Hubble tension or a transition of the Cepheid SnIa calibrator parameters?

We reanalyze the Cepheid data used to infer the value of the Hubble constant $H_0$ by calibrating type Ia supernovae. 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 $3\sigma$ level mismatch between the low and high galactic distance parameter values. We then use model selection criteria [Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC)], which penalize models with large numbers of parameters, to compare and rank the following types of $R_W$ and $M_H^W$ parameter variations: Base models: Universal values for $R_W$ and $M_H^W$ (no parameter variation), I: Individual fitted galactic $R_W$ with one universal fitted $M_H^W$, II: One universal fixed $R_W$ with individual fitted galactic $M_H^W$, III: One 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: One universal fitted $R_W$ with two universal fitted $M_H^W$ (near and far), and VI: Two universal fitted $R_W$ (near and far) with two universal fitted $M_H^W$ (near and far). We find that the AIC and BIC model selection 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 cosmic microwave background sound horizon $H_0=67.4\pm 0.5\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. 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 $100Myr$ ago.

Figure 1

The Hubble constant as a function of publication date, using a set of different tools. Symbols in orange denote the values of $H_0$ determined in the late Universe with a calibration based on the Cepheid distance scale (Key Project (KP) [21], Supernovae $H_0$ for the Equation of State (SH0ES) [16, 17, 18, 20, 22, 23], Carnegie Hubble Program (CHP) [24]). Symbols in purple denote the derived values of $H_0$ from analysis of the CMB data based on the sound horizon standard ruler (First Year WMAP (WMAP1) [25], Three Year WMAP (WMAP3) [26], Five Year WMAP (WMAP5) [27], Seven Year WMAP (WMAP7) [28], Nine Year WMAP (WMAP9) [29], Planck13 (P13) [30], Planck15 (P15) [31], Planck18 (P18) [1], BAO [32]). The orange and purple shaded regions demonstrate the evolution of the uncertainties in these values which have been decreasing for both methods. The most recent measurements disagree at greater than $4\sigma$ (from Ref. [2]).

Figure 2

The Hubble constant $H_0$ values with the 68% CL constraints derived by recent measurements. The value of the Hubble constant $H_0$ is derived by early-time approaches based on sound horizon, under the assumption of a $\mathrm{\Lambda }\mathrm{CDM}$ background. The shaded orange and purple bands show the tension between the values inferred from Cepheid calibrated SnIa and CMB observation (from Ref. [2]).

Figure 3

Fitting individual $R_W$ to Cepheid data as derived from our work (red points) and from Ref. [73] (blue points). For illustration purposes, the $D_L$ axis has been shifted slightly for our values so that the error bars do not overlap. The red and blue dotted lines correspond to $R_W=0.366$ and $R_W=0.369$, respectively. These $R_W$ values are taken using the derived individual parameters of anchor galaxies and M31 (due to its proximity) $R_{W,k}$.

Figure 4

The best fit $R_{W,bf}$ for various ${\mathrm{\Sigma }}_1$ and ${\mathrm{\Sigma }}_2$ datasets as a function of the critical dividing distance $D_c\in [0.01,37]\mathrm{Mpc}$ as derived using the individual $R_W$ (red points in Fig. 3). The dark red points correspond to the dataset with galaxies that have distance below $D_c$, whereas the red points regard galaxies with distances above $D_c$.

Figure 5

The $\sigma$ distances between the various ${\mathrm{\Sigma }}_1$ and ${\mathrm{\Sigma }}_2$ datasets as a function of the critical dividing distance $D_c$ as derived using the individual values of $R_W$. The red and blue lines correspond to the red (our results) and blue (the results in Ref. [73]) points of Fig. 4, respectively. A transition of the $\sigma$ distance at $D_c\simeq 22\mathrm{Mpc}$ is apparent.

Figure 6

Fitting individual $M_H^W$ to Cepheid data for global $R_W$ with a fixed value 0.386. Anchor galaxies are denoted with dark red points and SnIa host galaxies with green points. The dotted line corresponds to $M_H^W=-5.98\mathrm{mag}$ as derived using the individual values of anchor galaxies and M31 (due to its proximity) $M_{H,k}^W$.

Figure 7

The best fit $M_{H,bf}^W$ for various ${\mathrm{\Sigma }}_1$ and ${\mathrm{\Sigma }}_2$ datasets as a function of the critical distances $D_c$ as derived using the individual values of $M_H^W$ (points in Fig. 6). The dark green points correspond to the dataset with galaxies that have distance below $D_c$, whereas the green points regard galaxies with distances above $D_c$.

