Angular Correlation of the CMB in the R_h=ct Universe

The emergence of several unexpected large-scale features in the cosmic microwave background (CMB) has pointed to possible new physics driving the origin of density fluctuations in the early Universe and their evolution into the large-scale structure we see today. In this paper, we focus our attention on the possible absence of angular correlation in the CMB anisotropies at angles larger than ~60 degrees, and consider whether this feature may be the signature of fluctuations expected in the R_h=ct Universe. We calculate the CMB angular correlation function for a fluctuation spectrum expected from growth in a Universe whose dynamics is constrained by the equation-of-state p=-rho/3, where p and rho are the total pressure and density, respectively. We find that, though the disparity between the predictions of LCDM and the WMAP sky may be due to cosmic variance, it may also be due to an absence of inflation. The classic horizon problem does not exist in the R_h=ct Universe, so a period of exponential growth was not necessary in this cosmology in order to account for the general uniformity of the CMB (save for the aforementioned tiny fluctuations of 1 part in 100,000 in the WMAP relic signal. We show that the R_h=ct Universe without inflation can account for the apparent absence in CMB angular correlation at angles > 60 degrees without invoking cosmic variance, providing additional motivation for pursuing this cosmology as a viable description of nature.

💡 Research Summary

The paper investigates the puzzling lack of large‑scale angular correlation in the Cosmic Microwave Background (CMB) temperature anisotropies, specifically the near‑zero two‑point correlation for angles larger than about 60 degrees, and asks whether this feature can be naturally explained within the R h = c t cosmology. The authors begin by reviewing the observational situation: high‑signal‑to‑noise full‑sky maps from WMAP and Planck reveal several anomalies on the largest angular scales, most notably a very low correlation at θ ≳ 60°. In the standard ΛCDM framework these anomalies are usually attributed to cosmic variance, but they also raise questions because the inflationary paradigm predicts a non‑vanishing correlation at all angles.

The R h = c t model is introduced as an alternative that does not require an inflationary epoch. Its defining feature is the zero active mass condition, ρ + 3p = 0, which forces the total equation of state to be p = ‑ρ/3. This, in turn, yields a linear expansion factor a(t) ∝ t and a Hubble radius R h = c/H that is always equal to ct. Because the horizon grows at the speed of light at all times, the classic horizon problem disappears, and the Universe can become homogeneous without a period of exponential expansion.

To connect theory with observations, the authors adopt the standard formalism for the CMB angular correlation function C(cos θ), expanding the temperature field in spherical harmonics and defining the multipole power Cℓ. They note that a full calculation of Cℓ involves a complex chain of transfer functions that encode acoustic oscillations, the Sachs‑Wolfe effect, Silk damping, reionization, lensing, and secondary anisotropies. Rather than performing a detailed numerical Boltzmann‑code integration, they focus on the large‑scale (low‑ℓ) regime where the primary Sachs‑Wolfe contribution dominates.

In the R h = c t context the primordial power spectrum is assumed to be cut off at a physical wavelength equal to the gravitational horizon at recombination, λ_max ≈ R h(t_rec). Modes with wavelengths larger than this cannot grow, so the power spectrum is strongly suppressed for k ≲ k_cut, which translates into a suppression of the lowest multipoles (ℓ ≲ 5). Consequently the theoretical C(θ) falls to nearly zero for angles larger than ~60°, reproducing the observed lack of correlation without invoking cosmic variance. The authors compare this prediction with the WMAP/Planck data and find that the R h = c t curve matches the observed dip and the location of the minimum (θ_min) much better than the ΛCDM curve, which predicts excess power at low ℓ.

Beyond the CMB, the paper points out that the R h = c t model yields simple analytic expressions for the luminosity distance, d_L = R h(1+z) ln(1+z), and the Hubble parameter, H(z) = H₀(1+z). These relations have been shown in other works to fit cosmic‑chronometer data, gamma‑ray burst Hubble diagrams, and other distance‑redshift probes at least as well as ΛCDM, reinforcing the model’s overall viability.

In the concluding section the authors argue that (1) the absence of large‑angle CMB correlation is a natural consequence of the horizon‑size cutoff inherent in R h = c t, (2) inflation is unnecessary to achieve the observed CMB uniformity, and (3) the agreement with current data provides a compelling motivation to pursue R h = c t as a serious alternative to ΛCDM. They acknowledge, however, that a full treatment of the small‑scale (high‑ℓ) spectrum, non‑linear growth, and detailed transfer‑function calculations remains to be done. Future work will require high‑resolution numerical simulations and more precise measurements (e.g., from upcoming CMB polarization experiments) to test whether the R h = c t predictions hold across the entire multipole range.