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 Physics , 2000, Abstract: The methodology involved in deriving the Hubble Constant via the calibration of the corrected peak luminosities of Type Ia supernovae (SNe) is reviewed. We first present a re-analysis of the Calan-Tololo (C-T) and Center for Astrophysics (CfA) Type Ia SN surveys. Bivariate linear least squares and quadratic boot-strapped fits in peak apparent magnitude and light curve shape are employed to correct this heterogeneous sample of peak apparent magnitudes, resulting in an homogeneous (and excellent) secondary distance indicator: the so-called corrected peak luminosity. We next provide an empirical calibration for this corrected luminosity, using Cepheid-based distances for seven nearby spiral galaxies host to Type Ia SNe. Included in this sample is the spectroscopically peculiar SN 1991T (in NGC 4527), whose corrected peak luminosity is shown to be indistinguishable from that of so-called normal'' SNe. A robust value of the Hubble Constant is derived and shown to be H0=73+/-2(r)+/-7(s) km/s/Mpc.
 Physics , 1999, Abstract: Type Ia supernovae (SNe) are the best standard candles available today in spite of an appreciable intrinsic variation of their luminosities at maximum phase, and of probably non-uniform progenitors. For an unbiased use of type Ia SNe as distance indicators it is important to know accurately how the decline rate and colour at maximum phase correlate with the peak brightness. In order to calibrate the Hubble diagram of type Ia SNe, i.e. to derive the Hubble constant, one needs to determine the absolute brightness of nearby type Ia SNe. Globular cluster systems of early type Ia host galaxies provide suitable distance indicators. We discuss how Ia SNe can be calibrated and explain the method of Globular Cluster Luminosity Functions (GCLFs). At present, the distance to the Fornax galaxy cluster is most important for deriving the Hubble constant. Our present data indicate a Hubble constant of H_0=72+-4 km/s/Mpc. As an appendix, we summarise what is known about absolute magnitudes of Ia's in late-type galaxies.
 Physics , 2005, DOI: 10.1142/S0218271806008772 Abstract: We consider a cosmological model with a variable gravitational constant, G, based on a scalar-tensor theory. Using the recent observational data for the Hubble diagram of type Ia supernovae (SNeIa) we find a phenomenological expression describing the variation of G. The corresponding variation of the fine structure constant \alpha within multidimensional theories is also computed and is shown not to support known constraints on \Delta \alpha / \alpha.
 Physics , 2009, DOI: 10.1088/0067-0049/183/1/109 Abstract: This is the first of two papers reporting measurements from a program to determine the Hubble constant to 5% precision from a refurbished distance ladder. We present new observations of 110 Cepheid variables in the host galaxies of two recent Type Ia supernovae (SNe Ia), NGC 1309 and NGC 3021, using the Advanced Camera for Surveys on the Hubble Space Telescope (HST). We also present new observations of the hosts previously observed with HST whose SNe Ia provide the most precise luminosity calibrations: SN 1994ae in NGC 3370, SN 1998aq in NGC 3982, SN 1990N in NGC 4639, and SN 1981B in NGC 4536, as well as the maser host, NGC 4258. Increasing the interval between observations enabled the discovery of new, longer-period Cepheids, including 57 with P>60 days, which extend these period-luminosity (PL) relations. We present 93 measurements of the metallicity parameter, 12 + log[O/H], measured from HII regions in the vicinity of the Cepheids and show these are consistent with solar metallicity. We find the slope of the seven dereddened PL relations to be consistent with that of the Large Magellanic Cloud Cepheids and with parallax measurements of Galactic Cepheids, and we address the implications for the Hubble constant. We also present multi-band light curves of SN 2002fk (in NGC 1309) and SN 1995al (in NGC 3021) which may be used to calibrate their luminosities. In the second paper we present observations of the Cepheids in the H-band obtained with the Near Infrared Camera and Multi-Object Spectrometer on HST, further mitigating systematic errors along the distance ladder resulting from dust and chemical variations. The quality and homogeneity of these SN and Cepheid data provide the basis for a more precise determination of the Hubble constant.
 Physics , 1996, Abstract: Cross-filter K corrections for a sample of "normal" Type Ia supernovae (SNe) have been calculated for a range of epochs. With appropriate filter choices, the combined statistical and systematic K correction dispersion of the full sample lies within 0.05 mag for redshifts z<0.7. This narrow dispersion of the calculated K correction allows the Type Ia to be used as a cosmological probe. We use the K corrections with observations of seven SNe at redshifts 0.3 < z <0.5 to bound the possible difference between the locally measured Hubble constant (H_L) and the true cosmological Hubble constant (H_0).
