Cosmology Parameter Estimation from CMB Data for...
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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 Bayes’ Theorem: P(h, Ω m Ι data) = P(data Ι h, Ω m ) P(h, Ω m )/P(data) Likelihood: P(data Ι h, Ω m ) Marginalization: P=probability, h=Hubble parameter, Ω m = 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 H 0 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. ([email protected]) 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 ( Ω m ) Degeneracy Marginalize out the Hubble Parameter, h ! a 2 + k = 8πG 3 ρa 2 a Ω k = − k H 0 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: Ω k = –0.052 (+0.049, –0.055) This analysis: Ω k = –0.0014±0.0002 Inflation Model of Early Universe: Ω k = 0 P(Ω m data) = P( data h, Ω m ∫ )dh 0.2 0.4 0.6 0.8 1.0 0.5 0.6 0.7 0.8 0.9 1.0 Ωm h Planck Collaboration: ω m = h 2 Ω m = 0.143±0.01 This analysis: ω m = 0.166
Transcript of 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. ([email protected])
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
