The Cosmic Microwave Background Spectrum and a Determination of Fractal Space Dimensionality

Abstract

The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3+\epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The available data for the cosmic microwave background radiation spectrum are fitted by a Planck's radiation distribution generalized to non integer space dimensionality. Our analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to 2.726 $\pm$ $0.003\times 10^{-2}$ K and $\epsilon =-(0.957\pm 0.006)\times 10^{-5}$. This value for $\epsilon$ is shown to be consistent with what is found on a very different spatial scale based on a quantum field phenomenon. The $|\epsilon |$ is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have experienced in a spatial and temporal scale compared to that of the decoupling era.

6 pages, 2 figures

Cited by in corpus (16)

• Fractal universe and quantum gravity
• Quantum field theory, gravity and cosmology in a fractal universe
• Geometry and field theory in multi-fractional spacetime
• Dimension and Dimensional Reduction in Quantum Gravity
• Multifractional theories: an unconventional review
• Multi-scale gravity and cosmology
• Quantum gravity and gravitational-wave astronomy
• Cosmic microwave background and inflation in multi-fractional spacetimes
• Note on the Existence of Hydrogen Atoms in Higher Dimensional Euclidean Spaces
• Introduction to multifractional spacetimes
• New Standard Model constraints on the scales and dimension of spacetime
• Multifractional spacetimes from the Standard Model to cosmology
• Monte Carlo Study on Distortion of the Space-Dimension in COBE Monopole Data
• Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\ge 4$?
• Zero-frequency magnetic fluctuations in homogeneous cosmic plasma revisited
• Response of a canonical ensemble of quantum oscillators to a random metric