# On the renormalization group perspective of α-attractors

## Abstract

In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.

- Authors:

- Kavli Institute for Theoretical Physics China (KITPC), Key Laboratory of Theoretical Physics, Institute of Theoretical Physics (ITP), Chinese Academy of Sciences -CAS, Beijing 100190 (China)

- Publication Date:

- OSTI Identifier:
- 22667636

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 10; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALGORITHMS; ATTRACTORS; GRAVITATION; INFLATONS; QUANTUM GRAVITY; RENORMALIZATION; TRAJECTORIES; ULTRAVIOLET RADIATION

### Citation Formats

```
Narain, Gaurav, E-mail: gaunarain@itp.ac.cn.
```*On the renormalization group perspective of α-attractors*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/10/032.

```
Narain, Gaurav, E-mail: gaunarain@itp.ac.cn.
```*On the renormalization group perspective of α-attractors*. United States. doi:10.1088/1475-7516/2017/10/032.

```
Narain, Gaurav, E-mail: gaunarain@itp.ac.cn. Sun .
"On the renormalization group perspective of α-attractors". United States.
doi:10.1088/1475-7516/2017/10/032.
```

```
@article{osti_22667636,
```

title = {On the renormalization group perspective of α-attractors},

author = {Narain, Gaurav, E-mail: gaunarain@itp.ac.cn},

abstractNote = {In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.},

doi = {10.1088/1475-7516/2017/10/032},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 10,

volume = 2017,

place = {United States},

year = {Sun Oct 01 00:00:00 EDT 2017},

month = {Sun Oct 01 00:00:00 EDT 2017}

}