Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations

Abstract: Nonlinear effects are crucial in order to compute 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 the familiar BBGKY 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 LambdaCDM, 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, showing that they are much less contaminated by nonlinearities 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.

• The paper introduces a novel differential equation framework that computes the matter power spectrum and bispectrum in nonlinear regimes.
• It demonstrates that density-velocity correlations suffer less nonlinear contamination than density-density ones, aiding clearer BAO detection.
• The method flexibly accommodates modified gravity and massive neutrino scenarios, enhancing cosmological parameter extractions from surveys.

An Analytical Perspective on the Approach to Nonlinear Cosmological Perturbations

Cosmology is persistently confronting the challenge of precisely modeling the clustering statistics of matter, an endeavor highly pertinent for interpreting the observations of next-generation galaxy surveys. These surveys are poised to deliver unprecedented details concerning key cosmological elements such as dark energy, necessitating an accurate depiction of both linear and nonlinear matter distributions. In this context, Massimo Pietroni's study introduces a novel semi-analytical method named 'Flowing with Time' to enhance the modeling of nonlinear cosmological perturbations, particularly focusing on the calculation of the matter power spectrum (PS) and bispectrum (BS).

Pietroni's method hinges on a system of differential equations to derive correlation functions such as the power spectrum and bispectrum across various redshifts and momentum scales. This approach mirrors the BBGKY hierarchy, truncating at the trispectrum to encapsulate an infinite series of perturbative corrections. Distinctly beneficial for cosmologies deviating from the standard $\Lambda$CDM model, including scenarios with modified gravity and massive neutrinos, this framework aligns the growth of perturbations over time with the renormalization group (RG) paradigm, albeit with time serving as the flow parameter.

A crucial application demonstrated is modeling the Baryonic Acoustic Oscillation (BAO) features within the power spectrum. The results were benchmarked against various methodologies including traditional perturbation theory and N-body simulations. Pietroni's findings illustrate how density-velocity and velocity-velocity power spectra suffer less from nonlinear contamination than their density-density counterpart, suggesting potential alternative routes for discerning the BAO in forthcoming surveys.

Theoretically, the study scrutinizes the compatibility of this framework with existing resummation techniques and analytic perturbation theories. The differential equation-based approach provides a direct solution pathway, negating the need for complex field-theoretic derivations or prior approximations inherent to renormalized perturbation theory. This yields a broader applicability to diverse cosmologies, encompassing scale-dependent growth factors unaddressed by previous models.

Practically, this work anticipates enhancing the accuracy of cosmological parameter extractions from survey data, achieving a closer alignment with numerical simulations across a significant range of scales. The method's flexibility allows it to potentially incorporate additional cosmological components, such as massive neutrinos, without succumbing to the approximations traditionally used in past frameworks.

Encouragingly, initial results align well with N-body simulations, reinforcing the validity of Pietroni's methods. However, it's acknowledged that future iterations could incorporate trispectrum effects, refining accuracy at smaller scales. For high redshift surveys, the present approximation suffices, but as lower redshifts are examined, increased precision may necessitate extending the current model.

Overall, this paper contributes a theoretically robust and practically significant method for navigating the complexities of nonlinear cosmological perturbations. The approach promises to refine our cosmological insights, enabling more precise interpretations of future observational data and advancing the theoretical underpinnings of large-scale structure formation.