# Plots Made for the RoPP Review Article on Dark Energy

This page contains original plots made for our Reports on Progress in Physics review paper on dark energy.

D. Huterer and D.L. Shafer, "Dark energy two decades after: Observables, probes, consistency tests" (PDF ), Rep. Prog. Phys., 2017

## Hubble diagram with current (binned) SNIa and BAO data:

[Caption:] Evidence for the transition from deceleration in the past to acceleration today. The blue line indicates a model that fits the data well; it features acceleration at relatively late epochs in the history of the universe, beginning a few billion years ago but still billions of years after the big bang. For comparison, we also show a range of matter-only models in green, corresponding to $0.3 \leq \Omega_m \leq 1.5$ and thus spanning the open, flat, and closed geometries without dark energy. Finally, the red curve indicates a model that \emph{always} exhibits acceleration and that also does not fit the data. The black data points are binned distance moduli from the Supercal compilation \cite{Supercal} of 870~SNe, while the three red data points represent the distances inferred from the most recent BAO measurements (BOSS DR12 \cite{Alam:2016hwk}).

## Energy densities vs. redshift:

[Caption:] Energy density of species in the universe as a function of $(1 + z)$, where $z$ is the redshift. The dashed vertical line indicates the present time ($z = 0$), with the past to the left and future to the right. Note that matter ($\propto (1 + z)^3$) and radiation ($\propto (1 + z)^4$) energy densities scale much faster with the expanding universe than the dark energy density, which is exactly constant for a cosmological constant $\Lambda$. The shaded region for dark energy indicates the energy densities allowed at 1$\sigma$ (68.3\% confidence) by combined constraints from current data assuming the equation of state is allowed to vary as $w(z) = w_0 + w_a \, z/(1 +z)$.

## $\Omega_M$-$w$ plane, current constraints:

[Caption:] Constraints on cosmological parameters from our analysis of current data from three principal probes: SN Ia (JLA \cite{Betoule:2014frx}; blue), BAO (BOSS DR12 \cite{Alam:2016hwk}; green), and CMB (\textit{Planck} 2015 \cite{Ade:2015xua}; red). We show constraints on $\Omega_m$ and constant $w$. The contours contain 68.3\%, 95.4\%, and 99.7\% of the likelihood, and we assume a flat universe.

## $\Omega_M$-$w$ plane, historical constraints (1999-2009-2015):

[Caption:] History of constraints on key dark energy parameters $\Omega_m$ and a constant equation of state $w$, assuming a flat universe such that $\Omega_\text{de} = 1 - \Omega_m$. The three sets of contours show the status of measurements around the time of dark energy discovery (circa 1998; green), roughly a decade later following precise measurements of CMB anisotropies and the detection of the BAO feature (circa 2008; red), and in the present day, nearly two decades after discovery (circa 2016; blue).

## $w_0$-$w_a$ plane, current constraints:

[Caption:] Constraints on cosmological parameters from our analysis of current data from three principal probes: SN Ia (JLA \cite{Betoule:2014frx}; blue), BAO (BOSS DR12 \cite{Alam:2016hwk}; green), and CMB (Planck 2015 \cite{Ade:2015xua}; red). We show constraints on $w_0$ and $w_a$ in the parametrization from Eq. (17), marginalized over $\Omega_m$. The contours contain 68.3\%, 95.4\%, and 99.7\% of the likelihood, and we assume a flat universe.

## Illustration of the quantities in the $(w_0, w_a)$ parametrization:

[Caption:] Illustration of the main features of the popular parametrization of the equation of state \cite{Linder_wa,Chevallier_Polarski} given by $w(z) = w_0 + w_a \, z/(1 + z)$. We indicate the pivot redshift $z_p$, the corresponding value of the equation of state $w_p$, the intercept $w_0$, the slope (proportional to $w_a$), and a visual interpretation of the approximate uncertainties in $w_0$ and $w_p$.

## Effect of DE on cosmological observables:

[Caption:] Dependence of key cosmological observables on dark energy. The top left and right panels show, respectively, the comoving distance and growth suppression (relative to the matter-only case). The bottom left and right panels show, respectively, the CMB angular power spectrum $\mathcal{C}_\ell$ as a function of multipole $\ell$ and the matter power spectrum $P(k)$ as a function of wavenumber $k$. For each observable, we indicate the prediction for a fiducial $\Lambda$CDM model ($\Omega_m = 0.3$, $w = -1$) and then illustrate the effect of varying the indicated parameter. In each case, we assume a flat universe and hold the combination $\Omega_m h^2$ fixed.

## Current constraints in the $f$-$\sigma_8$ plane:

[Caption:] Constraints on the quantity $f\sigma_8$ at different redshifts from RSD and peculiar velocity surveys. At the lowest redshifts $z \approx 0$, peculiar velocities from galaxies and SNe Ia (leftmost \cite{Johnson:2014kaa} and rightmost \cite{Huterer:2016uyq} red points) and SNe Ia alone (purple data point; \cite{Turnbull:2011ty}) constrain the velocity power spectrum and effectively the quantity $f\sigma_8$. At higher redshifts, constraints on $f\sigma_8$ come from the RSD analyses from 6dFGS (maroon at $z = 0.067$; \cite{Beutler:2012px}), GAMA (pink points; \cite{Blake:2013nif}), WiggleZ (dark green; \cite{Blake:2011rj}), BOSS (dark blue; \cite{Beutler:2016arn}), and VIPERS (orange; \cite{delaTorre:2013rpa}). The solid line shows the prediction corresponding to the currently favored flat $\Lambda$CDM cosmology.

## Cluster counts:

[Caption:] Predicted cluster counts for a survey covering 5,000~deg$^2$ that is sensitive to halos more massive than $10^{14} \, h^{-1} M_\odot$, shown for a fiducial $\Lambda$CDM model as well as three variations as in Figure ( "Effect of DE on observables" above ).