cosmology parameter estimation from cmb data for...

Abstract Cosmology has become, over the last several years, a precise

science due to Cosmic Microwave Background (CMB) data from the WMAP and Planck missions. Extracting early universe physics from that data has, however, been largely left to experts, but that need not be the case. For example, determining whether the universe is flat, or has positive or negative curvature is possible by using Planck CMB data in conjunction with theoretical curves generated by NASA's CAMB Web Interface tool. Also, the matter parameter can be approximated by fitting the peaks of the CMB power spectrum to theoretical approximations taken from previous literature.

Acknowledgements The National Science Foundation, PAARE/ POCA (AST-0750814)

Matter Fraction

q  Bayes’ Theorem: P(h, Ωm Ι data) = P(data Ι h, Ωm) P(h, Ωm)/P(data) q  Likelihood: P(data Ι h, Ωm)

q  Marginalization: P=probability, h=Hubble parameter, Ωm = dark matter fraction

Curvature of the Universe

Relative size of the universe is measured by the scale factor, , that satisfies the Friedman equation that allows a definition of the curvature parameter

where H0 is the Hubble constant, ρ = matter-energy density, and k = +1 (positive curvature), –1 (negative curvature), or 0 (flat).

Cosmology Parameter Estimation from CMB Data for Undergrads Daniel M. Smith, Jr. (dsmith@scsu.edu)

Department of Biological & Physical Sciences, South Carolina State University, Orangeburg, SC 29117

Theoretical CMB Curves from CAMB

Chi Squared Calculation

Hubble Parameter (h)-Matter Fraction (Ωm) Degeneracy

Marginalize out the Hubble Parameter, h

!a2 + k = 8πG

3ρa2

a

Ωk = − kH0

2

Cosmic Microwave Background Data from Planck

-0.0025 -0.0020 -0.0015 -0.0010 -0.0005

2755

2760

2765

2770

OmegaK

ChiSq

Planck Collaboration: Ωk = –0.052 (+0.049, –0.055) This analysis: Ωk = –0.0014±0.0002 Inflation Model of Early Universe: Ωk = 0

P(Ωm data) = P(data h,Ωm∫ )dh

0.2 0.4 0.6 0.8 1.00.5

0.6

0.7

0.8

0.9

1.0

Ωm

h

Planck Collaboration: ωm= h2Ωm = 0.143±0.01 This analysis: ωm = 0.166