In response to the mounting observational discrepancies with the standard CDM paradigm, a number of alternative cosmological models have been developed. These approaches typically seek to relax certain assumptions of homogeneity, initial singularity, or geometric simplicity, and aim to explain both local and global anomalies. Here, we briefly review four major categories of such proposals.
1. Inhomogeneous Cosmologies: Lematre--Tolman--Bondi (LTB) Models
The Lematre--Tolman--Bondi (LTB) family of solutions generalizes the FLRW metric by allowing radial inhomogeneity while preserving spherical symmetry. These models have been proposed as explanations for:
Apparent acceleration without invoking dark energy,
Local variations in expansion rate,
The Hubble tension, via a giant local void or underdensity.
In particular, gigaparsec-scale voids have been posited in which Earth resides near the center. This yields an effective Hubble flow gradient, reconciling CMB-inferred H0H_0 with local supernova data. However, LTB models face several critical challenges:
They require a high degree of fine-tuning (e.g., Earth must be within ~10 Mpc of the void center to avoid large CMB dipoles),
They conflict with isotropy constraints from CMB and BAO measurements,
Structure formation simulations in LTB backgrounds often fail to reproduce galaxy distributions.
Nonetheless, LTB cosmologies opened a crucial door: questioning the necessity of global homogeneity in our large-scale universe.
2. Void-Centered Models and Gigaparsec-Scale Underdensities
Extending the idea of inhomogeneity, several models posit the existence of giant cosmic voids, such as the KBC void or WSM supervoid, to explain low-redshift cosmological anomalies. These underdensities have been used to:
Lower the effective matter density and reduce lensing effects,
Explain low CMB lensing amplitude or ISW anomalies,
Provide a foreground explanation for the CMB Cold Spot.
While such void models do not require a complete departure from CDM, they imply that our cosmic neighborhood is atypical, casting doubt on the Copernican principle. Moreover, high-precision surveys (e.g., DES, Euclid) have not yet confirmed the existence of voids with the required scale and depth to fully resolve the Hubble tension.
These efforts underscore the possibility that nontrivial topology or multiscale structure may underlie observed anisotropies---an idea we pursue more formally via fractal and multilayered geometries.
3. Cyclic, Bouncing, and Emergent Cosmologies
An entirely different class of models challenges the initial singularity of the Big Bang by postulating:
