Non-Linear Lagrangians and Cosmological Theory
01 Sep 1970-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 150, Iss: 1, pp 1-8
About: This article is published in Monthly Notices of the Royal Astronomical Society.The article was published on 1970-09-01 and is currently open access. It has received 1042 citations till now. The article focuses on the topics: Cosmological constant & Brane cosmology.
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TL;DR: In this article, the authors present a review of the most important aspects of the different classes of modified gravity theories, including higher-order curvature invariants and metric affine.
Abstract: Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology, and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories that include higher-order curvature invariants, and specifically the particular class of $f(R)$ theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. Here $f(R)$ theories of gravity are reviewed in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented---metric, Palatini, and metric affine---and the following topics are discussed: motivation; actions, field equations, and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; and astrophysical applications.
4,027 citations
Cites background or result from "Non-Linear Lagrangians and Cosmolog..."
...Indeed this is the case: f(R) gravity in the metric formalism is called metric f(R) gravity and f(R) gravity in the Palatini formalism is called Palatini f(R) gravity (Buchdahl, 1970)....
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...…action in the metric formalism.7 Remarkably, even though the two formalisms give the same results for linear actions, they lead to different results for more general actions (Buchdahl, 1970; Burton and Mann, 1998a,b; Exirifard and Sheikh-Jabbari, 2008; Querella, 1998; Shahid-Saless, 1987)....
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...…denotes differentiation with respect to the argument, ∇µ is the covariant derivative associated with the Levi-Civita connection of the metric, and ≡ ∇µ∇µ. Metric f(R) gravity was first rigorously studied in (Buchdahl, 1970).3 It has to be stressed that there is a mathematical jump in deriving eq....
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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 from "Non-Linear Lagrangians and Cosmolog..."
...The conditions required for a non-singular ‘bounce’ are given in [249], and oscillating solutions were considered in [208]....
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TL;DR: Various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds are reviewed.
Abstract: Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.
3,375 citations
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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
TL;DR: In this article, it was shown that the recently detected acceleration of the Uuniverse can be understood by considering a modification of the teleparallel equivalent of general relativity, with no need of dark energy.
Abstract: It is shown that the recently detected acceleration of the Uuniverse can be understood by considering a modification of the teleparallel equivalent of general relativity, with no need of dark energy. The solution also exhibits phases dominated by matter and radiation as expected in the standard cosmological evolution. We perform a joint analysis with measurements of the most recent type Ia supernovae, baryon acoustic oscillation peak, and estimates of the cosmic microwave background shift parameter data to constrain the only new parameter this theory has.
1,030 citations