[Paper Review] Tests of $\Lambda$CDM and Conformal Gravity using GRB and Quasars as Standard Candles out to $z \sim 8$

Carl Roberts, K. Horne+2 more|arXiv (Cornell University)|Nov 28, 2017

Gamma-ray bursts and supernovae1 references3 citations

TL;DR

This study tests conformal gravity (CG) against the standard ΛCDM model using gamma-ray bursts (GRBs) and quasars as standard candles up to redshift z ≈ 8. It finds that ΛCDM fits the data significantly better than CG, with Δχ² = 48, and identifies a severe λ fine-tuning problem in Mannheim's CG model, suggesting similar theoretical issues to ΛCDM despite its claim to resolve cosmic coincidence.

ABSTRACT

We compare the cosmology of conformal gravity (CG), (Mannheim 2006), to $\Lambda$CDM. CG cosmology has repulsive matter and radiation on cosmological scales, while retaining attractive gravity at local scales. Mannheim (2003) finds that CG agrees with $\Lambda$CDM for supernova data at redshifts $z<1$. We use GRBs and quasars as standard candles to contrast these models in the redshift range $0<z<8$. We find CG deviates significantly from $\Lambda$CDM at high redshift and that $\Lambda$CDM is favoured by the data with $\Delta\chi^2=48$. Mannheim's model has a bounded dark energy contribution, but we identify a $\lambda$ fine-tuning problem and a cosmic coincidence problem.

Motivation & Objective

• To test whether conformal gravity (CG) can reproduce cosmological observations as well as ΛCDM at high redshift.
• To investigate the viability of Mannheim's CG cosmology in light of recent high-redshift data from GRBs and quasars.
• To assess whether CG resolves the cosmic coincidence and fine-tuning problems of ΛCDM, or introduces analogous issues.
• To compare the Hubble diagrams of ΛCDM and CG using a combined dataset of 79 GRBs and 24 binned quasars up to z ≈ 8.

Proposed method

• Constructed a Hubble diagram using 79 un-binned GRB data points and 24 binned quasar data points up to z ≈ 8.
• Applied the Amati relation for GRBs via the Padé approximant method to calibrate luminosity distances.
• Used quasar X-ray and UV flux correlations to estimate distance moduli for quasars.
• Computed theoretical distance moduli for both ΛCDM and Mannheim's conformal gravity model using their respective cosmological solutions.
• Performed a χ² test comparing observed and predicted distance moduli for both models, with 103 total data points.
• Re-evaluated theoretical parameters in CG, particularly the Higgs self-coupling constant λ, to assess fine-tuning requirements.

Experimental results

Research questions

• RQ1 Does conformal gravity (CG) provide a better fit to high-redshift cosmological data than ΛCDM when using GRBs and quasars as standard candles?
• RQ2 What is the degree of fine-tuning required in Mannheim’s CG model to match observed cosmological parameters?
• RQ3 Does CG resolve the cosmic coincidence problem, or does it introduce a new form of fine-tuning similar to ΛCDM?
• RQ4 How do the predictions of CG and ΛCDM diverge at z > 2, and is this divergence statistically significant?
• RQ5 What constraints does the observed Hubble diagram up to z ≈ 8 place on the Higgs self-coupling constant λ in conformal gravity?

Key findings

• ΛCDM provides a significantly better fit to the combined GRB and quasar data than conformal gravity, with Δχ² = 48.
• The χ² test yields χ²_ΛCDM = 62.4 and χ²_Mannheim = 111, indicating strong statistical preference for ΛCDM.
• Conformal gravity deviates markedly from ΛCDM at redshifts z > 2, particularly in the Hubble diagram predictions.
• The Higgs self-coupling constant λ in Mannheim’s model is predicted to be approximately −10⁻¹⁷⁶, indicating an extreme fine-tuning problem.
• A new λ fine-tuning problem is identified in CG, analogous to the cosmological constant problem in ΛCDM, challenging its theoretical appeal.
• Despite claims of solving the cosmic coincidence problem, CG exhibits a similar issue involving the balance between ΩΛ and ΩK, requiring fine-tuning for the current epoch to be when the universe transitions from curvature to dark energy dominance.