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Revisiting a negative cosmological constant from low-redshift data
Luca Visinelli, Sunny Vagnozzi, Ulf Danielsson
TL;DR
Persistent high- versus low-redshift tensions motivate testing whether dark energy includes a negative cosmological constant alongside another component. The paper compares ΛCDM, wCDM, and a string-inspired phenomenological cCDM model using BAO and Type Ia supernova distances with Planck-rdrag and SH0ES-H0 anchors, finding no evidence for a negative cosmological constant and statistical preference for ΛCDM.
Problem
Persistent tensions between high- and low-redshift observations motivate testing whether dark energy is more complex than the positive cosmological constant in ΛCDM.
Method
The paper uses MCMC to compare ΛCDM, wCDM, and cCDM against BAO and Pantheon supernova distances, anchoring BAO with either Planck rdrag or SH0ES H0.
Results
The analysis finds no evidence for a negative cosmological constant and a mild preference for a phantom dark-energy component on top of it.
Takeaways & Limitations
Akaike-information-criterion comparisons statistically favor baseline ΛCDM over the wCDM and cCDM extensions.
Abstract
from arXiv · showhide
Persisting tensions between high-redshift and low-redshift cosmological observations suggest the dark energy sector of the Universe might be more complex than the positive cosmological constant of the $Λ$CDM model. Motivated by string theory, wherein symmetry considerations make consistent AdS backgrounds (\textit (i.e.) maximally symmetric spacetimes with a negative cosmological constant) ubiquitous, we explore a scenario where the dark energy sector consists of two components: a negative cosmological constant, with a dark energy component with equation of state $w_φ$ on top. We test the consistency of the model against low-redshift Baryon Acoustic Oscillation and Type Ia Supernovae distance measurements, assessing two alternative choices of distance anchors: the sound horizon at baryon drag determined by the \textit{Planck} collaboration, and the Hubble constant determined by the SH0ES program. We find no evidence for a negative cosmological constant, and mild indications for an effective phantom dark energy component on top. A model comparison analysis reveals the $Λ$CDM model is favoured over our negative cosmological constant model. While our results are inconclusive, should low-redshift tensions persist with future data, it would be worth reconsidering and further refining our toy negative cosmological constant model by considering realistic string constructions.
I. INTRODUCTION
The paper investigates whether persistent Hubble-constant and other low-redshift tensions could reflect a dark-energy sector more complex than positive-Λ ΛCDM, including a negative cosmological constant motivated by string theory. It compares ΛCDM, wCDM, and a phenomenological cCDM model using BAO and Type Ia supernova distances with alternative anchors.
- Motivation: The H0 tension compares H0 = (74.03 ± 1.42) km s−1 Mpc−1 from the local HST distance ladder with H0 = (67.36 ± 0.54) km s−1 Mpc−1 inferred from Planck under ΛCDM.The discrepancy is reported as having statistical significance of approximately greater than 4σ.
- Motivation: Late-time dark-energy modifications can preserve the sound horizon while increasing the angular-diameter distance, leading to a higher inferred H0.The mechanism changes the late-time expansion rate while leaving the early-time expansion rate and r_s(z_drag) unchanged.
- Motivation: A positive-energy minimally coupled quintessence field with wφ(z) ≥ −1 increases the late-time expansion rate, opposite to what is required to address the H0 tension.The paper therefore considers dark-energy components whose effective energy density or equation of state can differ from this standard case.
- Models: String theory motivates the scenario through consistent AdS backgrounds and light bosons or moduli that could produce an effective quintessence component, potentially with phantom behavior.The effective dark-energy component is treated phenomenologically rather than derived from a specified underlying Lagrangian.
- Models: The cCDM model combines a strictly negative cosmological-constant density Ωcc with a positive component of density Ωφ and equation of state wφ, requiring Ωcc + Ωφ > 0 for accelerated expansion.The analysis also compares this two-component model with ΛCDM and the one-parameter wCDM extension.
- Analysis: The paper uses MCMC to compare ΛCDM, wCDM, and cCDM against low-redshift BAO and Pantheon Type Ia supernovae, anchoring BAO either with SH0ES H0 or Planck rdrag.The two anchor choices correspond to the cosmic and inverse distance ladders.
II. OVERVIEW OF THE DATASETS USED
The dataset analysis combines BAO and Pantheon supernova distance measurements with two alternative anchors, Planck’s sound horizon and SH0ES’s H0. BAO observables probe transverse, radial, or isotropic distance combinations, while the analysis deliberately excludes several other late-time datasets.
- BAO: BAO measurements constrain transverse DA(zeff)/rdrag, radial H(zeff)rdrag, or the isotropic volume distance DV(zeff).The drag epoch is when baryons are released from Compton drag by photons.
- BAO: The analysis includes anisotropic BOSS DR12 and Lyman-α forest measurements plus isotropic 6dFGS and SDSS MGS measurements across low and high effective redshifts.The listed BOSS redshifts are zeff = 0.38, 0.51, and 0.61; the Lyman-α sample is at zeff = 2.40.
