표준 우주론 모형 검증

표준 우주론 모형은 몇 가지 가정에 기초합니다.

우주는 균일하고 등방적이다.
중력은 일반상대성이론(GR)으로 기술된다.

이 가정 아래에서 우주의 계량은 팽창하는 우주를 기술하는 프리드만–르메트르–로버트슨–워커(FLRW) 계량이 됩니다.

이 틀 안에서 현재의 표준 모형은 $Λ$ CDM입니다. 우주의 에너지는 후기 우주의 가속 팽창을 일으키는 우주상수 $Λ$ 가 지배하고, 물질은 차갑고 비바리온적인 성분인 암흑물질이 대부분을 차지합니다. 그러나 두 성분 모두 직접 검출된 적이 없고, 입자물리학의 표준 모형에도 포함되어 있지 않습니다. 따라서 그 바탕에 있는 가정들을 질문해 볼 수 있습니다. FLRW가 올바른 계량인가? 우주는 등방적이고 균일한가? 암흑에너지는 우주상수인가?

FLRW 계량과 곡률 검증

JLA(Joint Light-curve Analysis) 초신성 자료로 팽창 역사 $h (z) = H (z) / H_{0}$ 를 모형에 의존하지 않고 재구성한 뒤 SDSS-III/BOSS의 바리온 음향 진동 측정과 결합하여, Arman Shafieloo 박사와 저는 허블 상수 $H_{0}$ 와 끌림 시기(drag epoch)의 음향 지평선 $r_{d}$ 의 곱을 모형 독립적으로 측정했습니다. 또한 평탄한 FLRW 계량에 대한 새로운 리트머스 검증 $Θ (z)$ 를 도입했는데, 이는 클라크슨 검증 $O_{k} (z)$ 와 다음과 같이 연결됩니다.

O_{k} (z) = \frac{Θ ^{2} ( z ) - 1}{D ^{2} ( z )}, Θ (z) \equiv h (z) D^{'} (z) = FLRW 1 + Ω_{k, 0} D^{2} (z),

여기서 $D$ 는 $c / H_{0}$ 단위의 공동 거리입니다. FLRW 우주에서는 모든 적색이동에서 $O_{k} = Ω_{k, 0}$ 이고, 우주가 평탄하면 $Θ = 1$ , $O_{k} = 0$ 입니다.

결과는 평탄한 FLRW 우주와 일치했지만, CMASS 표본에서 약간의 긴장(tension) 징후가 보였습니다 (L'Huillier & Shafieloo, JCAP 01 (2017) 015).

모형 독립적인 일반상대성이론 검증

Arman Shafieloo 박사, 김형진(워털루 대학교)과 함께 이 재구성 결과를 적색이동 공간 왜곡에서 얻은 구조 성장 측정과 결합하여, 물질 밀도 $Ω_{m}$ , 밀도 요동의 진폭 $σ_{8}$ , 그리고 다음과 같이 정의되는 성장 지수 $γ$ 를 모형 독립적으로 제한했습니다.

f (z) \equiv \frac{d ln δ}{d ln a} ≃ Ω_{m} (z)^{γ},

일반상대성이론에서는 $γ ≃ 0.55$ 입니다. 결과는 $Λ$ CDM + GR과 일치했습니다 (L'Huillier, Shafieloo & Kim 2018, MNRAS 476, 3263).

이어서 Arman Shafieloo 박사, Alexei Starobinsky 교수와 함께 최신 Ia형 초신성 자료(Pantheon)와 구조 성장 측정(eBOSS DR14Q 포함)을 결합해 더 강한 제한을 얻었으며, 역시 $Λ$ CDM + GR과 일치했습니다 (Shafieloo, L'Huillier & Starobinsky 2018, PRD 98, 083526).

모형 독립적인 ΛCDM 검증으로 얻은 성장 지수 gamma와 sigma_8에 대한 제한 — ΛCDM 모형 검증 — Shafieloo, L'Huillier & Starobinsky (2018), Physical Review D.

우주론 모형 검증 관련 논문

논문 요약은 영어로 제공됩니다.

Reconstructed linear matter power spectrum divided by the fiducial prediction, with 68% and 95% Monte Carlo bands.

