Extra dimensions in the early universe

We investigate the possible occurrence of extra spatial dimensions (D=3+ϵ) in the early universe. A detailed calculation is presented which shows that the crucial signal is the apparent inequality of the cosmological Z-term between matching Lyman alpha (Lyα) and Lyman beta (Lyβ) spectral lines, both emission and absorption, when using the present epoch (laboratory) wavelengths. We present preliminary upper limits to the value of epsilon, to be improved by direct, more careful analysis of the spectra. We take catalogued quasar Lyα forest data and perform Studentʹs t-test to determine whether we should reject the null hypothesis (no fractal dimensions). Finally, a χ2 analysis is done for fitting ϵ in the early universe. The statistical tests and experimental data are all consistent with ϵ=0 for Z≤3.3, but the experimental data support non-zero ϵ values for Z≥4. However, it should be emphasized that the non-zero values of epsilon found for Z≥4 may be due to undiscovered systematic errors in the original data.