Vacuum dynamics in the Universe versus a rigid $Λ=$const

TL;DR

The paper investigates whether the cosmological constant $\Lambda$ is truly fundamental or mildly dynamical by testing running vacuum models (RVM) in which $\rho_D(H)=\frac{3}{8\pi G}(C_0+\nu H^2)+{\cal O}(H^4)$. Using a comprehensive data set—SNIa, BAO, $H(z)$, LSS, and CMB—the authors demonstrate that the RVM yields a substantially better fit than the standard $\Lambda$CDM (with $\Lambda$ constant), with the best-fit parameter $\nu$ at the level of $\sim\mathcal{O}(10^{-3})$ and strong model-selection evidence via AIC/BIC ($$\Delta\mathrm{AIC},\Delta\mathrm{BIC}>10$$ for the main variants). They further explore the impact on the $H_0$ tension, finding that dynamical vacuum models can reconcile Planck-like $H_0$ values with LSS data while the rigid $\Lambda$CDM struggles when the local Riess measurement is included. Overall, the work provides statistically robust support for mildly dynamical vacuum energy and highlights the potential implications for both fundamental physics and cosmological inferences of $H_0$ and structure growth.

Abstract

In this year, in which we celebrate 100 years of the cosmological term, $Λ$, in Einstein's gravitational field equations, we are still facing the crucial question whether $Λ$ is truly a fundamental constant or a mildly evolving dynamical variable. After many theoretical attempts to understand the meaning of $Λ$, and in view of the enhanced accuracy of the cosmological observations, it seems now mandatory that this issue should be first settled empirically before further theoretical speculations on its ultimate nature. In this work, we summarize the situation of some of these studies. Devoted analyses made recently show that the $Λ=$const. hypothesis, despite being the simplest, may well not be the most favored one. The overall fit to the cosmological observables $SNIa+BAO+H(z)+LSS+CMB$ singles out the class RVM of the "running" vacuum models, in which $Λ=Λ(H)$ is an affine power-law function of the Hubble rate. It turns out that the performance of the RVM as compared to the "concordance" $Λ$CDM model (with $Λ=$const.) is much better. The evidence in support of the RVM may reach $\sim 4σ$ c.l., and is bolstered with Akaike and Bayesian criteria providing strong evidence in favor of the RVM option. We also address the implications of this framework on the tension between the CMB and local measurements of the current Hubble parameter.

Figures (4)

• Figure 1: Likelihood contours in the $(\Omega_m,\nu_i)$-plane for the three DVMs I, II and III (we are restricting here to the vacuum case $w=-1$ in all cases) defined in \ref{['eq:QforModelRVM']}-\ref{['eq:QforModelQL']}. Shown are the regions corresponding to $-2\ln\mathcal{L}/\mathcal{L}_{max}=2.30$, $6.18, 11.81$, $19.33$, $27.65$ (corresponding to 1$\sigma$, 2$\sigma$, 3$\sigma$, 4$\sigma$ and 5$\sigma$ c.l.) after marginalizing over the rest of the fitting parameters indicated in Table 1. The elliptical shapes have been obtained applying the standard Fisher approach. We estimate that for the RVM, $94.80\%$ (resp. $89.16\%$) of the 4$\sigma$ (resp. 5$\sigma$) area is in the $\nu>0$ region. The $\Lambda$CDM ($\nu_i=0$) appears disfavored at $\sim 4\sigma$ c.l. in the RVM and $Q_{dm}$, and at $\sim 2.5\sigma$ c.l. for $Q_\Lambda$. For more details, see PRD2017.
• Figure 2: The large scale structure (LSS) formation data ($f(z)\sigma_8(z)$) and the theoretical predictions for models I, II and III in the case $w\neq- 1$ (i.e. the $w$DVMs). The computed values of $\sigma_8(0)$ for each model are also indicated. The curves for the cases Ia, IIIa and IIIb correspond to special scenarios for Models I and III, in which only the BAO and CMB data are used (not the LSS). Despite the agreement of the CMB measurement $H_0^{\rm Planck}$ with the Riess et al. local value $H_0^{\rm Riess}$ can be better for these special scenarios, the price to enforce such "agreement" is that the concordance with the LSS data is now spoiled (the curves for Ia and IIIa are higher). Case IIIb is our theoretical calculation of the impact on the LSS data for the scenario proposed in Melchiorri2017b, aimed at optimally relaxing the tension with $H_0^{\rm Riess}$. Unfortunately it is in severe disagreement with the LSS data. The last three scenarios lead to phantom-like DE and are all disfavored (at different degrees) by the LSS data PLB2017.
• Figure 3: Contour plots in the $(H_0,\Omega_{m})$-plane for the RVM (blue) and $w$RVM (orange) up to $2\sigma$, together with those for the $\Lambda$CDM (black) up to $5\sigma$, corresponding to the situation when the local $H_0$ value of Riess et al. RiessH02016 is included as a data point in the fit (cf. Table 2) PLB2017.
• Figure 4: Contour lines for the $\Lambda$CDM (black) and RVM (blue) up to $4\sigma$ in the $(H_0,\sigma_8(0))$-plane. 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). See PLB2017 for more details.