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NONPARAMETRIC DETERMINATION OF REDSHIFT EVOLUTION INDEX OF DARK ENERGY

July 2007
22(21):1569-1580

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We propose a nonparametric method to determine the sign of γ — the redshift evolution index of dark energy. This is important for distinguishing between positive energy models, a cosmological constant, and what is generally called ghost models. Our method is based on geometrical properties and is more tolerant to uncertainties of other cosmological parameters than fitting methods in what concerns the sign of γ. The same parametrization can also be used for determining γ and its redshift dependence by fitting. We apply this method to SNLS supernovae and to gold sample of re-analyzed supernovae data from Riess et al. Both datasets show strong indication of a negative γ. If this result is confirmed by more extended and precise data, many of the dark energy models, including simple cosmological constant, standard quintessence models without interaction between quintessence scalar field(s) and matter, and scaling models are ruled out. We have also applied this method to Gurzadyan–Xue models with varying fundamental constants to demonstrate the possibility of using it to test other cosmologies.

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July 26, 2007 2:42 WSPC/146-MPLA 02384

Modern Physics Letters A

Vol. 22, No. 21 (2007) 1569–1580

World Scientiﬁc Publishing Company

NONPARAMETRIC DETERMINATION OF REDSHIFT

EVOLUTION INDEX OF DARK ENERGY

HOURI ZIAEEPOUR

Mullard Space Science Laboratory, University College London, Holmbury St. Mary,

Dorking, Surrey, RH5 6NT, UK

hz@mssl.ucl.ac.uk

Received 13 April 2007

Revised 11 May 2007

We propose a nonparametric method to determine the sign of γ— the redshift evolu-

tion index of dark energy. This is important for distinguishing between positive energy

models, a cosmological constant, and what is generally called ghost models. Our method

is based on geometrical properties and is more tolerant to uncertainties of other cos-

mological parameters than ﬁtting methods in what concerns the sign of γ. The same

parametrization can also be used for determining γand its redshift dependence by ﬁtting.

We apply this method to SNLS supernovae and to gold sample of re-analyzed super-

novae data from Riess et al. Both datasets show strong indication of a negative γ. If this

result is conﬁrmed by more extended and precise data, many of the dark energy models,

including simple cosmological constant, standard quintessence models without interac-

tion between quintessence scalar ﬁeld(s) and matter, and scaling models are ruled out.

We have also applied this method to Gurzadyan–Xue models with varying fundamental

constants to demonstrate the possibility of using it to test other cosmologies.

Recent observations of Supernovae (SNe), Cosmic Microwave Background (CMB),

and Large Scale Structures (LSS) indicate that the dominant content of the

Universe is a mysterious energy with an equation of state very close to Einstein

cosmological constant. The equation of state is deﬁned by w, the ratio of pressure

pto density ρ,w=P/ρ. For a cosmological constant w=−1. The observed mean

value of wfor dark energy is very close to −1. Some of the most recent estima-

tions of ware: From combination of 3-year WMAP and SuperNova Legacy Survey

(SNLS),2w=−0.97+0.07

0.09 ; from combination of 3-year WMAP, large scale structure

and supernova data,2w=−1.06+0.016

−0.009; from combination of CMAGIC supernovae

analysis and baryon acoustic peak in SDSS galaxy clustering statistics at3z= 0.35,

w=−1.21+0.15

−0.12; and ﬁnally from baryon acoustic peak alone w=−0.8±0.18. It is

evident that with inclusion of one or two sigma uncertainties to measured mean val-

ues, the range of possible values for wruns across the critical value of −1. Moreover,

in all these measurements the value of wdepends on other cosmological parameters

1569

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NONPARAMETRIC DETERMINATION OF REDSHIFT EVOLUTION INDEX OF DARK ENERGY

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