A speculative cosmological hypothesis: our observable universe as a drifting sector inside a tractrix-shaped negatively curved background

This is a speculative hypothesis, not a claim of established physics.

I am trying to formulate a cosmological idea in a way that remains compatible with current observations while exploring whether our observable universe could be embedded in a larger, currently invisible structure.

Core idea:

The observable universe may be a locally flat, expanding, spherical-looking spacetime sector that emerged near the equatorial transition region of a larger tractrix-shaped pseudospherical background structure and has since been drifting along a trajectory toward the axis or a central gravitational sink of that larger invisible background.

In this model, ΛCDM remains the local approximation. The hypothesis does not try to replace the standard model. Instead, it asks whether ΛCDM might describe the inside view of a larger geometrical and dynamical system.

Basic flow:

𝓦 → equatorial spacetime nucleation → 𝓞 → internal expansion → growing CMB information shell → drift through 𝓑 → 𝓢

1. Core idea

The observable universe may not be the totality of physical reality. It may instead be a local spacetime sector, here called 𝓞, embedded in a larger, currently invisible background structure, here called 𝓑.

The “edge” of the observable universe is not a material boundary, a wall, or a rigid reference frame. It is an observational horizon: we only see the region from which light or other information has been able to reach us since the early universe.

Beyond that horizon, more spacetime may exist, even if it is not directly observable from our current position and cosmic time.

The hypothesis contains four main components:

1. The observable universe 𝓞 Our locally visible, spherical-looking spacetime sector.

2. The invisible background universe 𝓑 A larger negatively curved structure in which 𝓞 is embedded.

3. The white space 𝓦 A source sector that emits or generates spacetime, energy, matter, and information.

4. The central sink 𝓢 A black-hole-like gravitational endpoint or asymptotic attractor inside 𝓑.

The basic flow is:

𝓦 → equatorial spacetime nucleation → 𝓞 → internal expansion → growing CMB information shell → drift through 𝓑 → 𝓢

2. The observable universe 𝓞

The observable universe is the region accessible to us through light, the cosmic microwave background, galaxies, large-scale structure, gravitational lensing, and other signals.

From the inside, it appears:

• spatially nearly flat
• broadly homogeneous
• broadly isotropic
• expanding
• accelerating in its expansion, according to current cosmology

Its apparent spherical shape mainly refers to the observation horizon. From any observer’s position, the visible cosmos appears roughly spherical because light reaches the observer from all directions up to a finite lookback time.

This does not mean that the total universe must be a literal sphere.

In this hypothesis, the observable universe is not the whole cosmic system, but a local observational patch or embedded spacetime sector.

3. The invisible background universe 𝓑

The invisible background universe is the larger structure in which our observable universe may be embedded.

In this hypothesis, 𝓑 has global negative curvature. It can be idealized through a tractrix-shaped pseudospherical geometry.

A classical pseudosphere is a surface of constant negative Gaussian curvature generated by rotating a tractrix around its asymptote. For cosmology, this should not be understood as saying the universe is literally a two-dimensional pseudosphere. Rather, the tractrix pseudosphere functions as a guiding geometry for meridional slices of a higher-dimensional or more general background manifold.

The more careful formulation would be:

𝓑 is a higher-dimensional or otherwise larger background manifold whose meridional sections can be approximated by tractrix-like or pseudospherical geometry and whose global structure has negative curvature.

Negative curvature matters because:

• geodesics diverge
• distances can develop hyperbolically
• local and global geometry need not match
• a local patch can appear nearly flat even if the larger structure is curved

In this model, 𝓑 is not static. It grows through an influx of spacetime, energy, matter, and information from 𝓦.

4. The white space 𝓦 as source sector

Outside or beyond the invisible background universe lies a hypothetical source sector called white space, or 𝓦.

This white space is conceived as the opposite principle of a black hole.

A black hole:

• absorbs matter
• absorbs energy
• traps information
• curves spacetime strongly inward

The white space, by contrast, is imagined as an inverse process:

• it emits spacetime
• it releases energy and matter
• it opens or generates informational degrees of freedom
• it can produce Big-Bang-like events
• it feeds the growth of 𝓑

The white space may be described paradoxically as infinite yet shrinking. This does not necessarily mean that an ordinary spatial volume is getting smaller. More carefully, it could mean:

• a decrease of potential
• a reduction of available degrees of freedom
• an outflow of energetic states
• a transition from unstructured possibility into structured spacetime

In stricter language, 𝓦 would not be a normal place. It would be a spacetime-generating source sector, a boundary term, a bulk state, or a vacuum-like structure contributing effective terms to cosmic dynamics.

5. Origin of 𝓞 at the equator

In this hypothesis, our observable universe did not necessarily originate from the absolute beginning of all reality. Instead, it may have emerged from a local transition region between 𝓦 and 𝓑.