2026 · arXiv 프리프린트

Finding the distribution of matter using lenses – I: deconvolution-based reconstruction with CMB lensing

Dawn, A., Jiang, J.-Q., Hazra, D. K., L'Huillier, B., Shafieloo, A.

We reconstruct the linear matter power spectrum at $z = 0$ from joint Planck PR4, ACT DR6 and SPT-3G CMB lensing, using a modified Richardson–Lucy deconvolution. The result follows the linear prediction on large scales, lies systematically higher for $k ≳ 0.1 Mpc^{- 1}$ , and partly preserves the BAO feature.

arXiv:2609.08457

Reconstructions of a 5% oscillatory feature from 1000 noisy LSST-like mocks (blue), their median (green) and the truth (red).

2026 · arXiv 프리프린트

Finding the distribution of matter using lenses – II: deconvolution-based reconstruction with $3 \times 2$ pt measurements

Jiang, J.-Q., Dawn, A., Hazra, D. K., L'Huillier, B., Shafieloo, A.

A regularised Richardson–Lucy framework tests scale-dependent departures from the nonlinear matter power spectrum using galaxy clustering, galaxy–galaxy lensing and cosmic shear. On LSST Year-10-like mocks, oscillations of about 1% or more are recovered over $0.1 ≲ k ≲ 0.5 Mpc^{- 1}$ , and a 1% oscillation is detected at about $2.6 σ$ .

arXiv:2609.08460

Reconstructed cluster bias, normalised by the Wicker et al. 2023 model, as a function of redshift (left) and mass (right).

2026 · arXiv 프리프린트

Non-parametric estimation of the baryon gas fraction and the cosmological bias with clusters

Kim, H.†, Wicker, R., L'Huillier, B., Douspis, M., Salvati, L., Shafieloo, A.

From a model-independent expansion history reconstructed from supernovae, we infer with iterative smoothing how the hydrostatic mass bias of galaxy clusters depends on mass and redshift, using X-ray gas fractions. Reconciling clusters with CMB constraints requires this bias to evolve with time.

arXiv:2603.13763

Ok(z) from supernova reconstructions combined with DESI DR2, for three data sets, colour-coded by Δχ2; right: the resulting likelihoods. — $O_{k} (z)$ from supernova reconstructions combined with DESI DR2, for three data sets, colour-coded by $Δ χ^{2}$ ; right: the resulting likelihoods.

2026 · JCAP 08 (2026) 016

Model independent test of the FLRW metric and the curvature in light of DESI DR2

Millard, C.†, L'Huillier, B.*, Douspis, M.

We reconstruct distances and the Hubble rate from Pantheon+ and DES supernovae without assuming any dark energy model, and combine them with DESI DR2 baryon acoustic oscillations to test the FLRW metric and measure the spatial curvature. With Pantheon+ and DESI DR2 we find $Ω_{k, 0} = 0.04 5_{- 0.081}^{+ 0.045}$ , consistent with flatness and with Planck 2018.

DOI · arXiv:2601.20293

The curvature diagnostic Ok on mocks from four fiducial models: it recovers Ωk,0 = 0.1 when the input is curved. — The curvature diagnostic $O_{k}$ on mocks from four fiducial models: it recovers $Ω_{k, 0} = 0.1$ when the input is curved.

2025 · JCAP 05 (2025) 030

Litmus tests of the flat ΛCDM model and model-independent measurement of $H_{0} r_{d}$ with LSST and DESI

L'Huillier, B., Mitra, A., Shafieloo, A., Keeley, R. E., Koo, H.

Reconstructing the expansion history from simulated LSST supernovae and combining it with simulated DESI 5-year BAO, we forecast constraints of up to ±4% on the curvature and ±0.1 on $c / (H_{0} r_{d})$ , without assuming any form of dark energy.

DOI · arXiv:2407.07847

χ2 of the best-fit flat ΛCDM model on Pantheon+ (red) compared with its distribution over ΛCDM mocks (blue). — $χ^{2}$ of the best-fit flat ΛCDM model on Pantheon+ (red) compared with its distribution over ΛCDM mocks (blue).

2024 · Universe 10 (2024) 439

An analysis of variance of the Pantheon+ dataset: systematics in the covariance matrix?

Keeley, R. E., Shafieloo, A., L'Huillier, B.

The best-fit ΛCDM $χ^{2}$ of Pantheon+ is unusually small, and its residuals scatter less than the covariance matrix predicts, pointing to errors overestimated by about 7%. After accounting for this, no deviation from ΛCDM is found.

DOI · arXiv:2212.07917

Realistic forecast: reconstructed Geff/G and fσ8 for two modified-gravity scenarios (bump and dip). Both rule out GR at more than 2σ around z ≈ 1. — Realistic forecast: reconstructed $G_{eff} / G$ and $f σ_{8}$ for two modified-gravity scenarios (bump and dip). Both rule out GR at more than $2 σ$ around $z \approx 1$ .

2023 · Phys. Rev. D 108 (2023) 023504

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions. II. Modified gravity and massive neutrinos

Calderón, R., L'Huillier, B., Polarski, D., Shafieloo, A., Starobinsky, A. A.

We reconstruct the effective gravitational coupling $G_{eff} (z)$ as a Gaussian process from forecast stage-IV growth data. DESI-like surveys could detect departures from General Relativity if dark energy is well determined; massive neutrinos do not change this, but assuming a ΛCDM expansion biases the inferred $Ω_{m}$ and $σ_{8}$ .

DOI · arXiv:2301.00640

Gaussian-process reconstruction of the distance modulus relative to the truth, fully marginalised over hyperparameters and CPL parameters.

2023 · JCAP 02 (2023) 014

How to use GP: effects of the mean function and hyperparameter selection on Gaussian process regression

Hwang, S.-g.†, L'Huillier, B.*, Keeley, R. E., Jee, M. J., Shafieloo, A.

The choice of mean function and hyperparameters biases Gaussian process reconstructions of supernova distances: a zero mean gives unphysical results and a best-fit ΛCDM mean biases them. Marginalising over a family of mean functions and over the hyperparameters removes the bias, whatever the kernel.

DOI · arXiv:2206.15081

Joint reconstructions of the effective gravitational coupling, H(z) and fσ8(z) for three fiducial cosmologies; dashed lines show the truth. — Joint reconstructions of the effective gravitational coupling, $H (z)$ and $f σ_{8} (z)$ for three fiducial cosmologies; dashed lines show the truth.

2022 · Phys. Rev. D 106 (2022) 083513

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions I: dark energy beyond $Λ$

Calderón, R., L'Huillier, B., Polarski, D., Shafieloo, A., Starobinsky, A. A.

Gaussian processes reconstruct the dark energy density from forecast stage-IV supernova, BAO and redshift-space-distortion data, assuming only a flat FLRW universe that becomes matter-dominated at high redshift, which also yields the growth history. Several dark energy models can be distinguished from ΛCDM at $2 σ$ or more.

DOI · arXiv:2206.13820

Δχ2 distributions for ΛCDM and PEDE over Roman-like mocks from a third model; vertical lines mark the 95% and 99% limits. — $Δ χ^{2}$ distributions for ΛCDM and PEDE over Roman-like mocks from a third model; vertical lines mark the 95% and 99% limits.

2022 · JCAP 03 (2022) 047

Bayesian vs frequentist: comparing Bayesian model selection with a frequentist approach using the iterative smoothing method

Koo, H., Keeley, R. E., Shafieloo, A., L'Huillier, B.

On simulated Roman supernova data, Bayesian model selection finds the true model when it is among the candidates, but otherwise only picks the least wrong one. A frequentist test based on iterative smoothing can instead conclude that all tested models are false.

DOI · arXiv:2110.10977

Distributions of Δχ2 between the smoothed and best-fit models over WFIRST-like ΛCDM mocks, for ΛCDM, PEDE and Kink. — Distributions of $Δ χ^{2}$ between the smoothed and best-fit models over WFIRST-like ΛCDM mocks, for ΛCDM, PEDE and Kink.

2021 · JCAP 03 (2021) 034

Model selection and parameter estimation using the iterative smoothing method

Koo, H., Shafieloo, A., Keeley, R. E., L'Huillier, B.

Likelihood distributions derived from the non-parametric iterative smoothing method let us test a dark energy model and estimate its parameters without comparing it to an alternative. On WFIRST-like mocks we quantify how confidently different dark energy models can be distinguished.

