scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Second-order scalar-tensor field equations in a four-dimensional space

01 Sep 1974-International Journal of Theoretical Physics (Kluwer Academic Publishers-Plenum Publishers)-Vol. 10, Iss: 6, pp 363-384
TL;DR: 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.
Citations
More filters
Journal ArticleDOI
TL;DR: A comprehensive survey of recent work on modified theories of gravity and their cosmological consequences can be found in this article, where the authors provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a selfcontained, comprehensive and up-to-date introduction to the subject as a whole.

3,674 citations


Cites background or methods from "Second-order scalar-tensor field eq..."

  • ...The most general four dimensional scalar-tensor theory with second-order field equations was worked out by Horndeski in [623]....

    [...]

  • ...An even more general class of scalar tensor theories yielding second order field equations has recently been presented in [402], and is now known to be equivalent to Horndeski’s general theory [623] in four dimensions [710]....

    [...]

Journal ArticleDOI
TL;DR: In this article, the authors considered a modified theory of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and of the trace of the stress-energy tensor.
Abstract: We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

1,833 citations

Journal ArticleDOI
Luca Amendola1, Stephen Appleby2, Anastasios Avgoustidis3, David Bacon4, Tessa Baker5, Marco Baldi6, Marco Baldi7, Marco Baldi8, Nicola Bartolo9, Nicola Bartolo6, Alain Blanchard10, Camille Bonvin11, Stefano Borgani6, Stefano Borgani12, Enzo Branchini6, Enzo Branchini13, Clare Burrage3, Stefano Camera, Carmelita Carbone14, Carmelita Carbone6, Luciano Casarini15, Luciano Casarini16, Mark Cropper17, Claudia de Rham18, J. P. Dietrich19, Cinzia Di Porto, Ruth Durrer11, Anne Ealet, Pedro G. Ferreira5, Fabio Finelli6, Juan Garcia-Bellido20, Tommaso Giannantonio19, Luigi Guzzo14, Luigi Guzzo6, Alan Heavens18, Lavinia Heisenberg21, Catherine Heymans22, Henk Hoekstra23, Lukas Hollenstein, Rory Holmes, Zhiqi Hwang24, Knud Jahnke25, Thomas D. Kitching17, Tomi S. Koivisto26, Martin Kunz11, Giuseppe Vacca27, Eric V. Linder28, M. March29, Valerio Marra30, Carlos Martins31, Elisabetta Majerotto11, Dida Markovic32, David J. E. Marsh33, Federico Marulli8, Federico Marulli6, Richard Massey34, Yannick Mellier35, Francesco Montanari36, David F. Mota15, Nelson J. Nunes37, Will J. Percival32, Valeria Pettorino38, Valeria Pettorino39, Cristiano Porciani, Claudia Quercellini, Justin I. Read40, Massimiliano Rinaldi41, Domenico Sapone42, Ignacy Sawicki43, Roberto Scaramella, Constantinos Skordis43, Constantinos Skordis44, Fergus Simpson45, Andy Taylor22, Shaun A. Thomas, Roberto Trotta18, Licia Verde45, Filippo Vernizzi39, Adrian Vollmer, Yun Wang46, Jochen Weller19, T. G. Zlosnik47 
TL;DR: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015-2025 program as discussed by the authors, which will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shift of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.
Abstract: Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

1,211 citations

Journal ArticleDOI
TL;DR: In this paper, the generalized Galileons were used as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of Ginf lation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases.
Abstract: We study generalized Galileons as a framework to develop the most general single-field inflation models ever, Generalized G-inflation, containing yet further generalization of Ginf lation, as well as previous examples such as k-inflation, extended inflation, and new Higgs inflation as special cases. We investigate the background and perturbation evolution in this model, calculating the most general quadratic actions for tensor and scalar cosmological perturbations to give the stability criteria and the power spectra of primordial fluctuations. It is pointed out in the Appendix that the Horndeski theory and the generalized Galileons are equivalent. In particular, even the non-minimal coupling to the Gauss-Bonnet term is included in the generalized Galileons in a non-trivial manner. Subject Index: 440, 442, 453

1,093 citations

Journal ArticleDOI
TL;DR: In this article, a catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory is presented, and the current understanding of the structure and dynamics of compact objects in these theories is summarized.
Abstract: One century after its formulation, Einstein's general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

1,066 citations

References
More filters
Journal ArticleDOI
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.
Abstract: The role of Mach's principle in physics is discussed in relation to the equivalence principle. The difficulties encountered in attempting to incorporate Mach's principle into general relativity are discussed. A modified relativistic theory of gravitation, apparently compatible with Mach's principle, is developed.

4,787 citations

Journal ArticleDOI
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.
Abstract: The Einstein tensorGij is symmetric, divergence free, and a concomitant of the metric tensorgab together with its first two derivatives. In this paper all tensors of valency two with these properties are displayed explicitly. 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.

2,821 citations

Journal ArticleDOI
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.
Abstract: Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by Dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws. The integrals are extended over two- and three-dimensional domains that lie entirely in empty space but surround the regions containing matter; as for the latter, the vacuum field equations are not required to hold, but no further assumptions are made. It turns out that the gradient of the incident scalar field will contribute to the rate of change of the mass and linear momentum of a ‘particle’ an amount proportional to that particle's scalar-field source strength, which in turn is an arbitrary function of time, unless Dicke's special restriction is imposed. To this extent the motion of a test particle is indeterminate, contrary to experience.

692 citations

Journal ArticleDOI

138 citations

Journal ArticleDOI
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.
Abstract: The Euler-Lagrange equations corresponding to a Lagrange density which is a function of g ij and its first two derivatives are investigated. In general these equations will be of fourth order in g ij. Necessary and sufficient conditions for these Euler-Lagrange 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. This result is false in a space of higher dimension. Furthermore, the only permissible third order equation in the four-dimensional case is exhibited.

70 citations