# Reconstructing a f ( R ) theory from the α-Attractors

## Abstract

We show an analogy at high curvature between a f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} theory and the α-Attractors. We calculate the expressions of the parameters a , b and n as functions of α and the predictions of the model f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r . We find that the power law correction R {sup n} {sup −} {sup 1} allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on n {sub s}. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2}. Moreover, we also investigate the case of a single power law f ( R ) = γ R {sup 2} {sup −} {sup δ} theory, with γ and δ free parameters. We calculate analytically the predictions of this model on themore »

- Authors:

- Department of Physics, Universidade Federal do Espírito Santo, avenida Fernando Ferrari 514, 29075-910 Vitória, Espírito Santo (Brazil)

- Publication Date:

- OSTI Identifier:
- 22667670

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Cosmology and Astroparticle Physics

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1475-7516

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; ATTRACTORS; COMPUTERIZED SIMULATION; CORRECTIONS; FORECASTING; GENERAL RELATIVITY THEORY; GRAVITATIONAL WAVES

### Citation Formats

```
Miranda, T., Fabris, J. C., and Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br.
```*Reconstructing a f ( R ) theory from the α-Attractors*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/09/041.

```
Miranda, T., Fabris, J. C., & Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br.
```*Reconstructing a f ( R ) theory from the α-Attractors*. United States. doi:10.1088/1475-7516/2017/09/041.

```
Miranda, T., Fabris, J. C., and Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br. Fri .
"Reconstructing a f ( R ) theory from the α-Attractors". United States. doi:10.1088/1475-7516/2017/09/041.
```

```
@article{osti_22667670,
```

title = {Reconstructing a f ( R ) theory from the α-Attractors},

author = {Miranda, T. and Fabris, J. C. and Piattella, O. F., E-mail: tays.andrade@aluno.ufes.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: fabris@pq.cnpq.br},

abstractNote = {We show an analogy at high curvature between a f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} theory and the α-Attractors. We calculate the expressions of the parameters a , b and n as functions of α and the predictions of the model f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2} on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r . We find that the power law correction R {sup n} {sup −} {sup 1} allows for a production of gravitational waves enhanced with respect to the one in the Starobinsky model, while maintaining a viable prediction on n {sub s}. We numerically reconstruct the full α-Attractors class of models testing the goodness of our high-energy approximation f ( R ) = R + aR {sup n} {sup −} {sup 1} + bR {sup 2}. Moreover, we also investigate the case of a single power law f ( R ) = γ R {sup 2} {sup −} {sup δ} theory, with γ and δ free parameters. We calculate analytically the predictions of this model on the scalar spectral index n {sub s} and the tensor-to-scalar ratio r and the values of δ which are allowed from the current observational results. We find that −0.015 < δ < 0.016, confirming once again the excellent agreement between the Starobinsky model and observation.},

doi = {10.1088/1475-7516/2017/09/041},

journal = {Journal of Cosmology and Astroparticle Physics},

issn = {1475-7516},

number = 09,

volume = 2017,

place = {United States},

year = {2017},

month = {9}

}