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arxiv: 2605.13298 · v1 · submitted 2026-05-13 · 🌌 astro-ph.CO

Recognition: 2 theorem links

· Lean Theorem

Probing nonlinear structure formation beyond ΛCDM with the LSS bootstrap: a joint power spectrum and bispectrum analysis

Giorgia Biselli , Marco Marinucci , Guido D'Amico , Massimo Pietroni
Authors on Pith no claims yet

Pith reviewed 2026-05-14 17:33 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords LSS bootstrappower spectrumbispectrumEFTofLSSBOSSnonlinear structure formationbeyond ΛCDM
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The pith

The LSS bootstrap yields first MCMC constraints on deviations from ΛCDM using power spectrum and bispectrum.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes the first MCMC-derived bounds on parameters of the LSS bootstrap framework, which uses symmetry to model deviations from standard cosmology in linear growth and quadratic kernels. By analyzing BOSS galaxy data and simulations with combined power spectrum and bispectrum, it achieves percent-level precision on the growth rate parameter. The approach separates effects on background expansion from those on nonlinear structure formation. Readers would care because it provides a model-agnostic way to test cosmology with existing surveys without assuming specific beyond-ΛCDM theories.

Core claim

The authors show that within the EFTofLSS, the LSS bootstrap parametrization with parameters ε_f for linear growth rate modifications and ε_dγ for the quadratic kernel allows joint fitting of one-loop power spectrum and tree-level bispectrum. This yields ~7% constraints on ε_f and ~57% on ε_dγ from BOSS data, tightening to ~1% and ~25% with larger volume PT Challenge simulations when including the bispectrum quadrupole.

What carries the argument

The LSS bootstrap parametrization, which introduces fractional parameters ε_f and ε_dγ based on symmetry arguments to capture deviations in linear growth rate and quadratic perturbation theory kernel.

Load-bearing premise

The LSS bootstrap parametrization based on symmetry arguments alone correctly captures all relevant deviations from ΛCDM in the linear growth rate and quadratic kernel for the scales and redshifts probed by the data.

What would settle it

Repeating the analysis on an independent larger dataset and finding ε_f or ε_dγ values significantly different from the reported constraints would falsify the robustness of the bootstrap parametrization.

Figures

Figures reproduced from arXiv: 2605.13298 by Giorgia Biselli, Guido D'Amico, Marco Marinucci, Massimo Pietroni.

Figure 1
Figure 1. Figure 1: Impact of the choice of kmax on the posterior distributions for the PT Challenge simulations for the bispectrum monopole B0 (top panel) and quadrupole B2 (bottom panel). Both analyses are performed with ns and As fixed to the true values of the simulations [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Impact of the 1-loop bispectrum (red) on cosmological constraints with respect to the tree-level contribution (blue). [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Posteriors for the PT Challenge simulations, with [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Posterior means and 1σ intervals (colored bars) and MAP values, denoted by black diamond markers, for the PT Challenge simulations, with As free. Projection effects are reflected in the discrepancies between the MAP values and the maxima of the marginalized posterior distributions. In the BOSS analysis, the degeneracies are less pronounced because of the smaller survey volume and the corre￾spondingly broad… view at source ↗
Figure 5
Figure 5. Figure 5: Marginalized posterior distributions for the BOSS LOWZ and CMASS datasets with [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: displays the marginalized posterior distributions for the cosmological parameters, and the corresponding numerical constraints are summarized in Table III. When the bispectrum multipoles are included, the constraints on εf are only modestly improved relative to those obtained from the power spectrum alone, tightening from about 0.012 to 0.0097. In contrast, adding the bispectrum quadrupole is crucial for o… view at source ↗
Figure 7
Figure 7. Figure 7: Posterior distributions for the PT Challenge simulations, comparing results obtained by fixing [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Full posterior distributions from the analysis of BOSS power spectrum multipoles [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Full posterior distributions for the joint analysis of power spectrum and bispectrum multipoles of the PT Challenge [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
read the original abstract

We present the first MCMC-derived constraints on the parameters of the Large Scale Structure (LSS) bootstrap, a model-independent framework that captures deviations from $\Lambda$CDM using symmetry arguments alone. Focusing on modifications to the linear growth rate and to the quadratic perturbation-theory kernel -- quantified by the fractional parameters $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$, respectively -- we carry out a joint analysis of the one-loop galaxy power spectrum and the tree-level bispectrum multipoles within the EFTofLSS, employing the \texttt{PyBird} code extended to implement the bootstrap parametrization. We apply this analysis pipeline to two datasets: the BOSS DR12 LRG sample and the large-volume ``PT Challenge'' simulations. For BOSS, combining the power spectrum with the bispectrum monopole yields $\sim 7\%$ constraints on $\varepsilon_f$ and $\sim 57\%$ constraints on $\varepsilon_{d_{\gamma}}$. For the PT Challenge, whose survey volume is about 100 times larger, we reach $\sim 1\%$ precision on $\varepsilon_f$ and $\sim 25\%$ on $\varepsilon_{d_{\gamma}}$, including the bispectrum quadrupole in the analysis. Our results underscore the complementary roles of $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$ in separating changes to the background expansion from those affecting nonlinear structure formation, and they show that the LSS bootstrap offers a competitive, model-agnostic method for probing physics beyond $\Lambda$CDM with existing and upcoming galaxy surveys.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents the first MCMC-derived constraints on the LSS bootstrap parameters ε_f (fractional modification to linear growth rate) and ε_{d_γ} (fractional modification to quadratic PT kernel) using a joint analysis of the one-loop galaxy power spectrum and tree-level bispectrum multipoles within the EFTofLSS. The analysis employs an extended PyBird code and is applied to BOSS DR12 LRG data and PT Challenge simulations, yielding ~7% constraints on ε_f and ~57% on ε_{d_γ} for BOSS (PS + bispectrum monopole) and tighter ~1% / ~25% constraints for the larger-volume PT Challenge (including quadrupole).

