[Paper Review] Chasing Lambda

F. Frontera, M. Orlandini|arXiv (Cornell University)|Oct 10, 2007

Radio Astronomy Observations and Technology1 references3 citations

TL;DR

This paper uses Bayesian model selection to evaluate 10 cosmological models—five with dark energy and five with modified gravity—against four observational datasets (SNIa, CMB, BAO, and H(z)). It finds the ΛCDM model has a 74% posterior probability, indicating strong empirical support despite unresolved theoretical issues like the fine-tuning and coincidence problems.

ABSTRACT

Recent astronomical observations of SNIa, CMB, as well as BAO in the Sloan Digital Sky Survey, suggest that the current Universe has entered a stage of an accelerated expansion with the transition redshift at $z \simeq 0.5$. While the simplest candidates to explain this fact is cosmological constant/vacuum energy, there exists a serious problem of coincidence. In theoretical cosmology we can find many possible approaches alleviating this problem by applying new physics or other conception of dark energy. We consider state of art candidates for the description of accelerating Universe in the framework of the Bayesian model selection. We point out advantages as well as troubles of this approach. We find that the combination of four data bases gives a stringent posterior probability of the $Λ$CDM model which is 74%. This fact is a quantitative exemplification of a turmoil in modern cosmology over the $Λ$ problem.

Motivation & Objective

• To evaluate competing cosmological models of accelerated expansion using Bayesian model selection.
• To assess whether alternative dark energy or modified gravity models outperform the ΛCDM model given current observational data.
• To quantify the relative plausibility of the ΛCDM model versus alternatives using posterior probabilities.
• To examine the robustness of the ΛCDM model in light of the fine-tuning and coincidence problems in theoretical cosmology.
• To determine if observational data from SNIa, CMB, BAO, and H(z) favor ΛCDM or other models in a statistically rigorous way.

Proposed method

• The study employs Bayesian model comparison with equal prior probabilities for all 10 models under consideration.
• It combines four observational datasets: 192 SNIa, CMB shift parameter R, BAO parameter A, and 9 H(z) measurements.
• Likelihood functions are constructed for each dataset: Gaussian for SNIa (magnitudes), CMB (R), BAO (A), and H(z) (Hubble parameter).
• The total likelihood is the product of individual likelihoods: L = L_SN × L_R × L_A × L_H.
• Posterior probabilities are computed using Bayes' theorem, with model evidence derived from marginalizing over all parameters.
• The analysis compares models within two groups (dark energy models and modified gravity models) and across all models.

Experimental results

Research questions

• RQ1 What is the posterior probability of the ΛCDM model relative to other dark energy and modified gravity models?
• RQ2 Do alternative models such as phantom dark energy, quintessence, or Cardassian cosmology provide better fits to current cosmological data?
• RQ3 How does the inclusion of multiple datasets (SNIa, CMB, BAO, H(z)) affect model ranking in Bayesian model selection?
• RQ4 Is the ΛCDM model statistically favored over alternatives despite its theoretical shortcomings?
• RQ5 What is the relative performance of modified gravity models like DGP, BΛCDM, and interacting dark energy models?

Key findings

• The ΛCDM model has a posterior probability of 74% when all 10 models are considered, indicating strong empirical support.
• Among models with dark energy, ΛCDM is the best-performing model, with a posterior probability of 0.84 when priors are uniform.
• Among models with modified gravity, the Cardassian model ranks highest with a posterior probability of 0.09, though still significantly lower than ΛCDM.
• The generalized Chaplygin gas model has a posterior probability of 0.03, indicating low support from the data.
• The DGP model has a posterior probability of 0.07, and the interacting dark energy model has 0.13, both showing limited support.
• The posterior probability of the ΛCDM model remains high even when priors are reweighted to 10% per model, confirming its dominance across different prior assumptions.