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Advances in Astronomy Volume 2015 ,2015-08-24
Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy
Research Article
Jun-Jie Wei 1 , 2 Qing-Bo Ma 1 , 2 Xue-Feng Wu 1 , 3 , 4
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DOI:10.1155/2015/576093
Received 2014-12-01, accepted for publication 2015-04-02, Published 2015-04-02
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摘要

We update gamma-ray burst (GRB) luminosity relations among certain spectral and light-curve features with 139 GRBs. The distance modulus of 82 GRBs at z > 1.4 can be calibrated with the sample at z ≤ 1.4 by using the cubic spline interpolation method from the Union2.1 Type Ia supernovae (SNe Ia) set. We investigate the joint constraints on the Cardassian expansion model and dark energy with 580 Union2.1 SNe Ia sample ( z < 1.4 ) and 82 calibrated GRBs’ data ( 1.4 < z ≤ 8.2 ) . In ΛCDM, we find that adding 82 high- z GRBs to 580 SNe Ia significantly improves the constraint on Ω m - Ω Λ plane. In the Cardassian expansion model, the best fit is Ω m = 0.2 4 - 0.15 + 0.15 and n = 0.1 6 - 0.52 + 0.30    ( 1 σ ) , which is consistent with the ΛCDM cosmology ( n = 0 ) in the 1 σ confidence region. We also discuss two dark energy models in which the equation of state w ( z ) is parameterized as w ( z ) = w 0 and w ( z ) = w 0 + w 1 z / ( 1 + z ) , respectively. Based on our analysis, we see that our universe at higher redshift up to z = 8.2 is consistent with the concordance model within 1 σ confidence level.

授权许可

Copyright © 2015 Jun-Jie Wei et al. 2015
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

图表

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

(a) The Hubble diagram of 580 SNe Ia (red triangles) and 57 GRBs at z ≤ 1.4 (black dots) whose distance moduli are derived by using cubic spline interpolation. (b)–(f) The τ lag - L , E p - L , E p - E γ , τ RT - L , and E p - E iso correlations. The five correlations are calibrated with the sample at z ≤ 1.4 using cubic spline interpolation. The solid lines show the best-fitting results, while the dashed lines represent their 2 σ dispersion around the best fits.

Hubble diagram of 580 SNIa (red triangles) and 139 GRBs (dots) obtained using the interpolation method. The 57 GRBs at z ≤ 1.4 are obtained by interpolating from SNe Ia data (black dots); and the 82 GRBs at z > 1.4 (blue dots) are obtained with the five correlations calibrated with the sample at z ≤ 1.4 using the cubic spline interpolation method. The vertical dotted line represents z = 1.4 . The solid curve represents the best-fit cosmology for a flat Λ CDM universe: Ω m = 0.29 , Ω Λ = 0.71 .

(a) The contour confidence levels of ( Ω m , Ω Λ ) in the Λ CDM model from the data for 82 GRBs ( z > 1.4 ) (dark cyan dash-dotted lines), 580 SNe Ia (blue dashed lines), and 82 GRBs + 580 SNe Ia (red solid lines), respectively. The contours correspond to 1, 2, and 3 σ confidence regions. (b) The probability versus the transition redshift derived from the GRB and SNe Ia sample.

(a) The contour confidence levels of ( Ω m , Ω Λ ) in the Λ CDM model from the data for 82 GRBs ( z > 1.4 ) (dark cyan dash-dotted lines), 580 SNe Ia (blue dashed lines), and 82 GRBs + 580 SNe Ia (red solid lines), respectively. The contours correspond to 1, 2, and 3 σ confidence regions. (b) The probability versus the transition redshift derived from the GRB and SNe Ia sample.

The contour confidence levels of ( Ω m , n ) in the Cardassian expansion model from the data for 82 GRBs ( z > 1.4 ) (dark cyan dash-dotted lines), 580 SNe Ia (blue dashed lines), and 82 GRBs + 580 SNe Ia (red solid lines), respectively. The contours correspond to 1, 2, and 3 σ confidence regions.

Constraints on Ω m and w 0 from 1 σ to 3 σ confidence regions with dark energy whose equation state is constant. The contours are derived from GRBs (dark cyan dash-dotted lines), SNe Ia (blue dashed lines), and SNe Ia + GRBs (red solid lines), respectively.

Constraints on w 0 and w 1 from 1 σ to 3 σ confidence regions with dark energy whose equation state is w ( z ) = w 0 + w 1 z / ( 1 + z ) . The contours are derived from GRBs (dark cyan dash-dotted lines), SNe Ia (blue dashed lines), and SNe Ia + GRBs (red solid lines), respectively.

通讯作者

Xue-Feng Wu.Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210008, China, cas.cn;Chinese Center for Antarctic Astronomy, Nanjing 210008, China;Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing University-Purple Mountain Observatory, Nanjing 210008, China, nju.edu.cn.xfwu@pmo.ac.cn

推荐引用方式

Jun-Jie Wei,Qing-Bo Ma,Xue-Feng Wu. Utilizing the Updated Gamma-Ray Bursts and Type Ia Supernovae to Constrain the Cardassian Expansion Model and Dark Energy. Advances in Astronomy ,Vol.2015(2015)

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