This transition region is idealized as lying near the equator of the tractrix-shaped pseudospherical background.

The equator is the high-energy creation zone where spacetime from 𝓦 enters 𝓑.

From the internal perspective of a newly formed spacetime sector, this transition would appear as a Big Bang.

So the Big Bang is not denied. It is reinterpreted:

The Big Bang would be the beginning of our observable spacetime sector 𝓞, but not necessarily the absolute beginning of all reality.

Other observable universes or spacetime sectors could, in principle, nucleate at similar transition regions.

6. Drift of 𝓞 inside 𝓑

After its emergence, 𝓞 does not remain fixed at the equatorial origin. It moves along a path inside the larger background geometry.

This motion can be described as a geodesic drift.

In visual terms:

The spherical-looking observable universe 𝓞 emerges near the equator of the tractrix pseudosphere and drifts from there toward the axis or toward a deeper gravitational attractor.

This is not ordinary motion of a ball through empty space. It is the motion of an embedded spacetime region inside a larger manifold.

The intuitive motivation is that every known cosmic structure is dynamic:

• moons move around planets
• planets move around stars
• stars move inside galaxies
• galaxies move inside groups and clusters
• clusters move along large-scale structures
• the Milky Way itself has a measurable motion relative to the cosmic microwave background

This does not prove that the entire observable universe drifts through a larger background. But if such a background exists, absolute rest inside it would be the less natural assumption.

A cautious scientific version would be:

If our observable universe is embedded in a larger background universe, then geodesic drift or orbital-like motion inside that background is plausible. However, such motion would need to reveal itself through weak measurable traces: directional dependencies, CMB anomalies, gravitational lensing effects, or large-scale velocity fields.

7. The central sink 𝓢

Inside the invisible background universe, the hypothesis assumes a central or asymptotic gravitational sink.

In poetic terms, this can be imagined as an enormous central black hole. More carefully, it could be called:

• an asymptotic attractor
• a gravitational end-sink
• a central curvature focus
• an information-and-energy absorption structure

It is the opposite pole of 𝓦.

𝓦 is the source. 𝓢 is the sink. 𝓑 is the mediating background. 𝓞 is the local drifting spacetime sector inside it.

This creates a cosmic flow:

𝓦 → equatorial spacetime nucleation → 𝓞 → drift through 𝓑 → 𝓢

Or, in shorter form:

source → spacetime formation → expansion → drift → absorption

8. What does it mean that the universe is “flat”?

When cosmologists say that the universe is flat, they do not mean that it is thin or disk-shaped.

They mean that its large-scale spatial geometry is close to Euclidean.

A flat universe means:

• parallel lines remain parallel in the idealized large-scale limit
• large cosmic triangles have an angle sum of about 180 degrees
• the spatial geometry is nearly Euclidean
• the curvature parameter Ω_K is close to zero
• the density of the universe is close to the critical density

There are three basic possibilities:

1. Positive curvature Similar to the surface of a sphere.

2. Zero curvature Flat Euclidean geometry.

3. Negative curvature Open, hyperbolic, or pseudospherical geometry.

Current observations strongly indicate that our observable universe is very close to spatial flatness. Planck 2018, combined with BAO data, found Ω_K = 0.0007 ± 0.0019, consistent with flatness.

Source: https://doi.org/10.1051/0004-6361/201833910

For this hypothesis, that means:

The observable universe must not be claimed to be strongly curved. The hypothesis must explain why our local spacetime sector appears nearly flat even if it is embedded in a globally curved background.

9. Why local flatness can still fit the hypothesis

The observed flatness does not automatically contradict the hypothesis.

A small region of a much larger curved structure can appear locally flat. The surface of Earth appears flat in everyday life, even though it is globally curved.

Applied to this model:

𝓞 may be a local patch of a much larger tractrix-shaped background structure. If the curvature scale of 𝓑 is much larger than our current observational horizon, then observers inside 𝓞 would measure almost perfect flatness.

So flatness becomes a constraint, not a refutation:

The global negative curvature of 𝓑 must occur on a scale much larger than the currently observable cosmos.

10. Why a deviation from flatness would strengthen the hypothesis

If future measurements found a robust, repeatable deviation from perfect flatness, that would be important for this model.

Especially interesting would be a tiny negative residual curvature.

Such a deviation could mean:

• 𝓞 is only locally almost flat
• the global structure is larger and curved
• the measured flatness is a local approximation
• the tractrix/pseudosphere idea gains a geometrical foothold
• the observable universe may be a patch within a larger negatively curved manifold

Important caveat:

A deviation from flatness would not automatically prove this hypothesis. Other cosmological models could also explain it.

