f(R) theories

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   f(R) Theories Of Gravity

   T. Sotiriou, V. Faraoni · 2008 · Reviews of Modern Physics · cited 3,667 times · Not summarized yet

   f(R) Theories Of Gravity reviews the theory’s major aspects and formalisms, overlapping this paper’s survey of f(R) applications and constraints.

   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\char22{}metric, …

2. Very close Broader context Cited by this paper Not relevant

   f(R) Gravities \`a la Brans-Dicke

   T. Rador · 2007 · cited 22 times · Not summarized yet

   f(R) Gravities à la Brans-Dicke extends f(R) with a fundamental scalar field, connecting the review’s discussion of Brans-Dicke and related theories.

   Abstract

   We extend f(R) theories via the addition of a fundamental scalar field. The approach is reminiscent of the dilaton field of string theory and the Brans-Dicke model. f(R) theories attracted much attention recently in view of their potential to explain the acceleration of the universe. Extending f(R) models to theories with scalars can be motivated from the low energy effective action of string theory. There, a fundamental scalar (the dilaton), has a non-minimal coupling to the Ricci scalar. Furthermore beyond tree level actions will contain terms having higher (or lower) powers of R compared to the canonical Einstein-Hilbert term. Theories with f(R) will contain an extra scalar degree on top …

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   Limit to general relativity in f(R) theories of gravity

   G. J. Olmo · 2006 · Physical Review D · cited 197 times · Not summarized yet

   Limit to general relativity in f(R) theories examines the GR limit and spherical solutions, topics covered in this review’s discussion of viable f(R) gravity.

   Abstract

   We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity, f(R){yields}R. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original f(R) representation, solve the linearized equations, and compare our results with recent calculations of the literature. We observe that the linearized solutions are strongly affected by the cosmic evolution, which makes very unlikely that the cosmic speedup be due to f(R) m…

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   New models of f(R) theories of gravity

   J. Klusoň · 2009 · Physical Review D · cited 45 times · Not summarized yet

   New models of f(R) theories of gravity introduces f(R) models generalized from Hořava-Lifshitz gravity, another application of the framework reviewed here.

   Abstract

   We introduce new models of $f(R)$ theories of gravity that are a generalization of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity.

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   f(R) actions, cosmic acceleration and local tests of gravity

   I. Navarro, K. Van Acoleyen · 2006 · Journal of Cosmology and Astroparticle Physics · cited 174 times · Not summarized yet

   f(R) actions, cosmic acceleration and local tests of gravity studies whether spherical f(R) solutions satisfy local gravity tests while addressing cosmic acceleration.

   Abstract

   We study spherically symmetric solutions in f(R) theories and its compatibility with local tests of gravity. We start by clarifying the range of validity of the weak field expansion and show that, for many models proposed to address the dark energy problem, this expansion breaks down in realistic situations. This invalidates the conclusions of several papers that make inappropriate use of this expansion. For the stable models that modify gravity only at small curvatures we find that when the asymptotic background curvature is large we approximately recover the solutions of Einstein gravity through the so-called Chameleon mechanism, as a result of the non-linear dynamics of the extra scalar d…

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   Constraining f(R) theories with Type Ia Supernovae and Gamma Ray Bursts

   V. Cardone, A. Diaferio, S. Camera · 2009 · arXiv: Cosmology and Nongalactic Astrophysics · preprint, not peer reviewed · cited 2 times · Not summarized yet

   Constraining f(R) theories with Type Ia Supernovae and Gamma Ray Bursts tests f(R) models against astrophysical data and local-gravity requirements.

   Abstract

   Fourth - order gravity theories have received much interest in recent years thanks to their ability to provide an accelerated cosmic expansion in a matter only universe. In these theories, the Lagrangian density of the gravitational field has the form R + f(R), and the explicit choice of the arbitrary function f(R) must meet the local tests of gravity and the constraints from the primordial abundance of the light elements. Two popular classes of f(R) models, which are expected to fulfill all the above requirements, have recently been proposed. However, neither of these models has ever been quantitatively tested against the available astrophysical data. Here, by combining Type Ia Supernovae a…

7. Very close Review Cited by this paper Not relevant

   6+1 lessons from f(R) gravity

   T. Sotiriou · 2008 · cited 58 times · Not summarized yet

   6+1 lessons from f(R) gravity reviews lessons from the theory, which this paper also surveys across cosmology and gravity.

