Spin-Torsion Cosmology: A Visual Guide to the Research Program

The leftmost branch traces the theoretical foundations of the program. At its core is Einstein-Cartan-Holst (ECH) gravity, a minimal extension of general relativity that incorporates spacetime torsion as a dynamical variable. The framework has roots in loop quantum gravity (LQG), where the Barbero-Immirzi parameter \(\gamma\) controls the quantum geometry of spin networks.

The key physical mechanism is torsion-regulated bounces: the four-fermion contact interaction generated by torsion produces a repulsive contribution to the Friedmann equations at Planck-scale densities. This replaces the classical Big Bang singularity with a smooth bounce at a critical density of approximately \(\rho_{\rm crit} \approx 0.27\,\rho_{\rm Pl}\). The bounce density is not a free parameter—it is fixed by the spin-torsion coupling strength and the Standard Model fermion content.

Branching from the theoretical framework are the program's original ambitions: an effective cosmological constant from residual torsion effects (now closed by the 14 barriers), and the surviving predictions for birefringence and non-Gaussianity that emerged from the ECH structure independently of the dark energy program.

The barriers branch of the mind map catalogs the six most consequential structural obstructions. These are not merely difficulties or fine-tuning problems—they are proven impossibility results within the minimal model space.

The validation branch shows the program's empirical infrastructure. The Cobaya MCMC pipeline is the central tool, running against Planck CMB power spectra, BAO distance measurements, and Type Ia supernovae luminosity distances. Key specifications:

The final branch of the mind map shows the program's concrete deliverables—the artifacts that survive the research and are available for community use:

• LaTeX source: The complete manuscript source for the framework paper (Paper 1), maintained in the arxiv/ directory with full bibliography and figure source files.
• Technical Dossier: The complete research record, including all 24 branch investigations, 7 foundational studies, and intermediate calculations. Available in the research/ directory.
• Data Comparison Pipeline: The Cobaya MCMC configuration files, chain outputs, and analysis scripts in the reproducibility/ directory. Fully reproducible from raw Planck/BAO/SN likelihoods.
• Interactive Companion Website: This website (bigbounce.hubify.app), featuring the paper, interactive data visualizations, articles, and the visual guides on this page.

The left panel visualizes the barrier landscape—the web of impossibility results that closed the dark energy derivation program. The dominant theme is the tension between mass protection and geometric content: the ECH framework can produce light scalar fields (needed for dark energy) or geometrically distinctive couplings (needed for testability), but never both simultaneously.

The barriers are organized by severity:

• The Mass-Coupling Lock sits at the center as the most fundamental obstruction. It is not a fine-tuning problem but a structural consequence of the PGT Lagrangian: the torsion mass and coupling constant are algebraically locked, with no free parameter to adjust.
• The \(10^{17}\) detector gap quantifies the scale separation problem. The torsion effects are Planck-scale (\(\sim 10^{19}\) GeV), while the dark energy scale is \(\sim 10^{-33}\) eV—a gap of roughly \(10^{52}\) orders of magnitude in energy, or equivalently a fine-tuning of 1 part in \(10^{120}\) when translated to the vacuum energy. Even the less extreme version—propagating torsion masses versus collider energies—requires bridging a gap of at least \(10^{17}\) GeV.
• The summary statement at the barrier panel's base: "All minimal routes to DE are closed." This is not a claim of impossibility for all torsion-gravity models—only for the minimal (ECH/PGT) framework with standard matter content and no additional fields beyond what the torsion decomposition naturally provides.

The central panel uses the visual metaphor of barriers being broken through—not by overcoming the impossibility results (they stand), but by pivoting to the predictions that survive around the barriers. The dark energy program is closed, but the ECH framework still speaks through two channels that are orthogonal to the barrier obstructions:

• The ALP birefringence channel (Branch R) survives because the Nieh-Yan ALP's mass protection comes from the shift symmetry, and while this erases the geometric coupling to gravity (Barrier #2), it preserves the coupling to photons through the Chern-Simons term. The Topological-Shift Duality closes the gravitational channel but leaves the electromagnetic channel open.
• The matter-bounce non-Gaussianity channel (Branch V) survives because it depends only on the bounce dynamics and the symmetry of the contracting phase, not on any dark energy mechanism. The barriers close the late-time cosmology routes but leave the early-universe bounce phenomenology intact.

The right panel presents the two surviving predictions with their observational status:

The bottom panel of the infographic provides a concise feature comparison table summarizing the program's outcomes across its three original science targets: