No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Varying-G cosmology with type Ia supernovae
1.See, for example, S. Weinberg, Cosmology (Oxford U. P., New York, 2008), pp. 1–100.
6.A. G. Riess et al. (The High-Z Team), “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” Astron. J. 116, 1009–1038 (1998).
7.S. Perlmutter et al. (The Supernova Cosmology Project), “Measurements of omega and lambda from 42 high-redshift supernovae,” Astrophys. J. 517, 565–586 (1999).
8.The units of are mass per unit volume , where is the mass unit and the unit of length. However, it is common to choose units so that , thereby eliminating the distinction between mass and energy. For clarity, we keep the symbol in all expressions. Note that .
11.M. Kowalski et al., “Improved cosmological constraints from new, old, and combined supernova data sets,” Astrophys. J. 686, 749–778 (2008).
14.S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover, New York, 1967).
17.We have described the bolometric magnitude, that is, the magnitude of a star assuming we can measure the flux across all wavelengths. In practice, fluxes are measured in wavelength bands defined by standard filters, such as the -band filters (Ref. 18). An observed supernova spectrum is redshifted with respect to the spectrum in the rest frame of the supernova. Therefore, a filter will transmit a flux that differs from the one that would be measured in the supernova’s rest frame. Astronomers use corrections to map the measured flux back to its value in the object’s rest frame. Given a model of the object’s spectrum, it is possible, in principle, to infer the bolometric flux and hence the bolometric magnitude of the object. The distance modulus data compiled in Ref. 11 are derived from -band magnitude data.
18.H. Johnson and W. Morgan, “Fundamental stellar photometry for standards of spectral type on the revised system of the Yerkes spectral atlas,” Astrophys. J. 117, 313–352 (1953).
19.E. Gaztañaga, E. García-Berro, J. Isern, E. Bravo, and I. Domínguez, “Bounds on the possible evolution of the gravitational constant from cosmological type-Ia supernovae,” Phys. Rev. D 65, 023506-1–9 (2001);
19.E. García-Berro, Y. Kubyshin, P. Loren-Aguilar, and J. Isern, “The variation of the gravitational constant inferred from the Hubble diagram of type Ia supernovae,” Int. J. Mod. Phys. D 15, 1163–1174 (2006).
21.The absolute luminosity of a supernova cannot be determined independently of the Hubble constant . Consequently, in the fit of the modulus function to the data, it is only the shape of the function that contains useful information about the cosmology. The offset depends both on as well as on the flux corrections.
22.If the interval is divided into intervals of width , the midpoint rule is .
23.R. Brun et al.
, “ROOT data analysis package
24.The lifetimes can be computed given values for the parameters and . However, because we cannot extract a value of from the fits, we compute the lifetimes using the nominal value for the Hubble constant. We write all lifetimes in terms of the parameter to make clear how the numerical values will change if differs from the nominal value.
25.If the reported modulus uncertainties are Gaussian distributed, we expect to be sampled from a probability density with mean , where is the number of data points and is the number of adjustable parameters. ND is the number of degrees of freedom. Therefore, for a fit that neither overfits nor underfits, we expect . The quantity would be exactly equal to 2 if the constraints that define the parameter estimates were linear in the parameters.
26.See, for example, J. D. Barrow and P. Parsons, “The behavior of cosmological models with varying-G,” Phys. Rev. D 55, 1906–1936 (1997);
26.E. García-Berro, J. Isern, and Y. A. Kubyshin, “Astronomical measurements and constraints on the variability of fundamental constants,” Astron. Astrophys. Rev. 14, 113–170 (2007).
27.E. V. Linder (private communication, 2010).
Article metrics loading...
Full text loading...
Most read this month