   Abstract

   There has been a recent stimulus in the study of alternative theories of gravity lately, mostly triggered from combined motivation coming from cosmology/astrophysics and high energy physics. Among the proposed theories, one that has attracted much attention is f(R) gravity. It is certainly debatable whether such a simplistic modification of General Relativity can constitute a viable alternative theory of gravitation. However, it is quite straightforward to see the merits of such a theory when viewed as a toy theory whose role is to help us understand the implications and difficulties of beyond-Einstein gravity. Under this perspective, I review some of the main lessons we seem to have learned…

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   f(R) gravity and chameleon theories

   P. Brax, C. van de Bruck, A. Davis et al. · 2008 · Physical Review D · cited 236 times · Not summarized yet

   f(R) gravity and chameleon theories analyzes how chameleon effects can reconcile f(R) dark-energy models with experimental gravity tests.

   Abstract

   We analyze f(R) modifications of Einstein's gravity as dark energy models in the light of their connection with chameleon theories. Formulated as scalar-tensor theories, the f(R) theories imply the existence of a strong coupling of the scalar field to matter. This would violate all experimental gravitational tests on deviations from Newton's law. Fortunately, the existence of a matter dependent mass and a thin-shell effect allows one to alleviate these constraints. The thin-shell condition also implies strong restrictions on the cosmological dynamics of the f(R) theories. As a consequence, we find that the equation of state of dark energy is constrained to be extremely close to -1 in the rec…

Prior work it builds on

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   Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?

   S. Appleby, R. Battye · 2007 · Physics Letters B · cited 445 times · Not summarized yet

   Do consistent F(R) models mimic General Relativity plus Λ? examines whether viable accelerating models remain close to GR throughout cosmic history.

   Abstract

   Abstract Modified gravity models are subject to a number of consistency requirements which restrict the form that the function F ( R ) can take. We study a particular class of F ( R ) functions which satisfy various constraints that have been found in the literature. These models have a late time accelerating epoch, and an acceptable matter era. We calculate the Friedmann equation for our models, and show that in order to satisfy the constraints we impose, they must mimic general relativity plus Λ throughout the cosmic history, with exponentially suppressed corrections. We also find that the free parameters in our model must be fine tuned to obtain an acceptable late time accelerating phase.…

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   Stability of cosmological solutions in f ( R ) models of gravity

   I. Sawicki, Wayne Hu · 2007 · Physical Review D · cited 184 times · Not summarized yet

   Stability of cosmological solutions in f(R) models tests the stability and matter-era behavior of f(R) cosmologies discussed in this review.

   Abstract

   We reconcile seemingly conflicting statements in the literature about the behavior of cosmological solutions in modified theories of gravity where the Einstein-Hilbert Lagrangian for gravity is modified by the addition of a function of the Ricci scalar, $f(R)$. Using the example of $f(R)=\ifmmode\pm\else\textpm\fi{}{\ensuremath{\mu}}^{4}/R$ we show that only such choices of $f(R)$ where ${\mathrm{d}}^{2}f/\mathrm{d}{R}^{2}g0$ have stable high-curvature limits and well-behaved cosmological solutions with a proper era of matter domination. The remaining models enter a phase dominated by both matter and scalar kinetic energy where the scalar curvature remains low.

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   Solar System constraints to general f(R) gravity

   T. Chiba, Tristan L. Smith, A. Erickcek · 2006 · Physical Review D · cited 291 times · Not summarized yet

   Solar System constraints to general f(R) gravity evaluates whether f(R) models satisfy Solar System tests, a central issue in this review.

   Abstract

   It has been proposed that cosmic acceleration or inflation can be driven by replacing the Einstein-Hilbert action of general relativity with a function f(R) of the Ricci scalar R. Such f(R) gravity theories have been shown to be equivalent to scalar-tensor theories of gravity that are incompatible with Solar System tests of general relativity, as long as the scalar field propagates over Solar System scales. Specifically, the parameterized post-Newtonian (PPN) parameter in the equivalent scalar-tensor theory is gamma=1/2, which is far outside the range allowed by observations. In response to a flurry of papers that questioned the equivalence of f(R) theory to scalar-tensor theories, it was re…

4. Close Same question Used in depth by this paper A method it uses Not relevant

   Relativistic stars in f(R) and scalar-tensor theories

   E. Babichev, D. Langlois · 2009 · Physical Review D · cited 99 times · Not summarized yet

   Relativistic stars in f(R) and scalar-tensor theories constructs stellar solutions in models using chameleon screening, matching the review’s coverage of stars and local constraints.

