A test of the nature of cosmic acceleration using galaxy redshift distortions

TL;DR

This paper probes the nature of cosmic acceleration by measuring the growth rate of structure at $z ≈ 0.8$ from redshift-space distortions in a large VVDS survey. It analyzes the anisotropy of the redshift-space two-point correlation function $ξ(r_p,π)$ and fits a convolution-based model to obtain the linear distortion parameter $β = 0.70 ± 0.26$ and pairwise velocity dispersion $σ_{12}$. With an external estimate of the linear bias $b_L = 1.3 ± 0.1$ from CMB-normalized $σ_8$, they derive the growth rate $f(z=0.77) = β b_L = 0.91 ± 0.36$, consistent with a flat cosmological-constant model but not yet able to distinguish among alternative acceleration scenarios. The results demonstrate that redshift-space distortions are a viable, high-redshift probe of gravity and dark energy, and they project that future larger surveys could achieve significantly tighter constraints, enabling discrimination among competing models.

Abstract

Observations of distant supernovae indicate that the Universe is now in a phase of accelerated expansion the physical cause of which is a mystery. Formally, this requires the inclusion of a term acting as a negative pressure in the equations of cosmic expansion, accounting for about 75 per cent of the total energy density in the Universe. The simplest option for this "dark energy" corresponds to a cosmological constant, perhaps related to the quantum vacuum energy. Physically viable alternatives invoke either the presence of a scalar field with an evolving equation of state, or extensions of general relativity involving higher-order curvature terms or extra dimensions. Although they produce similar expansion rates, different models predict measurable differences in the growth rate of large-scale structure with cosmic time. A fingerprint of this growth is provided by coherent galaxy motions, which introduce a radial anisotropy in the clustering pattern reconstructed by galaxy redshift surveys. Here we report a measurement of this effect at a redshift of 0.8. Using a new survey of more than 10,000 faint galaxies, we measure the anisotropy parameter b = 0.70 +/- 0.26, which corresponds to a growth rate of structure at that time of f = 0.91 +/- 0.36. This is consistent with the standard cosmological-constant model with low matter density and flat geometry, although the error bars are still too large to distinguish among alternative origins for the accelerated expansion. This could be achieved with a further factor-of-ten increase in the sampled volume at similar redshift.

Figures (2)

• Figure 1: Estimate of the degree of distortion induced by coherent motions on the measured large-scale distribution of galaxies at high redshift. For a given mean density of matter, this depends on the amount of dark energy and is quantified by the level
• Figure 2: Estimates of the growth rate of cosmic structure compared to predictions from various theoretical models. Values of$f=\beta b_{\mathrm{L}}$ are plotted as a function of the inverse of the cosmic expansion factor $1+z=a(\mathrm{t})^{-1}$. Our new measurement at $z=0.77$ from the VVDS-Wide survey (red circle) is shown together with that from the 2dFGRS, computed from the published ${ }^{21}$ value of $\beta$; to do this, we adopted the bias value $b_{\mathrm{L}}=1.0 \pm 0.1$ estimated from higher-order clustering in the same survey ${ }^{20}$. We have also used very recent measurements from the 2 dF -SDSS LRG and QSO (2SLAQ) survey of luminous red galaxies ${ }^{27}$ (blue open square) to add one further point at $\mathrm{z}=0.55$. In this case, however, the values of $\beta$ and $b_{\mathrm{L}}$ are not fully independent, because they have been obtained by imposing simultaneous consistency with the clustering measured at $z=0$. In practice, this forces the resulting $f$ towards the flat $\Lambda$ model, that is, $\sim \Omega_{\mathrm{m}}{ }^{0.55}$. A more appropriate treatment would require an independent estimate of the bias for this sample ${ }^{23}$; this uncertainty is accounted for by the error bars, which in all cases correspond to $68 \%$ confidence intervals. The solid red line gives the growth rate for the standard cosmological-constant flat ( $\Omega_{\mathrm{m} 0}=0.25, \Omega_{\Lambda^{0}}=0.75$ ) model, while the dashed red line is the corresponding open model with the same matter density but no cosmological constant; the blue and green dashed curves describe models in which dark energy is coupled to dark matter ${ }^{5}$; the black dot-dashed line is the DGP braneworld model, an extra-dimensional