# Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism

## Abstract

We compute the complete post-Newtonian limit of both the metric and Palatini formulations of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.

- Authors:

- Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC (Spain)
- (Spain)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20713705

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 72; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.72.083505; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; COSMOLOGY; DENSITY; GRAVITATION; LAGRANGIAN FUNCTION; NONLINEAR PROBLEMS; SCALARS; SOLAR SYSTEM; TENSORS

### Citation Formats

```
Olmo, Gonzalo J., Facultad de Fisica, Universidad de Valencia, Burjassot-46100, Valencia, and Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201.
```*Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.083505.

```
Olmo, Gonzalo J., Facultad de Fisica, Universidad de Valencia, Burjassot-46100, Valencia, & Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201.
```*Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism*. United States. doi:10.1103/PhysRevD.72.083505.

```
Olmo, Gonzalo J., Facultad de Fisica, Universidad de Valencia, Burjassot-46100, Valencia, and Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201. Sat .
"Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism". United States. doi:10.1103/PhysRevD.72.083505.
```

```
@article{osti_20713705,
```

title = {Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism},

author = {Olmo, Gonzalo J. and Facultad de Fisica, Universidad de Valencia, Burjassot-46100, Valencia and Physics Department, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201},

abstractNote = {We compute the complete post-Newtonian limit of both the metric and Palatini formulations of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit bounds to the possible nonlinear terms of the lagrangian. We conclude that in both formalisms the lagrangian f(R) must be almost linear in R and that corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.},

doi = {10.1103/PhysRevD.72.083505},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 8,

volume = 72,

place = {United States},

year = {2005},

month = {10}

}