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. You are welcome to download and use these plots in your talks and papers;
in that case please cite:
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}).
[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 $w(z) = w_0
+ w_a \, z/(1 +z)$.
[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.
[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).
[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 $w_p$.
[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.
[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.
[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 ).