One of the few ways to measure the properties of dark energy is to extend the Hubble diagram (HD) to higher redshifts with gamma-ray bursts (GRBs). GRBs have at least five properties (their spectral lag, variability, spectral peak photon energy, time of the jet break, and the minimum rise time) that have correlations to the luminosity of varying quality. In this paper I construct a GRB HD with 69 GRBs over a redshift range from 0.17 to >6, with half the bursts having a redshift larger than 1.7. This paper uses over 3.6 times as many GRBs and 12.7 times as many luminosity indicators as any previous GRB HD work. For the gravitational lensing and Malmquist biases, I find that the biases are small, with an average of 0.03 mag and an rms scatter of 0.14 mag in the distance modulus. The GRB HD is well behaved and nicely delineates the shape of the HD. The reduced χ2 for the fit to the concordance model is 1.05, and the rms scatter about the concordance model is 0.65 mag. This accuracy is just a factor of 2.0 times that gotten for the same measure from all the big supernova surveys. I fit the GRB HD to a variety of models, including where the dark energy has its equation of state parameter varying as w(z) = w0 + waz/(1 + z). I find that the concordance model is consistent with the data, that is, the dark energy can be described well as a cosmological constant that does not change with time.

http://iopscience.iop.org/article/10.1086/511742/pdf

The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts

Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. The evolution and selection effects have thus been ignored, which might have important influence on the results. In this Letter, we divide the 48 long-duration GRBs in Amati (2006, 2007) into four groups with redshift from low to high, each group contains 12 GRBs. Then we fit each group with the Amati relation $\log E_\iso = a + b \log E_\p$, and check if the parameters $a$ and $b$ evolve with the GRB redshift. We find that $a$ and $b$ vary with the mean redshift of the GRBs in each group systematically and significantly. Monte-Carlo simulations show that there is only $\sim 4$ percent of chance that the variation is caused by the selection effect arising from the fluence limit. Hence, our results may indicate that GRBs evolve strongly with the cosmological redshift.

Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?

Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. The evolution and selection effects have thus been ignored, which might have important influence on the results. In this Letter, we divide the 48 long-duration GRBs in Amati (2006, 2007) into four groups with redshift from low to high, each group contains 12 GRBs. Then we fit each group with the Amati relation log Eiso = a + blog Epeak, and check if the parameters a and b evolve with the GRB redshift. We find that a and b vary with the mean redshift of the GRBs in each group systematically and significantly. Monte-Carlo simulations show that there is only � 4 percent of chance that the variation is caused by the selection effect arising from the fluence limit. Hence, our results may indicate that GRBs evolve strongly with the cosmological redshift.

/pdf/variation-of-the-amati-relation-with-cosmological-redshift-a-21ld4yyikk.pdf

Variation of the Amati relation with cosmological redshift: a selection effect or an evolution effect?

We use the measurement of gamma-ray burst (GRB) distances to constrain dark energy cosmological model parameters. We employ two methods for analyzing GRB data-fitting luminosity relation of GRBs in each cosmology and using distance measures computed from binned GRB data. Current GRB data alone cannot tightly constrain cosmological parameters and allow for a wide range of dark energy models.

http://iopscience.iop.org/article/10.1088/0004-637X/714/2/1347/pdf

Constraining dark energy with gamma-ray bursts

The behavior of the dark energy equation of state (EOS) is crucial in distinguishing different cosmological models. With a model independent approach, we constrain the possible evolution of the dark energy EOS. Gamma-ray bursts (GRBs) of redshifts up to $z>6$ are used, in addition to type Ia supernovae (SNe Ia). We separate the redshifts into 4 bins and assume a constant EOS parameter for dark energy in each bin. The EOS parameters are decorrelated by diagonalizing the covariance matrix. And the evolution of dark energy is estimated out of the uncorrelated EOS parameters. By including GRB luminosity data, we significantly reduce the confidence interval of the uncorrelated EOS parameter whose contribution mostly comes from the redshift bin of $0.5<z<1.8$. At high redshift where we only have GRBs, the constraints on the dark energy EOS are still very weak. However, we can see an obvious cut at about zero in the probability plot of the EOS parameter, from which we can infer that the ratio of dark energy to matter most probably continues to decrease beyond redshift 1.8. We carried out analyses with and without including the latest BAO measurements, which themselves favor a dark energy EOS of $w<-1$. If they are included, the results show some evidence of an evolving dark energy EOS. If not included, however, the results are consistent with the cosmological constant within $1 \sigma$ for redshift $0<z \lesssim 0.5$ and $2 \sigma$ for $0.5 \lesssim z<1.8$.

/pdf/constraining-the-evolution-of-dark-energy-with-type-ia-2b7zwxpb15.pdf

Constraining the evolution of dark energy with type Ia supernovae and gamma-ray bursts

[Abridged] Very recently, relations between the peak energy of Gamma-Ray Burst burst spectra, the isotropic-equivalent energy of the burst, and the radiated energy of the burst have been found. In a way that is exactly analogous to the way in which the relation between the peak luminosity and the rate of decline of the light curve of Type Ia supernovae can be used to make Type Ia supernovae excellent standard candles for cosmology, so too, the relations between Epk, Eiso, and Egamma point toward a methodology for using GRBs as excellent standard candles for cosmology. In addition, GRBs occur over the broad redshift range from z=0.1 to at least z=4.5, and both they and their afterglows are easily detectable out to z > 8. Thus GRBs show great promise as cosmological ``yardsticks'' to measure the rate of expansion of the universe over time, and therefore the properties of dark energy (i.e., Omega_M, Omega_Lambda, w_0, and w_a). 
We describe a concept for a possible MIDEX-class mission dedicated to using GRBs to constrain the properties of dark energy that would obtain these quantities for > 800 bursts in the redshift range 0.1 >~ z <~ 10 during a 2-year mission. This burst sample would enable both Omega_M and w_0 to be determined to +/- 0.07 and +/- 0.06 (68% CL), respectively, and w_a to be significantly constrained.

A Gamma-Ray Burst Mission to Investigate the Properties of Dark Energy

A Gamma-Ray Burst Mission to Investigate the Properties of Dark Energy A White Paper Submitted to the Dark Energy Task Force

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A Gamma-Ray Burst Mission to Investigate the Properties of Dark Energy

A Gamma-Ray Burst Mission to Investigate the Properties of Dark Energy A White Paper Submitted to the Dark Energy Task Force