[Paper Review] Cosmology with gamma-ray bursts: II Cosmography challenges and cosmological scenarios for the accelerated Universe

M. Demiański, E. Piedipalumbo+2 more|arXiv (Cornell University)|Sep 30, 2016

Gamma-ray bursts and supernovae50 references7 citations

TL;DR

This study performs a high-redshift cosmographic analysis using gamma-ray bursts (GRBs), type Ia supernovae, baryon acoustic oscillations, and Hubble parameter measurements to constrain cosmological parameters up to fifth order. It finds evidence at 1σ for a deviation from the ΛCDM model, with generalized Padé approximations improving constraints on the dark energy equation of state and indicating evolving dark energy.

ABSTRACT

Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that the space time ge- ometry is described by the Friedman-Lemaitre-Robertson-Walker metric, and adopting an approach that effectively uses only Taylor expansions of basic observables. Aims. We perform a high-redshift analysis to constrain the cosmographic expansion up to the fifth order. It is based on the Union2 type Ia supernovae data set, the gamma-ray burst Hubble diagram, a data set of 28 independent measurements of the Hubble param- eter, baryon acoustic oscillations measurements from galaxy clustering and the Lyman-α forest in the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), and some Gaussian priors on h and ΩM . Methods. We performed a statistical analysis and explored the probability distributions of the cosmographic parameters. By building up their regions of confidence, we maximized our likelihood function using the Markov chain Monte Carlo method. Results. Our high-redshift analysis confirms that the expansion of the Universe currently accelerates; the estimation of the jerk parameter indicates a possible deviation from the standard ΛCDM cosmological model. Moreover, we investigate implications of our results for the reconstruction of the dark energy equation of state (EOS) by comparing the standard technique of cosmography with an alternative approach based on generalized Padé approximations of the same observables. Because these expansions converge better, is possible to improve the constraints on the cosmographic parameters and also on the dark matter EOS. Conclusions. The estimation of the jerk and the DE parameters indicates at 1σ a possible deviation from the ΛCDM cosmological model.

Motivation & Objective

• To investigate the cosmological expansion history using high-redshift data, focusing on deviations from the standard ΛCDM model.
• To test the validity of cosmography up to fifth-order expansion parameters using diverse observational datasets.
• To compare standard cosmographic methods with generalized Padé approximations for improved convergence and tighter constraints on dark energy properties.
• To reconstruct the dark energy equation of state (EOS) using model-independent techniques, avoiding assumptions about its functional form.
• To break parameter degeneracies by incorporating Gaussian priors on h and ΩM from external measurements.

Proposed method

• A Markov Chain Monte Carlo (MCMC) method is used to explore the full posterior probability distribution of cosmographic parameters, ensuring convergence and robustness.
• The analysis combines the Union2 SNeIa Hubble diagram, a GRB Hubble diagram calibrated via the Ep,i–Eiso correlation, BAO measurements from SDSS-III BOSS, and direct H(z) measurements.
• Cosmographic parameters are derived from Taylor expansions of the luminosity distance dL(z) and Hubble parameter H(z), up to fifth order in redshift.
• Generalized Padé approximants are applied to the distance and Hubble rate, offering better convergence than standard Taylor series, especially at high redshift.
• The Padé parameters are projected onto the CPL parametrization space (w0, w1) to reconstruct the dark energy EOS and assess its time evolution.
• Constraints are enforced by requiring dL(z) > 0 and H(z) > 0 at each MCMC step to ensure physical consistency.

Experimental results

Research questions

• RQ1 Does the cosmographic expansion up to fifth order reveal a significant deviation from the ΛCDM model at 1σ confidence?
• RQ2 Can generalized Padé approximations improve the accuracy and convergence of cosmographic parameter estimation compared to standard Taylor expansions?
• RQ3 What constraints do combined GRB, SNeIa, BAO, and H(z) data place on the jerk parameter j0 and the dark energy equation of state w0 and w1?
• RQ4 Is the dark energy equation of state consistent with a constant value, or does the data favor a time-evolving EOS?
• RQ5 How do Gaussian priors on h and ΩM affect the degeneracy breaking and overall parameter constraints in the cosmographic analysis?

Key findings

• The deceleration parameter q0 confirms the current phase of cosmic acceleration, with strong statistical support.
• The jerk parameter j0 shows a 1σ indication of deviation from the ΛCDM prediction of j0 = 1, suggesting possible non-standard dynamics.
• Generalized Padé approximations yield better convergence and tighter constraints on cosmographic parameters than standard Taylor series.
• The reconstructed dark energy equation of state from Padé-based analysis indicates evolving dark energy, with best-fit w0 = -0.6149 and w1 = 0.3293, and 2σ intervals of (-0.6180, -0.6118) and (0.325, 0.333), respectively.
• The analysis rules out q0 > 0 at high significance, reinforcing the current acceleration phase.
• The Padé-based method provides stronger evidence for a non-constant dark energy EOS compared to standard cosmography, supporting dynamical dark energy models.