# Unimodular F ( R ) gravity

## Abstract

We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified F ( R ) gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular F ( R ) gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular F ( R ) inflationary scenarios are presented, and in some cases, concordance with Planck and BICEP2 observational data can be achieved.

- Authors:

- Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)
- Institut de Ciéncies de l'Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Cerdanyola del Vallès, Barcelona (Spain)
- Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22667556

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGICAL MODELS; EQUATIONS OF MOTION; GRAVITATION; METRICS; QUANTUM GRAVITY; RELATIVITY THEORY

### Citation Formats

```
Nojiri, S., Odintsov, S.D., and Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com.
```*Unimodular F ( R ) gravity*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/05/046.

```
Nojiri, S., Odintsov, S.D., & Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com.
```*Unimodular F ( R ) gravity*. United States. doi:10.1088/1475-7516/2016/05/046.

```
Nojiri, S., Odintsov, S.D., and Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com. Sun .
"Unimodular F ( R ) gravity". United States. doi:10.1088/1475-7516/2016/05/046.
```

```
@article{osti_22667556,
```

title = {Unimodular F ( R ) gravity},

author = {Nojiri, S. and Odintsov, S.D. and Oikonomou, V.K., E-mail: nojiri@gravity.phys.nagoya-u.ac.jp, E-mail: odintsov@ieec.uab.es, E-mail: v.k.oikonomou1979@gmail.com},

abstractNote = {We extend the formalism of the Einstein-Hilbert unimodular gravity in the context of modified F ( R ) gravity. After appropriately modifying the Friedmann-Robertson-Walker metric in a way that it becomes compatible to the unimodular condition of having a constant metric determinant, we derive the equations of motion of the unimodular F ( R ) gravity by using the metric formalism of modified gravity with Lagrange multiplier constraint. The resulting equations are studied in frames of reconstruction method, which enables us to realize various cosmological scenarios, which was impossible to realize in the standard Einstein-Hilbert unimodular gravity. Several unimodular F ( R ) inflationary scenarios are presented, and in some cases, concordance with Planck and BICEP2 observational data can be achieved.},

doi = {10.1088/1475-7516/2016/05/046},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 05,

volume = 2016,

place = {United States},

year = {Sun May 01 00:00:00 EDT 2016},

month = {Sun May 01 00:00:00 EDT 2016}

}