The Topology and Size of the Universe from CMB Temperature and Polarization Data
Grigor Aslanyan, Aneesh V. Manohar, Amit P. S. Yadav

TL;DR
This paper investigates the size and shape of the universe using WMAP data, setting lower bounds on possible topologies, and explores how polarization data can improve these constraints, with implications for future Planck observations.
Contribution
It introduces a new formalism for including polarization data in topology analysis and demonstrates its potential to tighten bounds on the universe's size.
Findings
Lower bounds on topology sizes are established at 1.5L_0, 1.4L_0, and 1.1L_0 for different models.
Inclusion of polarization data offers limited improvement with WMAP but promises significant gains with Planck.
Likelihood functions are non-Gaussian, necessitating simulations for accurate bounds.
Abstract
We analyze seven year and nine year WMAP temperature maps for signatures of three finite flat topologies M_0=T^3, M_1=T^2 x R^1, and M_2=S^1 x R^2. We use Monte-Carlo simulations with the Feldman-Cousins method to obtain confidence intervals for the size of the topologies considered. We analyze the V, W, and Q frequency bands along with the ILC map and find no significant difference in the results. The 95.5% confidence level lower bound on the size of the topology is 1.5L_0 for M_0, 1.4L_0 for M_1, and 1.1L_0 for M_2, where L_0 is the radius of the last scattering surface. Our results agree very well with the recently released results from the Planck temperature data. We show that the likelihood function is not Gaussian in the size, and therefore simulations are important for obtaining accurate bounds on the size. We then introduce the formalism for including polarization data in the…
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