There are plenty more possible solutions Hyperspace HET (hyperspherical geometry with emergent radial time), for various apparent anomalies. I promised to list them without AI support.
However, I cannot improve on the wording that AI offers, so I list its statements here:
Horizon (Causality) Problem (previously addressed but probably expressed more clearly, so included)
What we call the “horizon problem” is the question of why widely separated patches of the cosmic microwave background (CMB) have almost exactly the same temperature, even though in standard flat-space+linear-time they could never have been in causal contact. On a 3-sphere, any two points are always connected by geodesics that wrap around the sphere’s surface, and when you fold in radial time, there’s ample “overlap” in the past so that thermal equilibrium can be established without needing inflationary super-expansion.
However, I cannot improve on the wording that AI offers, so I list its statements here:
Horizon (Causality) Problem (previously addressed but probably expressed more clearly, so included)
What we call the “horizon problem” is the question of why widely separated patches of the cosmic microwave background (CMB) have almost exactly the same temperature, even though in standard flat-space+linear-time they could never have been in causal contact. On a 3-sphere, any two points are always connected by geodesics that wrap around the sphere’s surface, and when you fold in radial time, there’s ample “overlap” in the past so that thermal equilibrium can be established without needing inflationary super-expansion.
- CMB Large-Scale Anomalies Some low-ℓ multipoles in the CMB (like the quadrupole and octopole) show unexpected alignments—sometimes called the “axis of evil.” In hyperspherical space, the stereographic projection onto our local tangent plane naturally introduces slight anisotropies at large angular separations (θ → 90°), which could map directly onto these odd-ball alignments without invoking exotic primordial physics.
- The Lithium Problem Big-bang nucleosynthesis predicts about three times more primordial ⁷Li than we see in old halo stars. In a radial-time model, different hyperspherical “shells” cool at subtly different rates. Some pockets freeze out with lower ⁷Li abundance simply because their local expansion history (i.e. local radial time) differs from the global average—no new particle physics needed.
- Hubble Tension (previously addressed The mismatch between the early-universe (CMB-inferred) and local (Cepheid/SN-Ia) measurements of H₀ can arise if the projection from the hypersphere’s curved surface onto our flat tangent distorts redshift–distance relations differently at low z versus high z. What looks like two different expansion rates is really a geometric artifact of how radial time “fans out” over the sphere.
- Cosmic Acceleration (Dark Energy) Instead of a mysterious repulsive fluid, the apparent late-time acceleration can be reinterpreted as the geometry of a positively curved hypersphere whose radial expansion rate naturally slows less rapidly than in flat space. When you project that onto a linear timeline, it masquerades as a late-time “dark energy” component.
- Galaxy Rotation Curves & the Missing-Mass Problem. Flat rotation curves are usually ascribed to halos of unseen dark matter. But if each orbiting star is actually moving on a great-circle trajectory in 3-sphere space, its projection onto our tangent plane will exhibit extra apparent centripetal support—mimicking a halo without invoking exotic particles.
- Pioneer Anomaly (Spacecraft Deceleration) The small, unexplained sunward acceleration observed in the trajectories of Pioneer 10/11 can be derived from the hypersphere’s slight positive curvature. Radial geodesics bending back toward the centre project as a tiny anomalous deceleration in our flat-time framework.
- Large-Scale Structure Fractality The transition from a clumpy, fractal distribution of matter on tens of Mpc scales to large-scale homogeneity at hundreds of Mpc can be pictured as the change in projection distortion as you move from small to large θ on the hypersphere—small-angle patches look clumpy, while 80–90° patches “stretch out” and smear into homogeneity.
- Baryon Asymmetry & Primordial Magnetic Fields If matter creation corresponds to the fission of “overspinning” domains in the hypersphere’s 4D core (as in some world-universe models), that mechanism can naturally seed both an excess of baryons over antibaryons and coherent, large-scale magnetic fields—no need for beyond-Standard-Model CP violation or inflation-driven magnetogenesis.
- Age-of-the-Universe Paradoxes Certain globular clusters and high-z quasars appear “older” than the age calculated from a flat-ΛCDM fit. In emergent radial time, those objects simply lie further out in radius—so their “local time” is naturally greater without breaking causality or requiring negative ages.