DOI · arXiv:2009.12045

Where a universe with a negative cosmological constant still accelerates today (white), accelerated only in the past (dark grey), or never accelerated (light grey), for Ωm = 0.3. — Where a universe with a negative cosmological constant still accelerates today (white), accelerated only in the past (dark grey), or never accelerated (light grey), for $Ω_{m} = 0.3$ .

2021 · Phys. Rev. D 103 (2021) 023526

Negative cosmological constant in the dark sector?

Calderón, R., Gannouji, R., L'Huillier, B.*, Polarski, D.

We study dark sectors made of a negative cosmological constant plus a late-time accelerating component. The acceleration is often transient and some models eventually contract; current data show no decisive evidence for a negative $Λ$ , but the best fits are phantom at $z ≳ 1$ .

DOI · arXiv:2008.10237

Constraints on the JLA light-curve parameters from iterative smoothing (red) compared with ΛCDM, CPL and PEDE.

2020 · ApJ 899 (2020) 9

Model-independent constraints on Type Ia supernova light-curve hyper-parameters and reconstructions of the expansion history of the Universe

Koo, H., Shafieloo, A., Keeley, R. E., L'Huillier, B.

Reconstructing the expansion history from JLA supernovae with iterative smoothing while sampling the light-curve hyper-parameters, we find hyper-parameters consistent with those from ΛCDM, CPL and PEDE fits, and no significant redshift evolution.

DOI · arXiv:2001.10887

Reconstructions of Ωde(z) (left) and the growth index γ(z) (right) that fit the growth data better than ΛCDM, for three cases. — Reconstructions of $Ω_{de} (z)$ (left) and the growth index $γ (z)$ (right) that fit the growth data better than ΛCDM, for three cases.

2020 · MNRAS 494 (2020) 819

Defying the laws of Gravity I: model-independent reconstruction of the Universe expansion from growth data

L'Huillier, B., Shafieloo, A., Polarski, D., Starobinsky, A. A.

From redshift-space distortion data alone, we reconstruct the growth history with crossing statistics and Gaussian processes, derive the expansion history from it, and fit supernovae to constrain $Ω_{m, 0}$ and $σ_{8, 0}$ . The results are consistent with flat ΛCDM and General Relativity.

DOI · arXiv:1906.05991

Gaussian-process reconstructions of 1/H(z) and DL(z) from standard sirens and supernovae for a ΛCDM input, relative to the best-fit ΛCDM. — Gaussian-process reconstructions of $1/ H (z)$ and $D_{L} (z)$ from standard sirens and supernovae for a ΛCDM input, relative to the best-fit ΛCDM.

2020 · MNRAS 491 (2020) 3983

Debiasing cosmic gravitational wave sirens

Keeley, R. E., Shafieloo, A., L'Huillier, B., Linder, E. V.

Gaussian process regression can remove the bias in reconstructing $H (z)$ from gravitational-wave standard sirens, and combined with supernovae it tests $H_{0}$ and ΛCDM. Dark-siren redshifts need close to spectroscopic precision to avoid significant bias.

DOI · arXiv:1905.10216

Iterative smoothing of Pantheon: residuals, h(z), the Om diagnostic and w(z). Every curve fits the data better than the best-fit ΛCDM. — Iterative smoothing of Pantheon: residuals, $h (z)$ , the $O m$ diagnostic and $w (z)$ . Every curve fits the data better than the best-fit ΛCDM.

2019 · MNRAS 485 (2019) 2783

Model independent expansion history from supernovae: cosmology versus systematics

L'Huillier, B., Shafieloo, A., Linder, E. V., Kim, A. G.

A model-independent analysis of the Pantheon supernovae shows deviations from ΛCDM at $z ≳ 1$ . They vanish with a simple Malmquist-like correction, but neither $χ^{2}$ tests nor Gaussian processes find that this extra correction is statistically required.

DOI · arXiv:1812.03623

Θ(z) (top) and Ok(z) (bottom) from supernovae and BOSS/eBOSS BAO. A flat FLRW universe gives Θ = 1. — $Θ (z)$ (top) and $O_{k} (z)$ (bottom) from supernovae and BOSS/eBOSS BAO. A flat FLRW universe gives $Θ = 1$ .