Figure 8

The green line represents the $\sigma$ distances between the various ${\mathrm{\Sigma }}_1$ and ${\mathrm{\Sigma }}_2$ datasets as a function of the critical distances $D_c$ as derived using the individual values of $M_H^W$. In contrast the yellow lines correspond to 68% (one standard deviation) range of the $\sigma$ distances as a function of the critical distances $D_c$ produced by a Monte Carlo simulation of 100 sample datasets assuming artificial homogeneity of the $M_H^W$ data. The simulations have been performed for randomly varying $M_H^W$ values with a Gaussian probability distribution with mean $M_H^W=-6\mathrm{mag}$ provided by the full $M_H^W$ datapoints and standard deviation equal to the corresponding $1\sigma$ error.

Figure 9

The $\sigma$ distances as a function of the critical distances $D_c$ for 100 sample datasets with random distance values, normally distributed inside their individual $1\sigma$ range as derived using the individual values of $M_H^W$. A transition of the $\sigma$ distance at $D_c\simeq 22\mathrm{Mpc}$ remains present for practically all of the Monte Carlo samples.

Figure 10

The green lines represent the 68% range of the $\sigma$ distances as a function of the critical distances $D_c$ produced by a Monte Carlo simulation of 100 sample datasets. The simulations have been performed for randomly varying galaxy distance values with a Gaussian probability distribution with mean equal to the measured distance and standard deviation equal to the corresponding $1\sigma$ error. In contrast, the pink region corresponds to a Monte Carlo simulation of 100 sample datasets assuming artificial homogeneity of the $M_H^W$ data. In addition to this homogeneity the simulations have been performed for randomly varying galaxy distance values with a Gaussian probability distribution.

Figure 11

Fitting individual $M_H^W$ to Cepheid data with a free global $R_W$. Anchor galaxies are denoted with cyan points and SnIa host galaxies with magenta points. The dotted line corresponds to $M_H^W=-5.90\mathrm{mag}$ as derived using the individual values of anchor galaxies and M31 (due to its proximity) $M_{H,k}^W$.

Figure 12

The one-dimensional relative probability density values of the color-luminosity parameter and the Cepheid absolute magnitude as derived using the DSS method for the cases I, II, and III. All measurements are shown as normalized Gaussian distributions. Notice that the best-fit values one for galaxies at distances $D<D_c$ and one for galaxies at $D>D_c$ are inconsistent with each other at a level larger than $3\sigma$.

Figure 13

The best-fit values of the parameter $R_W$ for base/base-SH0ES, I and IV models as derived using Cepheid data. Note that in terms of the AIC and BIC, fitting for two universal values of $R_W$ with global $M_H^W$ is the preferred model (case IV, green region).

Figure 14

The best-fit values of the parameter $M_H^W$ for base/base-SH0ES, III and V models as derived using the Cepheid data. Note that in terms of the AIC and BIC, fitting for two universal values of $M_H^W$ with global $R_W$ is the preferred model among the models shown (case V, cyan region).

Figure 15

The $\mathrm{\Delta }$AIC and $\mathrm{\Delta }$BIC of models with different free-parameter set compared to base (subindex 1) and base-SH0ES (subindex 2) models. Clearly, the case IV (two universal $R_W$ and a global $M_H^W$) is the best model and on the other hand, the case II (a global $R_W$ and individual $M_H^W$) is the worst one.

Figure 16

The one-dimensional relative probability density value of SnIa absolute magnitude $M_B$ for all cases studied in this paper compared to that obtained using CMB calibration. All measurements are shown as normalized Gaussian distributions. Clearly, for all cases where we do not consider the universality of parameters $R_W$ and $M_H^W$ (i.e., I, II, III, IV, V, VI) the $M_B$ is consistent with the CMB determination value.

Figure 17

The one-dimensional relative probability density value of $H_0$ as derived using Eq. (5.1) (solid lines) and Eq. (5.3) (dashed lines) for all cases studied in this paper compared to that from the Planck CMB measurement (gray line). All measurements are shown as normalized Gaussian distributions. It is evident that for all cases where we break the assumption of universality of the parameters $R_W$ and $M_H^W$ (i.e., I, II, III, IV, V, VI) the derived values of $H_0$ are consistent with the corresponding predicted Planck CMB best-fit value.