On the renormalization of the effective field theory of large scale structures

By E. Pajer, M. Zaldarriaga. 2013

148 citations recorded by the source corpus.

Standard perturbation theory (SPT) for large-scale matter inhomogeneities is unsatisfactory for at least three reasons: there is no clear expansion parameter since the density contrast is not small on all scales; it does not fully account for deviations at large scales from a perfect pressureless fluid induced by short-scale non-linearities; for generic initial conditions, loop corrections are UV-divergent, making predictions cutoff dependent and hence unphysical. The Effective Field Theory of Large Scale Structures successfully addresses all three issues. Here we focus on the third one and show explicitly that the terms induced by integrating out short scales, neglected in SPT, have exactly the right scale dependence to cancel all UV-divergences at one loop, and this should hold at all loops. A particularly clear example is an Einstein deSitter universe with no-scale initial conditions Pin ~ kn. After renormalizing the theory, we use self-similarity to derive a very simple result for the final power spectrum for any n, excluding two-loop corrections and higher. We show how the relative importance of different corrections depends on n. For n ~ −1.5, relevant for our universe, pressure and dissipative corrections are more important than the two-loop corrections.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/04a8272887b31e9905a7b1fdaafa3c97f79a0cdc

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In Astronomy and Astrophysics

1. L. Senatore
2. Guido D'Amico
3. M. Zaldarriaga
4. Pierre Zhang
5. Rafael A. Porto
6. D. Baumann
7. Z. Vlah
8. D. Green

In Nuclear and High Energy Physics

1. L. Senatore
2. Rafael A. Porto
3. D. Baumann
4. Guido D'Amico
5. M. Zaldarriaga
6. Pierre Zhang
7. D. Green
8. E. Pajer

Citations in the corpus

• Renormalized halo bias (2014, methodology): “In the case of a scaling universe with P (q) ∝ qn, the finite part of F can be computed analytically using dimensional regularization [22]”
• Limits on wCDM from the EFTofLSS with the PyBird code (2020, methodology): “These calculations were accompanied by some theoretical developments of the EFTofLSS, such as a careful understanding of renormalization [8, 20, 21] (including rather-subtle aspects such as lattice-running [8] and a better understanding of the velocity field [10, 22]), of the several ways for extrac”
• The Effective Field Theory of Large Scale Structures at two loops (2013, methodology): “[8] has explicitly verified that indeed the EFTofLSS is able to make predictions for the scaling universes.”
• On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures (2015, background): “The Effective Field Theory of Large Scale Structures (EFTofLSS) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] is a theoretical framework that aims at developing a rigorous analytic understanding of the clustering of LSS, through a perturbative expansion in the size of the fluctuations.”
• The Effective Field Theorist's Approach to Gravitational Dynamics (2016, background): “On the other hand, the (renormalized) N -loop order in perturbation theory scales as [352, 354]”
• Bias in the effective field theory of large scale structures (2014, background): “In [5] (see also [21]), it has been shown that the universe can be well approximated by a piecewise scaling one, with power spectrum”
• The Hubble tension in light of the Full-Shape analysis of Large-Scale Structure data (2020, methodology): “These calculations were accompanied by some theoretical developments of the EFTofLSS, such as a careful understanding of renormalization [8, 20, 21] (including rather-subtle aspects such as lattice-running [8] and a better understanding of the velocity field [10, 22]), of several ways for extracting”
• The bispectrum in the Effective Field Theory of Large Scale Structure (2014, methodology): “[6] in the case of a scale-free universe.”
• The cosmological analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure (2019, background): “This also involved some additional theoretical developments, such as a careful understanding of renormalization [2, 36, 37] (including some rather-subtle aspects such as lattice-running [2]) and of the way of extracting the numerical value of the counterterms from simulations [2, 38], of the non-loc”
• The IR-resummed Effective Field Theory of Large Scale Structures (2014, methodology): “The fact that modes larger and smaller than k affect the power spectrum through different parameters is what allows SPT to be nondivergent for equal time correlators power law Universes in the range −3 < n < −1.”
• Biased Tracers in Redshift Space in the EFT of Large-Scale Structure (2016, background): “years the Effective Field Theory of Large-Scale Structure 1 (EFTofLSS) [2, 3, 4, 5] has provided a tool where predictions in the mildly non-linear regime can be delivered with an at-least-in-principle arbitrary theoretical precision, and most probably with a precision that should be enough for next ”
• The Lagrangian-space Effective Field Theory of large scale structures (2013, methodology): “As it was discussed in [7, 12], this is related to the UV divergences in the one-loop computations, that occur for n ≥ −1 when we remove the cutoff of the theory.”