 Physics , 1996, Abstract: An interesting way to calibrate the absolute magnitudes of remote Type Ia supernovae (SNe Ia) that are well out in the Hubble flow, and thus determine the value of the Hubble constant, H_0, has been introduced by van den Bergh. His approach relies on calculations of the peak absolute magnitudes and broad--band colors for SN Ia explosion models. It does not require any corrections for extinction by interstellar dust, and no SNe Ia are excluded on grounds of peculiarity. Within the last few years distances have been determined to the parent galaxies of six SNe Ia by means of Cepheid variables. Cepheid--based distances also have become available for three other SNe Ia if one is willing to use the distance to a galaxy in the same group in lieu of the distance to the parent galaxy itself. Here we determine the value of H_0 in a way that is analogous to that of van den Bergh, but now using Cepheid--based distances instead of calculated light curves. We obtain H_0 = 55 km/s/Mpc. This value, with Lambda=0 and Omega=1, corresponds to a cosmic expansion time of 12 Gyr, which is consistent with several recent determinations of the ages of globular clusters.
 Physics , 1999, DOI: 10.1086/307883 Abstract: In this paper, we make a comprehensive determination of the Hubble constant $H_0$ by using two parameters - the B-V color and the rate of decline $\Delta m_{15}$ - to simultaneously standardize the luminosities of all nearby Cepheid-calibrated type Ia supernovae (SNe Ia) and those of a larger, more distant sample of 29 SNe Ia. Each group is treated in as similar a manner as possible in order to avoid systematic effects. A simultaneous $\chi ^2$ minimization yields a standardized absolute luminosity of the Cepheid-calibrated supernovae as well as the Hubble constant obtained from the more distant sample. We find $H_0 = 62 km/s Mpc^{-1}$ and a standardized absolute magnitude of -19.46. The sensitivity of $H_0$ to a metallicity dependence of the Cepheid-determined distances is investigated. The total uncertainty $\delta H_0$, dominated by uncertainties in the primary Cepheid distance indicator, is estimated to be 5 km/s Mpc^{-1}.
 Physics , 1999, DOI: 10.1086/308306 Abstract: Cepheid-based distances to seven Type Ia supernovae (SNe)-host galaxies have been derived using the standard HST Key Project on the Extragalactic Distance Scale pipeline. For the first time, this allows for a transparent comparison of data accumulated as part of three different HST projects, the Key Project, the Sandage et al. Type Ia SNe program, and the Tanvir et al. Leo I Group study. Re-analyzing the Tanvir et al. galaxy and six Sandage et al. galaxies we find a mean (weighted) offset in true distance moduli of 0.12+/-0.07 mag -- i.e., 6% in linear distance -- in the sense of reducing the distance scale, or increasing H0. Adopting the reddening-corrected Hubble relations of Suntzeff et al. (1999), tied to a zero point based upon SNe~1990N, 1981B, 1998bu, 1989B, 1972E and 1960F and the photometric calibration of Hill et al. (1998), leads to a Hubble constant of H0=68+/-2(random)+/-5(systematic) km/s/Mpc. Adopting the Kennicutt et al. (1998) Cepheid period-luminosity-metallicity dependency decreases the inferred H0 by 4%. The H0 result from Type Ia SNe is now in good agreement, to within their respective uncertainties, with that from the Tully-Fisher and surface brightness fluctuation relations.
 Physics , 1999, Abstract: We investigate to which extent a time variation of the gravitational constant or other fundamental constants affects the best fit of the Hubble diagram of type Ia supernovae. In particular, we show that a slow increase of $G$ in the past, below experimental constraints, can reconcile the SNe Ia observations with an open zero-$\Lambda$ universe.
 Physics , 1999, Abstract: There are at least three ways in which a varying gravitational constant $G$ could affect the interpretation of the recent high-redhisft Type Ia supernovae results. If the local value of $G$ at the space-time location of distant supernovae is different, it would change both the thermonuclear energy release and the time scale of the supernova outburst. In both cases the effect is related to a change in the Chandrasekhar mass $M_{\rm Ch}\propto G^{-3/2}$. Moreover the integrated variation of $G$ with time would also affect cosmic evolution and therefore the luminosity distance relation. Here we investigate in a consistent way how these different effects of a varying $G$ could change the current interpretation of the Hubble diagram of Type Ia supernovae. We parametrize the variation of $G$ using scalar-tensor theories of gravity, such as the Jordan-Brans-Dicke theory or its extensions. It is remarkable that Dirac's hypothesis that $G$ should decrease with time can qualitatively explain the observed $\Delta m \simeq 0.2$ mag decrease at $z\simeq 0.5$ (with respect to a decelerating universe) and, at the same time, reduce the duration of the risetimes of distant Type Ia supernovae as recently reported.
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