2018 · Phys. Rev. D 98 (2018) 083526

Falsifying ΛCDM: model-independent tests of the concordance model with eBOSS DR14Q and Pantheon

Shafieloo, A., L'Huillier, B.*, Starobinsky, A. A.

Combining model-independent expansion reconstructions from Pantheon supernovae and BAO, we test the FLRW metric and flatness, and use eBOSS DR14Q growth data to constrain $Ω_{m}$ , $γ$ and $σ_{8}$ . Everything is consistent with a flat FLRW universe, General Relativity and $Λ$ , with some tension at $z > 1$ .

DOI · arXiv:1804.04320

Model-independent regions allowed by growth data (blue) compared with ΛCDM (red), at fixed γ = 0.55 (left) and fixed σ8 = 0.8 (right). — Model-independent regions allowed by growth data (blue) compared with ΛCDM (red), at fixed $γ = 0.55$ (left) and fixed $σ_{8} = 0.8$ (right).

2018 · MNRAS 476 (2018) 3263

Model-independent cosmological constraints from growth and expansion

L'Huillier, B., Shafieloo, A., Kim, H.†

We reconstruct the expansion history from supernovae and fit growth-rate data to constrain $Ω_{m}$ , the growth index $γ$ and $σ_{8}$ without a dark energy model. The results agree with ΛCDM in General Relativity, and requiring a positive dark energy density tightens them further.

DOI · arXiv:1712.04865

Θ(z) and the curvature diagnostic Ok(z) at the BOSS LOWZ and CMASS redshifts, one point per supernova-based reconstruction. A flat FLRW universe gives Θ = 1 and Ok = 0. — $Θ (z)$ and the curvature diagnostic $O_{k} (z)$ at the BOSS LOWZ and CMASS redshifts, one point per supernova-based reconstruction. A flat FLRW universe gives $Θ = 1$ and $O_{k} = 0$ .

2017 · JCAP 01 (2017) 015

Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement of $H_{0} r_{d}$

L'Huillier, B., Shafieloo, A.

Combining BOSS DR12 BAO with JLA supernovae, we measure $H_{0} r_{d}$ without assuming a cosmological model and introduce the $Θ (z)$ diagnostic of the flat-FLRW metric. The results are consistent with a flat FLRW universe within $2 σ$ .

DOI · arXiv:1606.06832

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FLRW 계량과 곡률 검증

모형 독립적인 일반상대성이론 검증

우주론 모형 검증 관련 논문

Finding the distribution of matter using lenses – I: deconvolution-based reconstruction with CMB lensing

Finding the distribution of matter using lenses – II: deconvolution-based reconstruction with 3×2pt measurements

Non-parametric estimation of the baryon gas fraction and the cosmological bias with clusters

Model independent test of the FLRW metric and the curvature in light of DESI DR2

Litmus tests of the flat ΛCDM model and model-independent measurement of H0​rd​ with LSST and DESI

An analysis of variance of the Pantheon+ dataset: systematics in the covariance matrix?

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions. II. Modified gravity and massive neutrinos

How to use GP: effects of the mean function and hyperparameter selection on Gaussian process regression

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions I: dark energy beyond Λ

Bayesian vs frequentist: comparing Bayesian model selection with a frequentist approach using the iterative smoothing method

Model selection and parameter estimation using the iterative smoothing method

Negative cosmological constant in the dark sector?

Model-independent constraints on Type Ia supernova light-curve hyper-parameters and reconstructions of the expansion history of the Universe

Defying the laws of Gravity I: model-independent reconstruction of the Universe expansion from growth data

Debiasing cosmic gravitational wave sirens

Model independent expansion history from supernovae: cosmology versus systematics

Falsifying ΛCDM: model-independent tests of the concordance model with eBOSS DR14Q and Pantheon

Model-independent cosmological constraints from growth and expansion

Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement of H0​rd​

Finding the distribution of matter using lenses – II: deconvolution-based reconstruction with $3 \times 2$ pt measurements

Litmus tests of the flat ΛCDM model and model-independent measurement of $H_{0} r_{d}$ with LSST and DESI

Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions I: dark energy beyond $Λ$

Model-independent test of the FLRW metric, the flatness of the Universe, and non-local measurement of $H_{0} r_{d}$