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Relaxing the $σ_8$-tension through running vacuum in the Universe

Adria Gomez-Valent, Joan Sola

TL;DR

The paper tackles the persistent $σ_8$ tension in the ΛCDM framework by advocating running vacuum models (RVMs) in which the vacuum energy density evolves with the Hubble rate, $ρ_Λ(H)=\frac{3}{8πG}(c_0+νH^2)$, with a small parameter $ν$. A vacuum–matter interaction $Q=νH(3ρ_m+4ρ_r)$ modifies both background expansion and linear perturbations, leading to a dominant transfer-function correction $Δ_T(x(ν))\approx -ν[7+6\ln(Ω_m/Ω_r)]$ that substantially lowers the predicted $σ_8$. Combined data from SNIa, BAO, $H(z)$, LSS, and CMB yield $σ_8$ values ~$0.731±0.018$ for the RVM versus ~$0.798±0.009$ for ΛCDM, with an improvement in fit statistics (AIC/BIC) and compatibility with weak-lensing $S_8$ constraints (e.g., $S_8=0.742±0.035$ from KiDS-450+2dFLenS). This provides a natural, economical resolution to the $σ_8$ tension and supports dynamical vacuum as a viable component of cosmic acceleration, aligning with LSS and weak-lensing observations and motivating further observational tests.

Abstract

It has recently been shown that the class of running vacuum models (RVMs) has the capacity to fit the overall cosmological observations better than the concordance $Λ$CDM model, therefore supporting the possibility of dynamical dark energy (DE). Apart from the cosmic microwave background (CMB) anisotropies, the most crucial datasets involved are: i) baryonic acoustic oscillations (BAO), and ii) direct large scale structure (LSS) formation data. Analyses mainly focusing on CMB and with insufficient BAO+LSS input generally fail to capture the dynamical DE signature, whereas the few existing studies accounting for the wealth of known CMB+BAO+LSS data (see in particular Solà, Gómez-Valent \& de Cruz Pérez 2015, 2017; and Zhao et al. 2017) do converge to the remarkable conclusion that dynamical DE might well be encoded in the current cosmological observations at a $3-4σ$ c.l. A decisive factor is the persistent $σ_8$-tension between the $Λ$CDM and the data. Because the issue is obviously pressing, we devote this work to explain how and why running vacuum in the expanding universe successfully relaxes the existing $σ_8$-tension and describes the LSS formation data significantly better than the $Λ$CDM.

Relaxing the $σ_8$-tension through running vacuum in the Universe

TL;DR

The paper tackles the persistent tension in the ΛCDM framework by advocating running vacuum models (RVMs) in which the vacuum energy density evolves with the Hubble rate, , with a small parameter . A vacuum–matter interaction modifies both background expansion and linear perturbations, leading to a dominant transfer-function correction that substantially lowers the predicted . Combined data from SNIa, BAO, , LSS, and CMB yield values ~ for the RVM versus ~ for ΛCDM, with an improvement in fit statistics (AIC/BIC) and compatibility with weak-lensing constraints (e.g., from KiDS-450+2dFLenS). This provides a natural, economical resolution to the tension and supports dynamical vacuum as a viable component of cosmic acceleration, aligning with LSS and weak-lensing observations and motivating further observational tests.

Abstract

It has recently been shown that the class of running vacuum models (RVMs) has the capacity to fit the overall cosmological observations better than the concordance CDM model, therefore supporting the possibility of dynamical dark energy (DE). Apart from the cosmic microwave background (CMB) anisotropies, the most crucial datasets involved are: i) baryonic acoustic oscillations (BAO), and ii) direct large scale structure (LSS) formation data. Analyses mainly focusing on CMB and with insufficient BAO+LSS input generally fail to capture the dynamical DE signature, whereas the few existing studies accounting for the wealth of known CMB+BAO+LSS data (see in particular Solà, Gómez-Valent \& de Cruz Pérez 2015, 2017; and Zhao et al. 2017) do converge to the remarkable conclusion that dynamical DE might well be encoded in the current cosmological observations at a c.l. A decisive factor is the persistent -tension between the CDM and the data. Because the issue is obviously pressing, we devote this work to explain how and why running vacuum in the expanding universe successfully relaxes the existing -tension and describes the LSS formation data significantly better than the CDM.

Paper Structure

This paper contains 6 sections, 13 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Running vacuum in interaction with matter
  3. The role of the LSS data
  4. Extracting the dynamical DE signal
  5. A natural solution to the $\sigma_8$-tension
  6. Conclusions

Figures (4)

  • Figure 1: Left: The $f(z)\sigma_8(z)$ data points and the theoretical curves for $\Lambda$CDM, XCDM and RVM. The values of $\sigma_8$ that we obtain for these models are quoted in the figure; Right: The relative difference in the theoretical curves for the RVM and XCDM with respect to $\Lambda$CDM, $\Delta_{f\sigma_8}(z)$ (in $\%$). In the RVM case it is computed from Eq. \ref{['eq:Dfs8']}, and similarly for the XCDM.
  • Figure 2: Left: Relative difference (in $\%$) between the transfer function \ref{['eq:BBKS']} of the RVM (parameters as in Table 1) and of the $\Lambda$CDM (with $\nu=0$ but the other parameters as before) as a function of $k$, i.e. $\Delta_T(k)= (T_{\rm RVM}(k)-T_\Lambda(k))/T_{\Lambda}(k)$; Right: Behavior of the function in the integrand of Eq. \ref{['eq:s88general']}. The range of wave numbers $k$ at which such function is significant for generating the relative differences induced by $\nu$ on $T(k)$ is marked off with red vertical dashed lines in both plots.
  • Figure 3: Upper-left: Weighted growth rate obtained by (i) setting all the parameters to the RVM ones (cf. Table 1); and (ii) keeping the same setting, except $\nu=0$. These correspond to the red and black lines, respectively; Upper-right: Relative difference $\Delta_{f\sigma_8}(z)$ (in $\%$) between the curves of the upper-left plot, see Eq. (\ref{['eq:Dfs8']}). The change induced by the nonvanishing vacuum parameter $\nu$ reaches about $- 6.3\%$ at $z\sim 0$; Lower-left: Relative difference (in $\%$) between the density contrasts $\delta_m(z)$ associated to the two scenarios explored in the upper-left plot. The differences in this case are positive and lower than $0.4\%$ for $z<1$; Lower-right: As before, but for the growth function $f(z)$. Around the present time, $\Delta_{f}(0)\simeq-0.8\%$.
  • Figure 4: Likelihood contours at $1\sigma$, $2\sigma$, $3\sigma$ and $4\sigma$ confidence level in the ($\Omega_m,\sigma_8)$ plane for the $\Lambda$CDM, the XCDM, the original quintessence model with inverse-power potential PR88 and the RVM, together with the recent observational constraint provided by KiDS-450 and 2dFLenS collaborations Joudaki2017, as extracted from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering, $S_8=0.742\pm 0.035$ (purple curves). Shown is the allowed $1\sigma$ band for $S_8$. Dynamical DE is clearly favored, specially the RVM.