The $H_0$ tension in light of vacuum dynamics in the Universe

TL;DR

The paper addresses the $H_0$ tension by evaluating dynamical vacuum models (DVMs), including the Running Vacuum Model (RVM) where $ρ_Λ(H)$ partially tracks the expansion rate. By allowing a small vacuum dynamics parameter $ν$ and, in extended cases, a near-vacuum EoS $w=-1+ε$, the authors show improved global fits to $SNIa+BAO+H(z)+LSS+CMB$, with a tendency toward Planck-scale $H_0$ and reduced $σ_8(0)$, strongly contrasting with rigid $Λ$CDM. Structure-formation data (LSS) prove crucial in distinguishing DVMs from ΛCDM and in constraining the dynamics, as ΛCDM struggles to accommodate both Planck and Riess measurements simultaneously. The analysis favors vacuum dynamics as a viable path to reconciling observations, though the DES results and potential systematics in $H_0$ measurements remain important considerations for future work. Note: The text includes a Note Added comparing DES Y1 results with Zhao et al. findings on dynamical DE, highlighting ongoing debates about the presence and strength of vacuum dynamics.

Abstract

Despite the outstanding achievements of modern cosmology, the classical dispute on the precise value of $H_0$, which is the first ever parameter of modern cosmology and one of the prime parameters in the field, still goes on and on after over half a century of measurements. Recently the dispute came to the spotlight with renewed strength owing to the significant tension (at $>3σ$ c.l.) between the latest Planck determination obtained from the CMB anisotropies and the local (distance ladder) measurement from the Hubble Space Telescope (HST), based on Cepheids. In this work, we investigate the impact of the running vacuum model (RVM) and related models on such a controversy. For the RVM, the vacuum energy density $ρ_Λ$ carries a mild dependence on the cosmic expansion rate, i.e. $ρ_Λ(H)$, which allows to ameliorate the fit quality to the overall $SNIa+BAO+H(z)+LSS+CMB$ cosmological observations as compared to the concordance $Λ$CDM model. By letting the RVM to deviate from the vacuum option, the equation of state $w=-1$ continues to be favored by the overall fit. Vacuum dynamics also predicts the following: i) the CMB range of values for $H_0$ is more favored than the local ones, and ii) smaller values for $σ_8(0)$. As a result, a better account for the LSS structure formation data is achieved as compared to the $Λ$CDM, which is based on a rigid (i.e. non-dynamical) $Λ$ term.

Figures (5)

• Figure 1: Left: The LSS structure formation data ($f(z)\sigma_8(z)$) versus the predicted curves by Models I, II and III, see equations (\ref{['eq:QforModelRVM']})-(\ref{['eq:QforModelQL']}) for the case $w=-1$, i.e. the dynamical vacuum models (DVMs), using the best-fit values in Table 1. The XCDM curve is also shown. The values of $\sigma_8(0)$ that we obtain for the models are also indicated. Right: Zoomed window of the plot on the left, which allows to better distinguish the various models.
• Figure 2: The LSS structure formation data ($f(z)\sigma_8(z)$) and the theoretical predictions for models (\ref{['eq:QforModelRVM']})-(\ref{['eq:QforModelQL']}), using the best-fit values in Tables 2 and 3. The curves for the cases Ia, IIIa correspond to special scenarios for Models I and III where the agreement with the Riess et al. local value $H_0^{\rm Riess}$RiessH02016 is better (cf. Table 3). The price, however, is that the concordance with the LSS data is now spoiled. Case IIIb is our theoretical prediction for the scenario proposed in Melchiorri2017b, aimed at optimally relaxing the tension with $H_0^{\rm Riess}$. Unfortunately, the last three scenarios lead to phantom-like DE and are in serious disagreement with the LSS data.
• Figure 3: Contour plots for the RVM (blue) and $w$RVM (orange) up to $2\sigma$, and for the $\Lambda$CDM (black) up to $5\sigma$ in the $(H_0,\Omega_{m}^0)$-plane. Shown are the two relevant cases under study: the plot on the left is for when the local $H_0$ value of Riess et al.RiessH02016 is included in the fit (cf. Table 2), and the plot on the right is for when that local value is not included (cf. Table 1). Any attempt at reaching the $H_0^{\rm Riess}$ neighborhood enforces to pick too small values $\Omega_{m}^0<0.27$ through extended contours that go beyond $5\sigma$ c.l. We also observe that the two ($w$)RVMs are much more compatible (already at $1\sigma$) with the $H_0^{\rm Planck}$ range than the $\Lambda$CDM. The latter, instead, requires some of the most external contours to reach the $H^{\rm Planck}_0$$1\sigma$ region whether $H_0^{\rm Riess}$ is included or not in the fit. Thus, remarkably, in both cases when the full data string SNIa+BAO+$H(z)$+LSS+CMB enters the fit the $\Lambda$CDM has difficulties to overlap also with the $H_0^{\rm Planck}$ range at $1\sigma$, in contrast to the RVM and $w$RVM.
• Figure 4: Contour lines for the $\Lambda$CDM (black) and RVM (blue) up to $4\sigma$ in the $(H_0,\sigma_8(0))$-plane. As in Fig. 3, we present in the left plot the case when the local $H_0$ value of Riess et al.RiessH02016 is included in the fit (cf. Table 2), whereas in the right plot the case when that local value is not included (cf. Table 1). Again, any attempt at reaching the $H_0^{\rm Riess}$ neighborhood enforces to extend the contours beyond the $5\sigma$ c.l., which would lead to a too low value of $\Omega_m^{0}$ in both cases (cf. Fig. 3) and, in addition, would result in a too large value of $\sigma_8(0)$ for the RVM. Notice that $H_0$ and $\sigma_8(0)$ are positively correlated in the RVM (i.e. $H_0$ decreases when $\sigma_8(0)$ decreases), whilst they are anticorrelated in the $\Lambda$CDM ($H_0$ increases when $\sigma_8(0)$ decreases, and vice versa). It is precisely this opposite correlation feature with respect to the $\Lambda$CDM what allows the RVM to improve the LSS fit in the region where both $H_0$ and $\sigma_8(0)$ are smaller than the respective $\Lambda$CDM values (cf. Fig. 1). This explains why the Planck range for $H_0$ is clearly preferred by the RVM, as it allows a much better description of the LSS data.
• Figure 5: Contour lines for the models $w$RVM (Ia) and $w$Q$_\Lambda$ (IIIa) up to $3\sigma$ in the $(H_0,\sigma_8(0))$-plane, depicted in orange and purple, respectively, together with the isolated point (in black) extracted from the analysis of Ref. Melchiorri2017b, which we call IIIb. The cases Ia, IIIa and IIIb correspond to special scenarios with $w\neq -1$ for Models I and III in which the value $H_0^{\rm Riess}$ is included as a data point and then a suitable strategy is followed to optimize the fit agreement with such value. The strategy consists to exploit the freedom in $w$ and remove the LSS data from the fit analysis. The plot clearly shows that some agreement is indeed possible, but only if $w$ takes on values in the phantom region ($w<-1$) (see text) and at the expense of an anomalous (too large) value of the parameter $\sigma_8(0)$, what seriously spoils the concordance with the LSS data, as can be seen in Fig. 2.