# Renormalized cosmological perturbation theory

## Abstract

We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing nonlinearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be writtenmore »

- Authors:

- Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, New York 10003 (United States)

- Publication Date:

- OSTI Identifier:
- 20782623

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.063519; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CORRECTIONS; COUPLING; DISTURBANCES; FEYNMAN DIAGRAM; NONLINEAR PROBLEMS; PERTURBATION THEORY; PROPAGATOR; QUANTUM FIELD THEORY; RENORMALIZATION

### Citation Formats

```
Crocce, Martin, and Scoccimarro, Roman.
```*Renormalized cosmological perturbation theory*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.063519.

```
Crocce, Martin, & Scoccimarro, Roman.
```*Renormalized cosmological perturbation theory*. United States. doi:10.1103/PHYSREVD.73.063519.

```
Crocce, Martin, and Scoccimarro, Roman. Wed .
"Renormalized cosmological perturbation theory". United States.
doi:10.1103/PHYSREVD.73.063519.
```

```
@article{osti_20782623,
```

title = {Renormalized cosmological perturbation theory},

author = {Crocce, Martin and Scoccimarro, Roman},

abstractNote = {We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing nonlinearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbation theory, where different loop corrections can become of the same magnitude in the nonlinear regime. In companion papers we compare the resummation of the propagator with numerical simulations, and apply these results to the calculation of the nonlinear power spectrum. Remarkably, the expressions in renormalized perturbation theory can be written in a way that closely resembles the halo model.},

doi = {10.1103/PHYSREVD.73.063519},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}