A measurement of the scale of homogeneity in the early Universe

Abstract

We present the first measurement of the homogeneity index, ℋ, a fractal or Hausdorff dimension of the early Universe from the Planck CMB temperature variations δT in the sky. This characterization of the isotropy scale is model-free and purely geometrical, independent of the amplitude of δT. We find evidence of homogeneity (ℋ = 0) for scales larger than θℋ = 65.9 ± 9.2 deg on the CMB sky. This finding is at odds with the ΛCDM prediction, which assumes a scale invariant infinite universe. Such anomaly is consistent with the well known low quadrupule amplitude in the angular δT spectrum, but quantified in a direct and model independent way. We estimate the significance of our finding for ℋ = 0 using a principal component analysis from the sampling variations of the observed sky. This analysis is validated with theoretical prediction of the covariance matrix and simulations, booth base purely on data or in the ΛCDM prediction. Assuming translation invariance (and flat geometry) we can convert the isotropy scale θℋ into a (comoving) homogeneity scale which is very close to the trapped surface generated by the observed cosmological constant Λ.

How the Big Bang Ends Up Inside a Black Hole

“…The main differences with Inflation is the origin of those perturbations and the existence of a cutoff in the spectrum of fluctuations given by R(τ). As illustrated in Figure 6-7, such cutoff has recently been measured in the CMB maps [9,12]. Current and future galaxy surveys are also able to measure this signal [39,105] which could also appear as a dipole [106].…”

“…These are independent because only the former depends on the measured values of H 0 in each horizon. A recent study of the homogeneity index in the CMB [12] finds a cutoff scale Θ H = 66 ± 9 degrees. This is shown as the black symbol in Figure 7 for the mean values of Ω m = 0.3 and H 0 = 67 Km/s/Mpc in the full CMB sky.…”

“…Here, we present a brief review that summarizes several recent papers [7][8][9][10][11][12][13] that suggest a simpler explanation: the Black Hole Universe (BHU). This review also includes some new results and ideas.…”

“…Figure 7. Comparison of the causal horizon H i sizes shown in Figure6and θ H from the homogeneity index[12] in comoving χH 0 and angular units, given the mean measured Ω m and H 0 in each horizon. This is compared to the BHU predictions (2R/a, green), χ §[8] (dashed) and χ Λ = r S /a (red) as a function of Ω m .…”

The angular scale of homogeneity with SDSS-IV DR16 luminous red galaxies

“…Such a test was originally proposed by [52], and performed by [53][54][55][56] using observational data from the 2MASS photo-z catalogue, SDSS-III DR12 LRGs, SDSS blue galaxies, and Planck's CMB temperature anisotropy maps, respectively. The first works showed that the angular homogeneity scale measurements are in good agreement with the standard model expectations, albeit the concordance was weaker in [56]. In addition, our analysis probes higher redshift ranges than previous galaxy-based works, since the latest SDSS LRG dataset is composed of objects in the 0.6 < z < 1.0 interval.…”