Significance. If the two-parameter LSS bootstrap ansatz is complete for the relevant scales, the work offers a symmetry-based, model-agnostic route to separate background-expansion effects from nonlinear-structure modifications in galaxy clustering. The reported precisions demonstrate that existing BOSS data already yield nontrivial bounds and that bispectrum information is complementary to the power spectrum; the PT Challenge results indicate scalability to future surveys.

major comments (1)
  1. [LSS bootstrap parametrization and scale cuts (Sections 2–3)] The central claim that ε_f and ε_{d_γ} fully parametrize all relevant deviations from ΛCDM at the scales k ≲ 0.15 h/Mpc probed by BOSS rests on the assumption that symmetry arguments alone exhaust modifications to the linear growth and quadratic kernel. At these wavenumbers the one-loop power spectrum and tree-level bispectrum receive contributions from higher-order or scale-dependent operators not fixed by the two-parameter ansatz; if present, such terms would be absorbed into the reported posteriors, rendering the ~57% constraint on ε_{d_γ} incomplete rather than model-agnostic. A dedicated test (e.g., injection of additional cubic-kernel terms or scale-dependent coefficients) is required to quantify the bias.
minor comments (2)
  1. [Abstract] The abstract quotes approximate precisions (“∼7%”, “∼57%”) without stating the precise k-range, covariance treatment, or prior choices; these details should be added for reproducibility.
  2. [Results section] Figure captions and text should explicitly note whether the PT Challenge constraints include the same scale cuts and nuisance-parameter marginalization as the BOSS analysis.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the single major comment below.

read point-by-point responses

  1. Referee: [LSS bootstrap parametrization and scale cuts (Sections 2–3)] The central claim that ε_f and ε_{d_γ} fully parametrize all relevant deviations from ΛCDM at the scales k ≲ 0.15 h/Mpc probed by BOSS rests on the assumption that symmetry arguments alone exhaust modifications to the linear growth and quadratic kernel. At these wavenumbers the one-loop power spectrum and tree-level bispectrum receive contributions from higher-order or scale-dependent operators not fixed by the two-parameter ansatz; if present, such terms would be absorbed into the reported posteriors, rendering the ~57% constraint on ε_{d_γ} incomplete rather than model-agnostic. A dedicated test (e.g., injection of additional cubic-kernel terms or scale-dependent coefficients) is required to quantify the bias.

    Authors: The LSS bootstrap parametrization is constructed from symmetry principles that fix the allowed modifications to the linear growth rate and quadratic kernel at the perturbative orders relevant for our analysis. By design, it is model-agnostic within the class of theories whose leading deviations from ΛCDM respect those symmetries. Higher-order kernels (e.g., cubic) enter the one-loop power spectrum only through terms that are either suppressed at k ≲ 0.15 h/Mpc or reabsorbed into the EFT counterterms already marginalized over in the fit. The chosen scale cuts and the inclusion of these counterterms ensure that any residual bias is subdominant, as confirmed by the consistency of our BOSS results with the much tighter constraints obtained from the PT Challenge simulations. We therefore maintain that the reported posteriors are valid and the constraints remain meaningful within the stated scope of the bootstrap. A dedicated injection test of additional operators lies beyond the present work but would be a natural extension; it is not required to support the current claims. revision: no

Circularity Check

0 steps flagged

No circularity: constraints derived directly from data fits to symmetry-based parametrization

full rationale

The paper defines the LSS bootstrap via symmetry arguments to introduce parameters ε_f and ε_{d_γ} for modifications to linear growth and quadratic kernels, then performs MCMC fits of these parameters to external BOSS DR12 data and PT Challenge simulations within the EFTofLSS using PyBird. No step reduces a reported constraint to a prior fitted value by construction, renames an input as a prediction, or relies on a self-citation chain for the central result; the quoted precisions (∼7% on ε_f, ∼57% on ε_{d_γ} for BOSS) are direct outputs of the likelihood analysis on independent datasets.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on two fitted fractional parameters and the assumption that symmetry-based parametrization plus EFTofLSS modeling fully captures the relevant deviations on the analyzed scales.

free parameters (2)
  • ε_f
    Fractional parameter for modifications to the linear growth rate; its posterior width is the reported ~7% constraint from BOSS.
  • ε_{d_γ}
    Fractional parameter for modifications to the quadratic perturbation-theory kernel; its posterior width is the reported ~57% constraint from BOSS.
axioms (2)
  • domain assumption Symmetry arguments alone suffice to parametrize deviations from ΛCDM in the linear growth rate and quadratic kernel
    Invoked in the definition of the LSS bootstrap framework.
  • domain assumption EFTofLSS one-loop power spectrum and tree-level bispectrum modeling is accurate for the scales and redshifts used
    Required for the joint analysis pipeline with PyBird.

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discussion (0)

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Reference graph

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