lagrangian which is at most of second order in the derivatives of the field functions.Abstract:
Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions.read more
Citations
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Tracker and scaling solutions in DHOST theories
TL;DR: In this paper, the authors derived the most general Lagrangian allowing for tracker solutions characterized by ϕ ˙ / H p = constant, where ϕ is the time derivative of a scalar field ϕ, H is the Hubble expansion rate, and p is a constant.
Journal ArticleDOI
Dynamics of chiral cosmology
TL;DR: In this article, a detailed analysis for the dynamics of Chiral cosmology in a spatially flat Friedmann-Lema\^itre-Robertson-Walker universe with a mixed potential term is performed.
Journal ArticleDOI
Energy Conditions in a Generalized Second-Order Scalar-Tensor Gravity
Muhammad Sharif,Saira Waheed +1 more
TL;DR: In this paper, the authors explored the energy conditions in the framework of the most general scalar-tensor theory with field equations involving second-order derivatives, and derived energy conditions with respect to deceleration, jerk, and snap parameters.
Journal ArticleDOI
Canonical variational completion and 4D Gauss–Bonnet gravity
TL;DR: In this paper, it was shown that the renormalized truncated Gauss-Bonnet equations cannot be obtained from any action at all (either diffeomorphism invariant or not), in any dimension, and that the suggested field equations can be variationally completed, choosing either the metric or its inverse as field variables; both approaches yield consistently the same Lagrangian whose variation leads to fourth-order field equations.
Journal ArticleDOI
Polarizations of Gravitational Waves in Horndeski Theory
Shaoqi Hou,Yungui Gong,Yunqi Liu +2 more
TL;DR: In this paper, the authors analyzed the polarization content of gravitational waves in Horndeski theory and showed that there is an additional mode which is the mixture of the transverse breathing and longitudinal polarizations.
References
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Journal ArticleDOI
Mach's principle and a relativistic theory of gravitation
Carl H. Brans,R. H. Dicke +1 more
TL;DR: In this paper, the role of Mach's principle in physics is discussed in relation to the equivalence principle and the difficulties encountered in attempting to incorporate Mach's principles into general relativity are discussed.
Journal ArticleDOI
The Einstein Tensor and Its Generalizations
TL;DR: In this paper, the number of independent tensors of this type depends crucially on the dimension of the space, and, in the four dimensional case, the only tensors with these properties are the metric and the Einstein tensors.
Journal ArticleDOI
Comments on the scalar-tensor theory
TL;DR: In this article, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws, and the integrals are extended over two-and three-dimensional domains that lie entirely in empty space but surround the regions containing matter.
Journal ArticleDOI
The uniqueness of the einstein field equations in a four-dimensional space.
TL;DR: In this article, the Euler-Lagrange equations corresponding to a Lagrange density which is a function of g ≥ 2 and its first two derivatives are investigated and necessary and sufficient conditions for these equations to be of second order are obtained and it is shown that in a four-dimensional space the Einstein field equations (with cosmological term) are the only permissible second order Euler Lagrange equations.
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