1. Introduction
1.1 The Rise and Limitations of the CDM Model
The CDM (Lambda Cold Dark Matter) model has long served as the cornerstone of modern cosmology, providing a remarkably successful framework to describe the large-scale evolution of the universe. Built upon Einstein's General Relativity (GR) and assuming a homogeneous and isotropic universe, CDM incorporates cold dark matter as the dominant matter component and a cosmological constant () representing dark energy. The model accurately reproduces the angular power spectrum of the Cosmic Microwave Background (CMB), the large-scale distribution of galaxies, and baryon acoustic oscillation (BAO) measurements.
However, as observational precision has increased, particularly with missions such as Planck, WMAP, and Gaia, cracks have begun to emerge in the CDM framework. These cracks take the form of persistent tensions between predictions and measurements, and growing evidence of anisotropies that challenge the assumption of isotropy on cosmic scales.
1.2 Overview of Hubble and Curvature Tensions
One of the most pressing challenges to CDM is the Hubble tension---the significant and statistically robust discrepancy between the value of the Hubble constant H0H_0 inferred from early universe measurements (such as CMB data from Planck, yielding H067.4H_0 \approx 67.4 km/s/Mpc) and that obtained from late-time observations, such as Cepheid-calibrated Type Ia supernovae by the SH0ES team (yielding H073.2H_0 \approx 73.2 km/s/Mpc). This ~5 tension has resisted resolution even with extended models involving extra relativistic species, evolving dark energy, or early dark energy scenarios.
Simultaneously, a curvature tension has emerged. While CDM assumes a spatially flat universe, some analyses of combined datasets (CMB, BAO, Supernovae Ia) suggest a mild preference for positive curvature, which conflicts with the nearly flat universe implied by standard inflationary scenarios and the minimal CDM best-fit model. In particular, the Planck team's extended analyses suggest a closed universe at ~2 confidence, prompting reconsideration of the flat-space assumption in cosmology.
These tensions suggest that either unknown systematics exist in observations, or the foundational assumptions of the cosmological model---such as perfect isotropy, homogeneity, and the nature of gravity---require reevaluation.
1.3 Role of Anisotropy and Cosmic Rotation
Another class of challenges to CDM arises from large-scale anomalies in the CMB and the large-scale structure of the universe, which hint at departures from statistical isotropy. Examples include the alignment of low-l multipoles (the so-called "Axis of Evil"), hemispherical power asymmetry, dipole-quadrupole alignment, and cold spots, all of which suggest the presence of preferred directions in the cosmos.
While these anomalies are often dismissed as statistical flukes, their persistence across datasets and analysis pipelines suggests a deeper origin. A compelling explanation for such directional anomalies involves the possibility that the universe possesses a small but non-zero global rotation, which would manifest as vorticity in the spacetime metric.
