Flowing with time: a new approach to non-linear cosmological perturbations

By M. Pietroni. 2008

228 citations recorded by the source corpus.

Non-linear effects are crucial for computing the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order correlations are obtained—at any redshift and for any momentum scale—by integrating a system of differential equations. The method is similar to that of the familiar BBGKY (Bogoliubov–Born–Green–Kirkwood–Yvon) hierarchy. Truncating at the level of the trispectrum, the solution of the equations corresponds to the summation of an infinite class of perturbative corrections. Compared to other resummation frameworks, the scheme discussed here is particularly suited to cosmologies other than ΛCDM (CDM: cold dark matter), such as those based on modifications of gravity and those containing massive neutrinos. As a first application, we compute the baryonic acoustic oscillation feature of the power spectrum, and compare the results with perturbation theory, the halo model, and N-body simulations. The density–velocity and velocity–velocity power spectra are also computed, revealing that they are much less contaminated by non-linearities than the density–density one. The approach can be seen as a particular formulation of the renormalization group, in which time is the flow parameter.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/09b86197560807e3559bf0c7166fc275caa67f5c

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Citations in the corpus

Accurate halo-model matter power spectra with dark energy, massive neutrinos and modified gravitational forces (2016, background): “The mildly non-linear effect of neutrinos can be investigated using perturbation theory (e.g., Wong 2008; Pietroni 2008; Saito et al. 2008, 2009; Lesgourgues et al. 2009; Upadhye et al. 2014; Peloso et al. 2015) , or via simulations, which show that the non-linear power is suppressed by a greater…”
Neutrino Mass in Cosmology: Status and Prospects (2011, methodology): “oup The timeow renormalisation group (RG) method is a simple extension of the perturbative method introduced above, but incorporates resummation of certain classes of perturbative terms to all orders [66]. Aside from its simplicity and ease-of-use, the timeow RG method has the advantage that it has ”
The nonperturbative functional renormalization group and its applications (2020, methodology): “This has been implemented within real-time approaches in [470, 472, 473] and [471, 477, 478].”
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].”
Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering (2009, background): “…R T H E MO D E L F O R TH E S H A P E O F ξ (r) In recent years, substantial progress has been made in understanding the non-linear gravitational evolution of density fluctuations (Crocce & Scoccimarro 2006a, 2008; Matarrese & Pietroni 2007; Matsubara 2008; Pietroni 2008; Taruya & Hiramatsu 2008).”