Planck 2013 results. XVI. Cosmological parameters | Astronomy & Astrophysics (A&A)

Planck 2013 results

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Table 1

Cosmological parameters used in our analysis.

Notes. For each, we give the symbol, prior range, value taken in the base ΛCDM cosmology (where appropriate), and summary definition (see text for details). The top block contains parameters with uniform priors that are varied in the MCMC chains. The ranges of these priors are listed in square brackets. The lower blocks define various derived parameters.

^(a)

For dynamical dark energy models with constant equation of state, we denote the equation of state by w and adopt the same prior as for w₀.

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Parameter	Prior range	Baseline	Definition

ω_b ≡ Ω_bh² ........	[0.005,0.1]	...	Baryon density today
ω_c ≡ Ω_ch² ........	[0.001,0.99]	...	Cold dark matter density today
100θ_MC ........	[0.5,10.0]	...	100 × approximation to r_∗/D_A (CosmoMC)
τ ........	[0.01,0.8]	...	Thomson scattering optical depth due to reionization
Ω_K ........	[− 0.3,0.3]	0	Curvature parameter today with Ω_tot = 1 − Ω_K
∑ m_ν ........	[0,5]	0.06	The sum of neutrino masses in eV
........	[0,3]	0	Effective mass of sterile neutrino in eV
w₀ ........	[−3.0, −0.3]	−1	Dark energy equation of state^a, w(a) = w₀ + (1 − a)w_a
w_a ........	[− 2,2]	0	As above (perturbations modelled using PPF)
N_eff ........	[0.05,10.0]	3.046	Effective number of neutrino-like relativistic degrees of freedom (see text)
Y_P ........	[0.1,0.5]	BBN	Fraction of baryonic mass in helium
A_L ........	[0,10]	1	Amplitude of the lensing power relative to the physical value
n_s ........	[0.9,1.1]	...	Scalar spectrum power-law index (k₀ = 0.05 Mpc^-1)
n_t ........	n_t = − r_0.05/ 8	Inflation	Tensor spectrum power-law index (k₀ = 0.05 Mpc^-1)
dn_s/ dlnk ........	[−1,1]	0	Running of the spectral index
ln(10¹⁰A_s) ........	[2.7,4.0]	...	Log power of the primordial curvature perturbations (k₀ = 0.05 Mpc^-1)
r_0.05 ........	[0,2]	0	Ratio of tensor primordial power to curvature power at k₀ = 0.05 Mpc^-1

Ω_Λ ........		...	Dark energy density divided by the critical density today
t₀ ........		...	Age of the Universe today (in Gyr)
Ω_m ........		...	Matter density (inc. massive neutrinos) today divided by the critical density
σ₈ ........		...	RMS matter fluctuations today in linear theory
z_re ........		...	Redshift at which Universe is half reionized
H₀ ........	[20,100]	...	Current expansion rate in km s^-1Mpc^-1
r_0.002 ........		0	Ratio of tensor primordial power to curvature power at k₀ = 0.002 Mpc^-1
10⁹A_s ........		...	10⁹ × dimensionless curvature power spectrum at k₀ = 0.05 Mpc^-1
ω_m ≡ Ω_mh² ........		...	Total matter density today (inc. massive neutrinos)

z_∗ ........		...	Redshift for which the optical depth equals unity (see text)
r_∗ = r_s(z_∗) ........		...	Comoving size of the sound horizon at z = z_∗
100θ_∗ ........		...	100 × angular size of sound horizon at z = z_∗ (r_∗/D_A)
z_drag ........		...	Redshift at which baryon-drag optical depth equals unity (see text)
r_drag = r_s(z_drag) ........		...	Comoving size of the sound horizon at z = z_drag
k_D ........		...	Characteristic damping comoving wavenumber (Mpc^-1)
100θ_D ........		...	100 × angular extent of photon diffusion at last scattering (see text)
z_eq ........		...	Redshift of matter-radiation equality (massless neutrinos)
100θ_eq ........		...	100 × angular size of the comoving horizon at matter-radiation equality
r_drag/D_V(0.57) ........		...	BAO distance ratio at z = 0.57 (see Sect. 5.2)