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We first discuss why there remains continuing, strong motivation to investigate Hubbles Constant. Then we review new evidence from an investigation of the Galactic Open Clusters containing Cepheids by Hoyle et al. that the metallicity dependence of the Cepheid P-L relation is stronger than expected. This result is supported by a new analysis of mainly HST Distance Scale Key Project data which shows a correlation between host galaxy metallicity and the rms scatter around the Cepheid P-L relation. If Cepheids do have a significant metallicity dependence then an already existing scale error for Tully-Fisher distances becomes worse and the distances of the Virgo and Fornax clusters extend to more than 20Mpc, decreasing the value of H_0. Finally, if the Cepheids have a metallicity dependence then so do Type Ia Supernovae since the metallicity corrected Cepheid distances to eight galaxies with SNIa now suggests that the SNIa peak luminosity is fainter in metal poor galaxies. As well as having important implications for H_0, this would also imply that the evidence for a non-zero cosmological constant from the SNIa Hubble Diagram may be subject to corrections for metallicity which are as big as the effects of cosmology.
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We first discuss why the uncomfortable fine-tuning of the parameters of the Lambda-CDM cosmological model provides continuing, strong motivation to investigate Hubbles Constant. Then we review evidence from the HST Key Project that there is a significant scale error between raw Cepheid and Tully-Fisher distances. An analysis of mainly HST Distance Scale Key Project data shows a correlation between host galaxy metallicity and the rms scatter around the Cepheid P-L relation, which may support a recent suggestion that the P-L metallicity dependence is stronger than expected. If Cepheids do have a significant metallicity dependence then the Tully-Fisher scale error increases and the distances of the Virgo and Fornax clusters extend to more than 20Mpc, decreasing the value of Ho. Finally, if the Cepheids have a metallicity dependence then so do Type Ia Supernovae since the metallicity corrected Cepheid distances to eight galaxies with SNIa would then suggest that the SNIa peak luminosity is fainter in metal poor galaxies, with important implications for SNIa estimates of qo as well as Ho.
The current tension between the direct and the early Universe measurements of the Hubble Constant, $H_0$, requires detailed scrutiny of all the data and methods used in the studies on both sides of the debate. The Cepheids in the type Ia supernova (SNIa) host galaxy NGC 5584 played a key role in the local measurement of $H_0$. The SH0ES project used the observations of this galaxy to derive a relation between Cepheids periods and ratios of their amplitudes in different optical bands of the Hubble Space Telescope (HST), and used these relations to analyse the light curves of the Cepheids in around half of the current sample of local SNIa host galaxies. In this work, we present an independent detailed analysis of the Cepheids in NGC 5584. We employ different tools for our photometric analysis and a completely different method for our light curve analysis, and we do not find a systematic difference between our period and mean magnitude measurements compared to those reported by SH0ES. By adopting a period-luminosity relation calibrated by the Cepheids in the Milky Way, we measure a distance modulus $mu=31.810pm0.047$ (mag) which is in agreement with $mu=31.786pm0.046$ (mag) measured by SH0ES. In addition, the relations we find between periods and amplitude ratios of the Cepheids in NGC 5584 are significantly tighter than those of SH0ES and their potential impact on the direct $H_0$ measurement will be investigated in future studies.
We re-analyze the Cepheid data used to infer the value of $H_0$ by calibrating SnIa. We do not enforce a universal value of the empirical Cepheid calibration parameters $R_W$ (Cepheid Wesenheit color-luminosity parameter) and $M_H^{W}$ (Cepheid Wesenheit H-band absolute magnitude). Instead, we allow for variation of either of these parameters for each individual galaxy. We also consider the case where these parameters have two universal values: one for low galactic distances $D<D_c$ and one for high galactic distances $D>D_c$ where $D_c$ is a critical transition distance. We find hints for a $3sigma$ level mismatch between the low and high galactic distance parameter values. We then use AIC and BIC criteria to compare and rank the following types of models: Base models: Universal values for $R_W$ and $M_H^{W}$ (no parameter variation), I Individual fitted galactic $R_W$ with a universal fitted $M_H^{W}$, II Universal fixed $R_W$ with individual fitted galactic $M_H^{W}$, III Universal fitted $R_W$ with individual fitted galactic $M_H^{W}$, IV Two universal fitted $R_W$ (near and far) with one universal fitted $M_H^{W}$, V Universal fitted $R_W$ with two universal fitted $M_H^{W}$ (near and far), VI Two universal fitted $R_W$ with two universal fitted $M_H^{W}$ (near and far). We find that the AIC and BIC criteria consistently favor model IV instead of the commonly used Base model where no variation is allowed for the Cepheid empirical parameters. The best fit value of the SnIa absolute magnitude $M_B$ and of $H_0$ implied by the favored model IV is consistent with the inverse distance ladder calibration based on the CMB sound horizon $H_0=67.4pm 0.5,km,s^{-1},Mpc^{-1}$. Thus in the context of the favored model IV the Hubble crisis is not present. This model may imply the presence of a fundamental physics transition taking place at a time more recent than $100,Myrs$ ago.
In this paper, we derive a physical argument for the existence of Period-luminosity and period-luminosity-colour relations at maximum light. We examine in detail a sample of Cepheids in the Large Magellanic Cloud, and compare the variance of some PL and PLC type distance indicators based on mean and maximum light. We show that a PLC relation based on maximum light leads to a distance estimator with a dispersion about $10 %$ smaller than its counterpart using mean light. We also show that a PLC type relation constructed using observations at both maximum and mean light has a significantly $( > 50 %)$ smaller dispersion than a PLC relation using either maximum or mean light alone. A comparable $( > 30 %)$ reduction in the dispersion of the corresponding distance estimator, however, in this case requires the relation be applied to a large $( n > 30)$ group of equidistant Cepheids in, e.g., a distant galaxy. Recent HST observations of IC4182, M81 and M100 already provide suitable candidate data sets for this relation.
Distances measured using Cepheid variable stars have been essential for establishing the cosmological distance scale and the value of the Hubble constant. These stars have remained the primary extragalactic distance indicator since 1929 because of the small observed scatter in the relationship between their pulsation period and luminosity, their large numbers, which allow many independent measures of the distance to a galaxy, and the simplicity of the basic physics underlying their variability. Potential systematic uncertainties in the use of the LMC-calibrated Cepheid period-luminosity relation to determine distances using HST are estimated to be 8-10%. Here we describe the results of a search for Cepheids in the nearby galaxy NGC 4258, which has an independently determined geometric distance of 7.2 +/- 0.5 Mpc (Herrnstein et al. 1999). We obtain a Cepheid distance of 8.1 +/- 0.4 (excluding possible systematic errors affecting all HST Cepheid distances) Mpc; there is a 1.3 sigma difference between the two measurements. If the maser-based distance is adopted and other HST Cepheid distances are revised according to our results, the derived value of the Hubble constant would be increased by 12 +/- 9%, and the corresponding age of the Universe would decrease by the same factor.
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