Renormalized cosmological perturbation theory

By Martín Crocce, R. Scoccimarro. 2005

458 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/baf1ca6dab321dd7e832298f01496a80066a83b4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

Citations in the corpus

Convolution Lagrangian perturbation theory for biased tracers (2012, methodology): “The resummation described above has this property, which is not shared by the resummations used in LRTor RPT (Crocce & Scoccimarro 2006).”
Time-sliced perturbation theory II: baryon acoustic oscillations and infrared resummation (2016, methodology): “In [9], the RPT formalism [31] was used to obtain a formula of the form.”
Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample (2009, background): “The primary consequence is a damping on small scales, which can be well approximated by a Gaussian smoothing (Bharadwaj 1996; Crocce & Scoccimarro 2006, 2008; Eisenstein et al. 2007; Matsubara 2008a,b).”
The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias (2007, methodology): “New promising techniques such as a renormalized perturbation theory approach (Crocce & Scoccimarro 2006b,a, 2007; McDonald 2007; Matarrese & Pietroni 2007) may be used to obtain bet- 7 ter predictions for the power spectrum and bispectrum.”
The clustering of galaxies in the SDSS‐III Baryon Oscillation Spectroscopic Survey: cosmological implications of the large‐scale two‐point correlation function (2012, background): “…was originally proposed by Crocce & Scoccimarro (2008) and it is based on the theoretical framework of Renormalized Perturbation Theory (RPT, Crocce & Scoccimarro 2006), where the non-linear power spectrum PNL(k, z) can be computed as the sum of two terms PNL(k, z) = G(k, z) 2PL(k, z) +…”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the full shape of the clustering wedges in the data release 10 and 11 galaxy samples (2013, methodology): “The parametrization of equation (10) is motivated by renormalized perturbation theory (RPT; Crocce & Scoccimarro 2006) and is the basis of the parametrization of the non-linear correlation function proposed by Crocce & Scoccimarro (2008).”
Transients from initial conditions in cosmological simulations (2006, methodology): “A detailed comparison of the nonlinear power spectrum in our simulations to fitting formulae, one-loop PT and renormalized PT (Crocce & Scoccimarro 2006) will be discussed elsewhere.”
Flowing with time: a new approach to non-linear cosmological perturbations (2008, methodology): “In section 4 we compare the present approach to those of [22, 23, 13, 14], and also with the one, closer in spirit, of [26].”
The Effective Field Theory of Large Scale Structures at two loops (2013, methodology): “The effective theory differs from the so-called standard perturbation theory (SPT), and relatives (see for example [3, 4] or [5]), by additional terms in the equations of motion for the overdensities that parameterize relevant short-distance physics.”
Single-field consistency relations of large scale structure part II: resummation and redshift space (2013, methodology): “where φb is the initial condition, φb = Ψb(y = 0), and gab(y) is the linear propagator which is given by [13]”
Cosmological non-linearities as an effective fluid (2010, background): “Our work builds on a long history of studies in non-linear perturbation theory [23, 24, 25, 26, 27, 28, 29, 30, 31, 2], numerical simulations [32, 33, 34, 35], and effective field theory [5, 6, 8, 37].”