Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence
Datadriven modelindependent reconstructions of the dark energy equation of state w(z) are presented using Planck 2015 era CMB, BAO, SNIa and Lymanα data. These reconstructions identify the w(z) behaviour supported by the data and show a bifurcation of the equation of state posterior in the range 1.5 < z < 3. Although the concordance ΛCDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as ‘phantom dark energy’) is identified within the 1.5σ confidence intervals of the posterior distribution. In order to identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback–Leibler divergence. Moreover, this formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lymanα datasets. Furthermore, SNIa and BAO constrain most strongly around redshift range 0.1  0.5, whilst the Lymanα data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the ΛCDM modelmore »
 Authors:

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 Battcock Center, Cambridge (United Kingdom). Cavendish Lab.; Kavli Inst. for Cosmology Cambridge (United Kingdom)
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Battcock Center, Cambridge (United Kingdom). Cavendish Lab.
 Publication Date:
 Report Number(s):
 BNL1125662016JA
Journal ID: ISSN 00358711; KA2301020
 Grant/Contract Number:
 SC00112704
 Type:
 Accepted Manuscript
 Journal Name:
 Monthly Notices of the Royal Astronomical Society
 Additional Journal Information:
 Journal Name: Monthly Notices of the Royal Astronomical Society; Journal ID: ISSN 00358711
 Publisher:
 Royal Astronomical Society
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; methods: data analysis; methods: statistical; dark energy; equation of state; cosmological parameters
 OSTI Identifier:
 1336117
Hee, S., Vázquez, J. A., Handley, W. J., Hobson, M. P., and Lasenby, A. N.. Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence. United States: N. p.,
Web. doi:10.1093/mnras/stw3102.
Hee, S., Vázquez, J. A., Handley, W. J., Hobson, M. P., & Lasenby, A. N.. Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence. United States. doi:10.1093/mnras/stw3102.
Hee, S., Vázquez, J. A., Handley, W. J., Hobson, M. P., and Lasenby, A. N.. 2016.
"Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence". United States.
doi:10.1093/mnras/stw3102. https://www.osti.gov/servlets/purl/1336117.
@article{osti_1336117,
title = {Constraining the dark energy equation of state using Bayes theorem and the Kullback–Leibler divergence},
author = {Hee, S. and Vázquez, J. A. and Handley, W. J. and Hobson, M. P. and Lasenby, A. N.},
abstractNote = {Datadriven modelindependent reconstructions of the dark energy equation of state w(z) are presented using Planck 2015 era CMB, BAO, SNIa and Lymanα data. These reconstructions identify the w(z) behaviour supported by the data and show a bifurcation of the equation of state posterior in the range 1.5 < z < 3. Although the concordance ΛCDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as ‘phantom dark energy’) is identified within the 1.5σ confidence intervals of the posterior distribution. In order to identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback–Leibler divergence. Moreover, this formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lymanα datasets. Furthermore, SNIa and BAO constrain most strongly around redshift range 0.1  0.5, whilst the Lymanα data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the ΛCDM model was favoured at more than 2 logunits in Bayes factors over all the models tested despite the weakly preferred w(z) structure in the data.},
doi = {10.1093/mnras/stw3102},
journal = {Monthly Notices of the Royal Astronomical Society},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {12}
}