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Resumming Cosmic Perturbations

Sabino Matarrese, Massimo Pietroni

TL;DR

The paper develops a Renormalization Group framework to non-perturbatively evolve cosmic perturbations in the fluid/dark-matter regime, deriving exact evolution equations for the power spectrum and higher-order correlators. By introducing an intrinsic UV cutoff emerging from velocity dispersion, it enables accurate predictions of nonlinear BAO features down to zero redshift, aligning well with N-body simulations in a ΛCDM cosmology. The approach reinterprets LSS dynamics via a generating functional and RG flow, yielding a controlled resummation that improves over standard perturbation theory and can be extended to more general cosmologies and dynamical dark energy. This method promises a practical, scalable tool for precision cosmology in the nonlinear regime relevant to upcoming galaxy surveys and weak lensing analyses.

Abstract

Renormalization Group (RG) techniques have been successfully employed in quantum field theory and statistical physics. Here we apply RG methods to study the non-linear stages of structure formation in the Universe. Exact equations for the power spectrum, the bispectrum, and all higher order correlation functions can be derived for any underlying cosmological model. A remarkable feature of the RG flow is the emergence of an intrinsic UV cutoff, due to dark matter velocity dispersion, which improves the convergence of the equations at small scales. As a consequence, the method is able to follow the non-linear evolution of the power-spectrum down to zero redshift and to length-scales where perturbation theory fails. Our predictions accurately fit the results of $N$-body simulations in reproducing the ``Baryon Acoustic Oscillations'' features of the power-spectrum, which will be accurately measured in future galaxy surveys and will provide a probe to distinguish among different dark energy models.

Resumming Cosmic Perturbations

TL;DR

The paper develops a Renormalization Group framework to non-perturbatively evolve cosmic perturbations in the fluid/dark-matter regime, deriving exact evolution equations for the power spectrum and higher-order correlators. By introducing an intrinsic UV cutoff emerging from velocity dispersion, it enables accurate predictions of nonlinear BAO features down to zero redshift, aligning well with N-body simulations in a ΛCDM cosmology. The approach reinterprets LSS dynamics via a generating functional and RG flow, yielding a controlled resummation that improves over standard perturbation theory and can be extended to more general cosmologies and dynamical dark energy. This method promises a practical, scalable tool for precision cosmology in the nonlinear regime relevant to upcoming galaxy surveys and weak lensing analyses.

Abstract

Renormalization Group (RG) techniques have been successfully employed in quantum field theory and statistical physics. Here we apply RG methods to study the non-linear stages of structure formation in the Universe. Exact equations for the power spectrum, the bispectrum, and all higher order correlation functions can be derived for any underlying cosmological model. A remarkable feature of the RG flow is the emergence of an intrinsic UV cutoff, due to dark matter velocity dispersion, which improves the convergence of the equations at small scales. As a consequence, the method is able to follow the non-linear evolution of the power-spectrum down to zero redshift and to length-scales where perturbation theory fails. Our predictions accurately fit the results of -body simulations in reproducing the ``Baryon Acoustic Oscillations'' features of the power-spectrum, which will be accurately measured in future galaxy surveys and will provide a probe to distinguish among different dark energy models.

Paper Structure

This paper contains 12 sections, 92 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Eulerian theory revisited
  3. Generating functionals
  4. Renormalization Group Equations
  5. The propagator and the emergence of an intrinsic UV cutoff
  6. Exact RG equation
  7. Approximations
  8. 1-loop
  9. Large $k$ resummation
  10. RG result
  11. The power-spectrum
  12. Conclusions

Figures (10)

  • Figure 1: The Feynman rules.
  • Figure 2: RG equation for the propagator $G_{ab,\lambda}$
  • Figure 3: The infinite class of diagrams resummed by the RG in the approximation leading to Eq. (\ref{['resu']}).
  • Figure 4: The 1-loop contribution to the combination of Eq. (\ref{['combination']}).
  • Figure 5: The propagator in a $\Lambda$CDM model at $z=0,1,2$, from left to right. Solid lines represent the results of the integration of Eq. (\ref{['hRG']}). Dashed lines are 1-loop results.
  • ...and 5 more figures