Outline
Part I: Use CosmoMC to extract cosmological parameters from WMAP7 data
Part II: Inves%gate extra terms into the cl spectrum Run CosmoMC on cl only Create mock cl based on WMAP7 Introduce terms such as warp features into the cl, see how they change the likelihood
CosmoMC
Step 1: Download and compile CosmoMC Comes with its own version of CAMB Uses the WMAP7 Likelihood code
Step 2: set parameters: CosmoMC can vary Ωbh2, Ωdmh2, θ100, τ, Ωk, fν, w, ns, nt, nrun, ln(1010AS), r, ASZ
Derived parameters t0, zre, H0
Here I vary only Ωbh2, Ωdmh2, θ100, τ, ns, log10(1010AS), ASZ
Fit with no priors except flat age prior
CosmoMC: astro-‐ph/0205436; CAMB: Lewis et al. 2000
WMAP7 Likelihood Code
Step 3: Install WMAP7 likelihood code
Large due to complicated data set
10 possible contribu%ons to likelihood:
TTTT χ2
TTTT Low-‐l χ2
TTTT Low-‐l determinant TTTT beam correc%on
TETE χ2
TETE determinant
TE/EE/BB Low-‐l χ2
TE/EE/BB Low-‐l Determinant TBTB χ2
TBTB determinant
hdp://lambda.gsfc.nasa.gov/product/map/dr4/likelihood_get.cfm
Running CosmoMC
Each chain ran on 8 threads (CPUs), 4 chains total
1000 samples ≈ 9 minutes, 200,000 ≈ 28 hours
Analyzing the output
10
Use getdist to analyze and combine chains
The Gelman-‐Rubin diagnos%c (devia%on between chains) is OK (< 0.01)
Acceptance rate = 1 / mul%plicity = 32% 200,000 samples 2,000 samples
Covariance matrix
Original covariance matrix which comes with CosmoMC
Plomng the log of the absolute values
Note the small values good parameter choices
Covariance matrix
Covariance matrix derived in the run with 200,000 samples
Differences mainly in poorly constrained ASZ
This looks OK
Results – Comparison to official
Parameter This computa0on Official WMAP7 Devia0on (σ)
Ωbh2 0.02252 ± 0.57×10-‐3 0.02258 ± 0.57×10-‐3 0.10
Ωdmh2 0.1118 ± 0.55×10-‐2 0.1109 ± 0.56×10-‐2 0.16
100 θ 1.0392 ± 0.27×10-‐2 1.0388 ± 0.27×10-‐2 0.14
τ 0.0883 ± 0.015 0.088 ± 0.015 0.02
ns 0.9687 ± 0.014 0.963 ± 0.014 0.41
ln(1010AS) 3.0832 ± 0.035 3.190 +0.044 -‐0.046 (?) 2.32 (?)
ASZ 1.0017 ± 0.58 0.97 +0.68 -‐0.97 0.05
ΩΛ 0.7288 ± 0.029 0.734 ± 0.029 0.17
t0 (Gyr) 13.756 ± 0.13 13.75 ± 0.13 0.05
Ωm 0.2712 ± 0.029 0.266 ± 0.029 0.18
zre 10.588 ± 1.21 10.5 ± 1.2 0.07
H0 70.581 ± 2.57 71.0 ± 2.5 0.17
hdp://lambda.gsfc.nasa.gov/product/map/dr4/params/lcdm_sz_lens_wmap7.cfm
Outline of Part II
Generate mock realiza%ons of cl based on a WMAP7 cosmology, and WMAP7-‐like noise
Run CosmoMC on WMAP7 cl only (ignoring the actual sky map, pixel likelihood etc.)
Run CosmoMC on the mock cl, recover the same cosmology as with the real cl data
Insert other terms into the underlying cosmology (e.g. warp features), check whether they give systema%cally beder likelihood
Cosmology from cl only
10 likelihood terms for WMAP7, some nega%ve
Hacked CosmoMC to only use “Master TTTT”
Get much beder results when adding correc%on terms (beam correc%on etc.)
Finding the correct best fit cl
Komatsu et al. 2009, Table 1 hdp://lambda.gsfc.nasa.gov/product/map/dr4/params/lcdm_sz_lens_wmap7.cfm
WMAP7 best fit cl (logarithmic)
Dominated by cosmic variance at low l, and beam noise at high l
Note the low quadrupole in WMAP
Mock cl
Extract noise Nl from likelihood code data file, since WMAP7 data files contain very strange noise quan%%es
Try to generate mock cl using: