These three tensions---each rooted in different cosmic epochs and observational domains---collectively suggest that standard cosmology might be missing an organizing principle or deeper structure that connects large-scale topology, local expansion histories, and early structure emergence.
This work introduces a novel framework integrating fractal-layered topological cosmology, where inhomogeneous, anisotropic expansion and quantum-topological initial conditions naturally produce:
Layer-dependent Hubble gradients,
Anisotropic large-angle CMB correlations,
Accelerated early structure formation without resorting to inflation.
In what follows, we present the geometric and field-theoretic basis for this approach, and demonstrate its capacity for observational falsifiability through simulations and current/future survey data.
References
[1] A. G. Riess et al., Astrophys. J., 876, 85 (2019).
[2] Planck Collaboration, Astron. Astrophys., 641, A6 (2020).
[3] L. Verde, T. Treu, and A. G. Riess, Nature Astronomy, 3, 891--895 (2019).
[4] V. Poulin et al., Phys. Rev. D, 98, 083525 (2018).
[5] K. Kenworthy et al., Astrophys. J., 875, 145 (2019).
[6] C. Clarkson et al., Rep. Prog. Phys., 74, 112901 (2011).
[7] G. Efstathiou, Mon. Not. R. Astron. Soc., 346, L26 (2003).
[8] M. Hansen et al., Astrophys. J., 704, 1448 (2009).
[9] C. Copi et al., Mon. Not. R. Astron. Soc., 367, 79 (2006).
[10] A. Gruppuso et al., JCAP, 07, 040 (2016).
[11] J.-P. Luminet et al., Nature, 425, 593--595 (2003).
[12] L. Contaldi et al., JCAP, 07, 002 (2003).
[13] A. Pontzen and A. Challinor, Class. Quant. Grav., 25, 045013 (2008).
[14] R. J. Bouwens et al., Nature, 616, 266 (2023).
[15] L. A. Boylan-Kolchin, Nat. Astron., 7, 497--503 (2023).
[16] D. J. Eisenstein et al., Astrophys. J., 633, 560 (2005).
[17] F. Sun and A. Loeb, Astrophys. J. Lett., 945, L12 (2023).
[18] P. Mocz et al., Phys. Rev. D, 103, 043508 (2021).
B. Limitations of CDM and Inflationary Cosmology
The CDM (Lambda Cold Dark Matter) model, underpinned by a spatially flat Friedmann--Lematre--Robertson--Walker (FLRW) geometry and a nearly scale-invariant primordial power spectrum seeded by cosmic inflation, has achieved remarkable empirical success. It accurately describes the evolution of cosmic microwave background (CMB) anisotropies, the distribution of large-scale structure, and late-time cosmic acceleration. However, mounting tensions across observational and theoretical domains have revealed inherent limitations in both the CDM framework and the inflationary paradigm it is often paired with.
1. Limitations of CDM
