(i) Fine-Tuning and the Cosmological Constant Problem
CDM treats dark energy as a cosmological constant \Lambda, leading to the so-called "vacuum catastrophe": the theoretical prediction for vacuum energy density from quantum field theory overshoots the observed value by 120 orders of magnitude. This profound fine-tuning issue has persisted without a convincing resolution, suggesting that the model may be incomplete at a fundamental level.
(ii) Inability to Accommodate Observed Cosmic Inhomogeneities
While CDM assumes large-scale homogeneity and isotropy, recent observations (e.g., bulk flows, dipole anisotropies beyond the CMB, and large voids) imply potential departures from these assumptions. The model lacks intrinsic mechanisms to describe regional variations in the expansion rate or curvature, unless these are introduced ad hoc via Lematre--Tolman--Bondi (LTB) spacetimes or perturbative corrections.
(iii) Model Rigidity and Parameter Degeneracy
CDM relies on six tightly constrained parameters, which while predictive, also render the model inflexible to accommodate anomalies without invoking additional dark components, modified gravity, or non-standard neutrino physics. This rigidity can obscure the emergence of deeper organizing principles potentially encoded in spacetime structure or topology.
2. Limitations of the Inflationary Paradigm
(i) Initial Singularity and Pre-Inflation Ambiguity
Inflation does not eliminate the initial singularity problem; rather, it is built upon the assumption that inflation can begin in a highly homogeneous patch with specific quantum vacuum conditions. There remains no universally accepted mechanism for the onset of inflation, nor a consensus on what preceded it. Moreover, the trans-Planckian problem questions the validity of treating quantum fluctuations in modes originating below the Planck scale.
(ii) Lack of Predictive Uniqueness
Inflationary cosmology admits a vast "multiverse" of possible outcomes depending on the inflaton potential, leading to a landscape of models with widely varying predictions. This flexibility undermines the falsifiability of inflation as a whole. For example, single-field slow-roll inflation can accommodate a broad range of spectral indices and tensor-to-scalar ratios depending on the assumed potential.
