Monte Carlo study on distortion of the space-dimension in COBE monopole data

A concise explanation of studies on distortion of space-time dimension is briefly introduced. Second we obtain the limits (i.e., bounded values) of the dimensionless chemical potential μ, the Sunyaev–Zeldovich (SZ) effect y and distortion of the space-dimension ε by Monte Carlo (MC) analysis of the parameter set (T, d=3+ε, μ, and y) in cosmic microwave data assuming that the SZ effect is positive (y>0). In this analysis, the magnitude of the space-dimension d with distortion of the space-dimension ε is defined by d=3+ε. The limits of μ and y are determined as |μ|<9×10^?5 (2σ) (μ=(?3.9±2.6)×10^?5 (σ)), |y|<5×10^?6 (2σ) (y=(2.0±1.4)×10^?6 (σ)), while the distortion of the space-dimension is |ε|<6×10^?5 (2σ) (ε=(?0.78±2.50)×10^?5 (σ)). The magnitudes of these three estimated limits are ordered as . The estimated limit of |y|<5×10^?6 appears to be related to re-ionization processes occurring at redshift z _ri ～10. We also present data analysis assuming a relativistic SZ effect.