Testing Low-Redshift Cosmic Acceleration with Large-Scale Structure

We examine the cosmological implications of measurements of the void-galaxy cross-correlation at redshift $z=0.57$ combined with baryon acoustic oscillation (BAO) data at $0.1<z<2.4$. We find direct evidence of the late-time acceleration due to dark energy at $>10\sigma$ significance from these data alone, independent of the cosmic microwave background (CMB) and supernovae. Using a nucleosynthesis prior on ${\mathrm{\Omega }}_b{h}^2$, we measure the Hubble constant to be $H_0=72.3\pm 1.9\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ from $\mathrm{BAO}+\mathrm{voids}$ at $z<2$, and $H_0=69.0\pm 1.2\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$ when adding Lyman-$\alpha$ BAO at $z=2.34$, both independent of the CMB. Adding voids to CMB, BAO, and supernova data greatly improves measurement of the dark energy equation of state, increasing the figure of merit by $>40\%$, but remaining consistent with flat $\mathrm{\Lambda }$ cold dark matter.

Figure 1

(Left) Measurement of the Alcock-Paczynski parameter $F_{\mathrm{AP}}=D_{M}H/c$ and growth rate $f{\sigma }_8$ from the BOSS CMASS sample (68% and 95% contours) [8, 38, 40]. Planck constraints are extrapolations from CMB fits assuming $\mathrm{\Lambda }\mathrm{CDM}$. (Right) Correlation coefficients for the constituent BAO, FS, and void measurements in this sample, estimated from mocks [8].

Figure 2

(Left) Distance scale $D(z)/r_d$ and (right) Hubble rate $H(z)r_d$ measurements from different surveys, relative to their values in the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model from Planck. (Left) solid error bars (BOSS and eBOSS $\mathrm{Ly}\alpha$) denote $D_M/r_d$. Points with dashed error bars (6dFGS, MGS, and eBOSS quasars) measure only $D_V/r_d$. The orange open circles are the consensus $\mathrm{BAO}+\mathrm{FS}$ results from BOSS DR12 galaxies only. The red filled circles are from the same data, but rebinned and including void information at $z=0.57$. Uncertainties are correlated for points in common between both panels. Shaded regions show Planck uncertainties.

Figure 3

Marginalized 68.3% and 95.2% contours for ${\mathrm{\Omega }}_m$ and $H_0$ in $\mathrm{\Lambda }\mathrm{CDM}$ from Planck, and from BAO and voids combined with a BBN prior on ${\mathrm{\Omega }}_b{h}^2$, independent of the CMB. “Gal. BAO” refers to all BAO measurements at $z<2$, favoring high $H_0$. “All BAO” includes the $\mathrm{Ly}\alpha$ result at $z=2.34$, which pulls the final value down to $H_0=69.0\pm 1.2\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. Gray bands show local distance ladder result of Ref. [1].

Figure 4

Marginalized constraints on ${\mathrm{\Omega }}_m$ and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}$ obtained from BOSS voids, Pantheon SNe, BAO, and Planck CMB, assuming $w=-1$. The line indicates spatially flat models. $\mathrm{BAO}+\mathrm{voids}$ give ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=0.600\pm 0.058$, a $>10\sigma$ detection of acceleration.

Figure 5

Constraints on the DE EOS parameters $w_0=w(z=0)$ and $w_a$ in nonspatially flat models. The void $F_{\mathrm{AP}}$ measurement leads to a 43% increase in the figure of merit over the best combination of other data.