# Systematic renormalization of the effective theory of Large Scale Structure

## Abstract

A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k{sup 2} and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.

- Authors:

- Physics Department, Sharif University of Technology,Azadi Ave., Tehran (Iran, Islamic Republic of)
- (IPM),Farmanieh Ave., Tehran (Iran, Islamic Republic of)
- School of Natural Sciences, Institute for Advanced Study,Princeton, NJ, 08540 (United States)
- Institute for Theoretical Physics and Center for Extreme Matter and Emergent Phenomena,Utrecht University, 1 Einstein Dr., Leuvenlaan 4, Utrecht, 3584 CE The (Netherlands)

- Publication Date:

- Sponsoring Org.:
- SCOAP3, CERN, Geneva (Switzerland)

- OSTI Identifier:
- 22572086

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2016; Journal Issue: 05; Other Information: PUBLISHER-ID: JCAP05(2016)063; OAI: oai:repo.scoap3.org:15821; cc-by Article funded by SCOAP3. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 License. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COSMOLOGY; ENERGY SPECTRA; FEYNMAN DIAGRAM; MATHEMATICAL OPERATORS; NONLUMINOUS MATTER; PERTURBATION THEORY; QUANTUM FIELD THEORY; RENORMALIZATION; UNIVERSE

### Citation Formats

```
Abolhasani, Ali Akbar, School of Physics, Institute for Research in Fundamental Sciences, Mirbabayi, Mehrdad, and Pajer, Enrico.
```*Systematic renormalization of the effective theory of Large Scale Structure*. United States: N. p., 2016.
Web. doi:10.1088/1475-7516/2016/05/063.

```
Abolhasani, Ali Akbar, School of Physics, Institute for Research in Fundamental Sciences, Mirbabayi, Mehrdad, & Pajer, Enrico.
```*Systematic renormalization of the effective theory of Large Scale Structure*. United States. doi:10.1088/1475-7516/2016/05/063.

```
Abolhasani, Ali Akbar, School of Physics, Institute for Research in Fundamental Sciences, Mirbabayi, Mehrdad, and Pajer, Enrico. Tue .
"Systematic renormalization of the effective theory of Large Scale Structure". United States.
doi:10.1088/1475-7516/2016/05/063.
```

```
@article{osti_22572086,
```

title = {Systematic renormalization of the effective theory of Large Scale Structure},

author = {Abolhasani, Ali Akbar and School of Physics, Institute for Research in Fundamental Sciences and Mirbabayi, Mehrdad and Pajer, Enrico},

abstractNote = {A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k{sup 2} and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.},

doi = {10.1088/1475-7516/2016/05/063},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 05,

volume = 2016,

place = {United States},

year = {Tue May 31 00:00:00 EDT 2016},

month = {Tue May 31 00:00:00 EDT 2016}

}