   Abstract

   We study relativistic stars in the context of scalar-tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider two types of models: scalar-tensor theories with an inverse power law potential and f(R) theories. Using a relaxation algorithm, we construct numerically static relativistic stars, both for constant energy density configurations and for a polytropic equation of state. We can reach a gravitational potential up to {Phi}{approx}0.3 at the surface of the star, even in f(R) theories with an 'unprotected' curvature singularity. However, we find static configurati…

5. Very close Same question A method it uses Not relevant

   Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology

   S. Fay, S. Nesseris, L. Perivolaropoulos · 2007 · Physical Review D · cited 77 times · Not summarized yet

   Can f(R) Modified Gravity Theories Mimic a LCDM Cosmology reconstructs f(R) models to reproduce a specified cosmic history, a question covered by this review.

   Abstract

   We consider f(R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f(R) by demanding a background {lambda}CDM cosmology. In particular we impose the following requirements: (a) A background cosmic history H(z) provided by the usual flat {lambda}CDM parametrization though the radiation (w{sub eff}=1/3), matter (w{sub eff}=0), and de Sitter (w{sub eff}=-1) eras. (b) Matter and radiation dominate during the ''matter'' and ''radiation'' eras, respectively, i.e. {omega}{sub m}=1 when w{sub eff}=0 and {omega}{sub r}=1 when w{sub eff}=1/3. We have found that the cosmological dynamical system constrained to obey the {lambda}CDM cosmic history has fou…

Papers that cite it

1. Close Review Not relevant

   Modified gravity and cosmology

   Timothy Clifton, Pedro G. Ferreira, Antonio Padilla et al. · 2012 · Physics Reports · cited 4,185 times · Not summarized yet

   Modified gravity and cosmology surveys modified-gravity theories and their cosmological consequences, including f(R) and several theories discussed here.

   Abstract

   In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, scalar–tensor, Einstein–æther, and Bimetric theories, as well as TeVeS, f(R), general higher-order theories, Hořava–Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza–Klein, Randall–Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scal…

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   Unified cosmic history in modified gravity: From F ( R ) theory to Lorentz non-invariant models

   Shin’ichi Nojiri, Sergei D. Odintsov · 2011 · Physics Reports · cited 4,573 times · Not summarized yet

   Unified cosmic history in modified gravity: From F(R) theory to Lorentz non-invariant models surveys modified-gravity approaches to cosmic history, including F(R) theory.

3. Close Broader context Not relevant

   f ( T ) teleparallel gravity and cosmology

   Yi-Fu Cai, Salvatore Capozzıello, Mariafelicia De Laurentis et al. · 2016 · Reports on Progress in Physics · cited 1,528 times · Not summarized yet

   f(T) teleparallel gravity and cosmology reviews cosmological and astrophysical applications of a torsion-based alternative, adjacent to the modified theories discussed here.

   Abstract

   Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T) gravity, where f (T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T) gravity, both at the background and perturbation levels, in d…

4. Very close Review Not relevant

   PALATINI APPROACH TO MODIFIED GRAVITY: f(R) THEORIES AND BEYOND

   Gonzalo J. Olmo · 2011 · International Journal of Modern Physics D · cited 773 times · Not summarized yet

   Palatini Approach to Modified Gravity: f(R) Theories and Beyond reviews Palatini modified gravity, including cosmology, solar-system tests, and stellar structure.

   Abstract

   We review the recent literature on modified theories of gravity in the Palatini approach. After discussing the motivations that lead to consider alternatives to Einstein's theory and to treat the metric and the connection as independent objects, we review several topics that have been recently studied within this framework. In particular, we provide an in-depth analysis of the cosmic speed-up problem, laboratory and solar system tests, the structure of stellar objects, the Cauchy problem, and bouncing cosmologies. We also discuss the importance of going beyond the f(R) models to capture other phenomenological aspects related with dark matter/energy and quantum gravity.

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   Constraining $f(R)$ gravity and evolving dark energy via large-scale structure and phase-space trajectories

   Tshepo Mathibela, Á. de la Cruz-Dombriz, S. Nesseris · 2026 · Not summarized yet

   Constraining f(R) gravity and evolving dark energy via large-scale structure and phase-space trajectories fits viable f(R) models to cosmological observations.

   Abstract

   We present a joint observational analysis confronting viable $f(R)$ modified gravity theories, specifically the Hu \&Sawicki and Starobinsky models, with background and large-scale structure (LSS) data. Utilizing Monte-Carlo Markov chain (MCMC) sampling across datasets including baryon acoustic oscillations (BAO), type Ia supernovae (SNeIa), cosmic microwave background (CMB) distance priors, and linear growth measurements ($f\sigma_8$, $f$, $\sigma_8$), we place tight constraints on the model parameters governing deviations from General Relativity. For the full dataset combination, we obtain $\log_{10} b_\mathrm{HS} = -6.325_{-1.138}^{+1.216}$ for the Hu \&Sawicki model and $b_\mathrm{S} = (…