# R{sup 2}log R quantum corrections and the inflationary observables

## Abstract

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is f(R)=R+α R{sup 2}+β R{sup 2} ln R. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index n{sub s} and the tensor to scalar ratio yield 4 × 10{sup -4}∼< r∼<0.03 and 0.94∼< n{sub s} ∼< 0.99. i.e. r is an order of magnitude bigger or smaller than the original Starobinsky model which predicted r∼ 10{sup -3}. Further enhancement of r gives a scale invariant n{sub s}∼ 1 or higher. Other inflationary observables are d n{sub s}/dln k ∼> -5.2 × 10{sup -4}, μ ∼< 2.1 × 10{sup -8} , y ∼< 2.6 × 10{sup -9}. Despite the enhancement in r, if the recent BICEP2 measurement stands, this model is disfavoured.

- Authors:

- DESY Theory Group, Notkestrasse 85, D-22607 Hamburg (Germany)
- Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St.George Street, Toronto, ON, M5S 3H8 (Canada)
- School of Particles and Accelerators, Institute for Research in Fundamental Sciences, P.O.Box 19395-5531, Tehran (Iran, Islamic Republic of)
- Institut für Theoretische Physik, Universität Hamburg, Notkestrasse 85, D-22761 Hamburg (Germany)

- Publication Date:

- OSTI Identifier:
- 22375904

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2014; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CORRECTIONS; COSMOLOGICAL INFLATION; MATHEMATICAL SPACE; MATTER; SCALARS; SPACE-TIME; TENSORS; YIELDS

### Citation Formats

```
Ben-Dayan, Ido, Westphal, Alexander, Jing, Shenglin, Torabian, Mahdi, and Zarate, Lucila, E-mail: ido.bendayan@desy.de, E-mail: shenglin.jing@utoronto.ca, E-mail: mahdi@ipm.ir, E-mail: alexander.westphal@desy.de, E-mail: lucila.zarate@desy.de.
```*R{sup 2}log R quantum corrections and the inflationary observables*. United States: N. p., 2014.
Web. doi:10.1088/1475-7516/2014/09/005.

```
Ben-Dayan, Ido, Westphal, Alexander, Jing, Shenglin, Torabian, Mahdi, & Zarate, Lucila, E-mail: ido.bendayan@desy.de, E-mail: shenglin.jing@utoronto.ca, E-mail: mahdi@ipm.ir, E-mail: alexander.westphal@desy.de, E-mail: lucila.zarate@desy.de.
```*R{sup 2}log R quantum corrections and the inflationary observables*. United States. doi:10.1088/1475-7516/2014/09/005.

```
Ben-Dayan, Ido, Westphal, Alexander, Jing, Shenglin, Torabian, Mahdi, and Zarate, Lucila, E-mail: ido.bendayan@desy.de, E-mail: shenglin.jing@utoronto.ca, E-mail: mahdi@ipm.ir, E-mail: alexander.westphal@desy.de, E-mail: lucila.zarate@desy.de. Mon .
"R{sup 2}log R quantum corrections and the inflationary observables". United States.
doi:10.1088/1475-7516/2014/09/005.
```

```
@article{osti_22375904,
```

title = {R{sup 2}log R quantum corrections and the inflationary observables},

author = {Ben-Dayan, Ido and Westphal, Alexander and Jing, Shenglin and Torabian, Mahdi and Zarate, Lucila, E-mail: ido.bendayan@desy.de, E-mail: shenglin.jing@utoronto.ca, E-mail: mahdi@ipm.ir, E-mail: alexander.westphal@desy.de, E-mail: lucila.zarate@desy.de},

abstractNote = {We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is f(R)=R+α R{sup 2}+β R{sup 2} ln R. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index n{sub s} and the tensor to scalar ratio yield 4 × 10{sup -4}∼< r∼<0.03 and 0.94∼< n{sub s} ∼< 0.99. i.e. r is an order of magnitude bigger or smaller than the original Starobinsky model which predicted r∼ 10{sup -3}. Further enhancement of r gives a scale invariant n{sub s}∼ 1 or higher. Other inflationary observables are d n{sub s}/dln k ∼> -5.2 × 10{sup -4}, μ ∼< 2.1 × 10{sup -8} , y ∼< 2.6 × 10{sup -9}. Despite the enhancement in r, if the recent BICEP2 measurement stands, this model is disfavoured.},

doi = {10.1088/1475-7516/2014/09/005},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2014,

place = {United States},

year = {Mon Sep 01 00:00:00 EDT 2014},

month = {Mon Sep 01 00:00:00 EDT 2014}

}