The variance of the CMB temperature gradient: a new signature of a multiply connected Universe (2106.13205v2)

Abstract: In this work we investigate the standard deviation of the Cosmic Microwave Background (CMB) temperature gradient field as a signature for a multiply connected nature of the Universe. CMB simulations of a spatially infinite universe model within the paradigm of the standard cosmological model present non-zero two-point correlations at any angular scale. This is in contradiction with the extreme suppression of correlations at scales above $60^{\circ}$ in the observed CMB maps. Universe models with spatially multiply connected topology contain typically a discrete spectrum of the Laplacian with a specific wave-length cut-off and thus lead to a suppression of the correlations at large angular scales, as observed in the CMB (in general there can be also an additional continuous spectrum). Among the simplest examples are 3-dimensional tori which possess only a discrete spectrum. To date, the universe models with non-trivial topology such as the toroidal space are the only models that possess a two-point correlation function showing a similar behaviour as the one derived from the observed Planck CMB maps. In this work it is shown that the normalized standard deviation of the CMB temperature gradient field does hierarchically detect the change in size of the cubic 3-torus, if the volume of the Universe is smaller than $\simeq 2.5 \cdot 10^3$ Gpc$^3$. It is also shown that the variance of the temperature gradient of the Planck maps is consistent with the median value of simulations within the standard cosmological model. All flat tori are globally homogeneous, but are globally anisotropic. However, this study also presents a test showing a level of homogeneity and isotropy of all the CMB map ensembles for the different torus sizes considered that are nearly at the same weak level of anisotropy revealed by the CMB in the standard cosmological model.

• The paper introduces a novel analysis of the CMB temperature gradient’s standard deviation to signal a multiply connected universe topology.
• Numerical simulations reveal that toroidal models exhibit suppressed correlations and distinct Laplacian spectra consistent with Planck observations.
• The study estimates viable 3-torus dimensions at approximately 3 to 3.5 times the Hubble length, complementing traditional correlation methods.

Overview of "The variance of the CMB temperature gradient: A new signature of a multiply connected Universe"

The paper investigates the Cosmic Microwave Background (CMB) anisotropies as potential indicators of a multiply connected universe topology. Specifically, it introduces the analysis of the CMB temperature gradient's standard deviation as a novel diagnostic for identifying a universe with multiply connected spatial sections, contrasting it with the standard, simply connected cosmological model predictions.

Context and Background

The nature of the universe's topology remains an open question in cosmology. While local physics and geometry have been well-explained by General Relativity, large-scale topology is ambiguous. Observational data, particularly from the CMB, provide crucial information about possible geometric constraints. The discrepancy in two-point correlation functions in CMB observations from standard $\Lambda$CDM models suggests potential topological implications.

Main Contributions

1. Novel Analysis of Temperature Gradients: The authors propose using the standard deviation of the CMB temperature gradient as a method to detect multiply connected topologies. This approach supplements existing geometric and correlation-based studies.
2. Simulation and Numerical Results: CMB simulations demonstrate how different topological models, notably the cubic 3-torus, maintain a discrete Laplacian spectrum, inherently leading to suppressed correlations at scales above 60 degrees. This matches better with observed Planck and WMAP CMB data than infinite space models.
3. Hierarchical Dependence of Topology: The research illustrates a hierarchical ordering of CMB map features from toroidal models of varying dimensions, further contrasting these with standard cosmic models. Smaller toroidal dimensions exhibit more distinctive temperature gradient characteristics.
4. Application to Current Observational Data: By analyzing Planck data, the paper finds concordance with toroidal universes of finite volumes, estimating the side length of viable $3-$tori around 3.0 to 3.5 times the Hubble length based on temperature gradient statistics.
5. Advantages Over Traditional Methods: Traditional methods such as CMB two-point correlation functions are complemented by this approach, offering an independent cross-validation of cosmic topology hypotheses without making direct assumptions on power spectrum homogenization.

Implications and Future Directions

The paper's findings contribute practical implications for understanding cosmic topology through accessible statistical tools applied to CMB data. If substantiated by further analysis and observational data, these methodologies could refine cosmological models to consider finite, multiply connected universes. Future research might explore polarizations and other observables, enhancing the robustness of topology detection.

Moreover, the work suggests an expansion of this methodology toward identifying other complex topologies, offering a promising path for subsequent simulations and observational verification. Integrating AI methodologies could potentially enhance pattern recognition and simulation efficiencies, advancing this domain significantly.

In conclusion, the paper provides a significant stride in leveraging CMB observations for inferring universal topology, contributing both a novel methodological framework and corroborative evidence for addressing one of modern cosmology's fundamental questions.