- Supernovae: Pantheon supplies luminosity distances for 1048 Type Ia supernovae over 0.01 < z ≤ 2.3.The catalogue is marginally model-dependent because light-curve biases were corrected assuming ΛCDM, although an independent JLA analysis finds weak dependence.
- Anchors: BAO measurements constrain the combination H0rdrag, so the analysis anchors them either to Planck’s rdrag = (147.05 ± 0.30) Mpc or SH0ES’s H0 = (74.03 ± 1.42) km s−1 Mpc−1.Each anchor is implemented through a Gaussian likelihood in the corresponding quantity.
- Scope: The study restricts its low-redshift dataset to BAO and supernovae, excluding direct H(z) determinations, compressed CMB likelihoods, cosmic chronometers, and gamma-ray-burst distances.The authors leave inclusion of these datasets for future work because they could improve constraints on a negative cosmological constant.
III. OVERVIEW OF MODELS AND MODEL COMPARISON
The paper compares ΛCDM, wCDM, and cCDM models with increasing complexity, including a strictly negative cosmological constant in cCDM. It samples their parameters against the data and uses AIC to assess whether additional complexity is warranted.
- Model setup: The analysis models radiation, neutrinos, baryons, and cold dark matter through density parameters, with invisible components grouped as Ωinv(z).The neutrino sector assumes three active neutrinos, including one with mass 0.06 eV.
- Model setup: ΛCDM has four parameters, wCDM adds a constant wφ that may enter the phantom regime, and cCDM adds a strictly negative Ωcc.The corresponding parameter spaces are four-, five-, and six-dimensional.
- Parameter inference: Posterior parameters are sampled with an MCMC analysis using Metropolis-Hastings and flat priors, except for the anchor, which has a Gaussian prior.The analysis is performed separately for each model parameter space.
- Model comparison: ΛCDM and wCDM are nested because ΛCDM is recovered at w = −1, whereas cCDM cannot recover either model because Ωcc must remain negative.Consequently, adding the negative cosmological constant does not necessarily improve the fit.
- Model comparison: The Akaike information criterion compares fit quality against parameter count, requiring Δχ2 ≥ 2Δk to justify added complexity.The models contain k = 4, 5, and 6 parameters for ΛCDM, wCDM, and cCDM respectively; this corresponds to Δχ2 = 2 for wCDM and Δχ2 = 4 for cCDM relative to ΛCDM.
IV. RESULTS
Across both BAO-anchor choices, the cCDM model provides no evidence for a nonzero negative cosmological constant and is not preferred over ΛCDM. The data mildly prefer phantom dark energy, while key inferred parameters remain similar across the extended models and anchors.
- Parameter constraints: The cCDM model yields no evidence for a nonzero negative cosmological constant, providing only a lower bound of Ωcc ≳ −14 for either anchor.Both wCDM and cCDM show a 1σ preference for phantom dark energy, with cCDM shifting wφ upward toward −1.
- Anchor dependence: H0 ≈68.5 km s−1 Mpc−1 is recovered for all three models when BAO measurements are anchored to Planck’s rdrag, so cCDM does not alleviate the H0 tension.Using SH0ES H0 as the anchor instead gives an inferred rdrag about 8% lower than the Planck-anchored value.
- Parameter constraints: ΩM = 0.36 ± 0.05 is inferred for both wCDM and cCDM across anchors, compared with ΩM = 0.31 ± 0.02 for ΛCDM.Other parameters are likewise similar between wCDM and cCDM and across anchor choices, while extended-model uncertainties can be larger.
- Model comparison: For Planck-anchored BAO, ΔAIC = 1.9 for wCDM and ΔAIC = 3.6 for cCDM, favoring ΛCDM despite small fit improvements.The corresponding relative likelihoods over ΛCDM are approximately 0.38 and 0.16.
- Model comparison: For H0-anchored BAO, ΔAIC = 1.3 for wCDM and ΔAIC = 4.8 for cCDM, with relative likelihoods of approximately 0.52 and 0.09 over ΛCDM.The cCDM fit worsens in this anchoring scenario.
V. CONCLUSIONS
The cCDM toy model combines a negative cosmological constant with a positive-energy dark-energy component and is tested against low-redshift distance data using Planck or SH0ES anchoring. The analysis finds no evidence for a negative cosmological constant, a mild preference for phantom behavior, and statistical preference for baseline ΛCDM.
- The cCDM model combines a negative cosmological constant with a positive-energy dark-energy component whose equation of state may be phantom.
- The model is tested against recent BAO and Pantheon Type Ia supernova distance measurements using either Planck rdrag or SH0ES H0 as an anchor.
- No evidence supports a negative cosmological constant, with only the loose lower bound Ωc ≳ −14 obtained.
- The dark-energy component above the negative cosmological constant shows a mild preference for a phantom equation of state, wφ < −1.
- Akaike information criterion comparisons statistically favor baseline ΛCDM over the wCDM and cCDM extensions.
- The conclusions are less optimistic than earlier indications for negative dark-energy density because this work fits a string-inspired toy model with constant equation of state rather than reconstructing the density non-parametrically.