But:

A robust measurement of Ω_K ≠ 0, especially in the sense of an open or negatively curved geometry, would strengthen the hypothesis because it would suggest that the observable spacetime sector is not exactly described by the flat standard assumption.

Technical note:

In many cosmological conventions, Ω_K > 0 corresponds to an open, negatively curved geometry. This is easy to confuse, but important.

11. The CMB sphere as a dynamic observation shell

The cosmic microwave background, or CMB, is not a solid wall at the edge of the universe. It is the oldest directly observable electromagnetic radiation, originating from the time when the universe became transparent, about 380,000 years after the Big Bang.

Source: https://science.nasa.gov/universe/overview/

What we see today as the CMB is a spherical projection around our observational position: the surface of last scattering.

Important point:

The CMB itself is not growing as an object. Rather, our observable CMB shell shifts with cosmic time.

A future observer would receive CMB photons from a slightly different, farther-out region of the last-scattering surface than we do today.

In that sense:

The CMB sphere is a growing or shifting information shell that gradually samples other regions of the formerly invisible cosmos.

This is extremely important for the hypothesis:

The observable universe is not only spatially embedded and drifting; it is also observationally dynamic. Its information boundary changes over time.

The CMB sphere is therefore not a wall, but a kind of cosmic scanning surface.

12. The CMB sphere and the invisible background universe

Inside the tractrix-background hypothesis, the CMB sphere has a special role.

If 𝓞 is embedded in 𝓑, then the CMB sphere is the oldest electromagnetic information shell through which we can probe our embedded spacetime sector.

It does not directly show 𝓑 itself. But it may contain indirect traces:

• large-scale temperature anomalies
• hemispherical asymmetries
• preferred axes
• lensing effects from matter distribution
• correlations with large-scale structure
• weak traces of drift or projection

CMB photons are gravitationally deflected by the intervening matter distribution. This is CMB lensing, and it is used to reconstruct information about matter and geometry between recombination and the present. ESA describes Planck’s CMB lensing measurements as a way to study the large-scale matter distribution across cosmic history.

Source: https://www.cosmos.esa.int/web/planck/publications

For this hypothesis:

If 𝓞 drifts along a path through a tractrix-shaped background, extremely weak traces of that drift might appear in the CMB sphere, CMB lensing, large-scale anomalies, or correlations with matter structure.

13. Accelerated expansion and the limit of future visibility

The CMB sphere and the observational horizon may make more of the formerly invisible cosmos accessible over time. But this visibility is not unlimited.

The expansion of the universe is accelerating. The discovery of the accelerating expansion through distant supernovae was awarded the 2011 Nobel Prize in Physics.

Source: https://www.nobelprize.org/nobel_prizes/physics/laureates/2011/

NASA describes dark energy as the unknown component associated with the accelerated expansion, while emphasizing that future missions aim to determine whether dark energy is a cosmological constant, a dynamic field, or a sign that gravity needs modification on cosmic scales.

Source: https://science.nasa.gov/universe/overview/

For this model:

The CMB sphere may reveal more formerly invisible regions over time, but accelerated expansion limits what can ever become observable.

Therefore, the invisible background universe is not merely “not yet visible.” Parts of it may remain permanently beyond future observational access.

14. Accelerated expansion as a possible embedding effect

In the standard model, accelerated expansion is described through dark energy or the cosmological constant Λ.

This hypothesis does not deny accelerated expansion. It reinterprets it as potentially effective.

Possible interpretations inside this model:

1. 𝓦 feeds additional spacetime or degrees of freedom into 𝓑.
2. This influx appears inside 𝓞 as dark energy.
3. The drift of 𝓞 through tractrix-shaped geometry creates projection effects.
4. The internal expansion of 𝓞 and the growth of 𝓑 overlap.
5. 𝓢 may create large-scale gradients or directional effects.

DESI results released in 2025 strengthened hints that dark energy may evolve over cosmic time, although this has not reached the 5σ discovery threshold normally required in physics.

Source: https://www.desi.lbl.gov/2025/03/19/more-than-a-hint-of-evolving-dark-energy-new-results-and-data-from-desi/

For this hypothesis:

A dynamic dark energy would fit a source/embedding model more naturally than a perfectly constant cosmological constant. However, it would not prove the existence of 𝓦.

15. Possible gravitational phenomena beyond the observable universe

The hypothesis becomes especially interesting if there are hints that the observable universe cannot be fully explained by internal structures alone.

Several observational categories matter here.

15.1 Dark Flow

The so-called Dark Flow idea interpreted large-scale motions of galaxy clusters as possible evidence for gravitational influences beyond the observable horizon.

That fits the hypothesis conceptually:

If mass or curvature structures outside our visible region caused large-scale motion, this could be interpreted as an indirect sign of 𝓑.

However, Dark Flow is not robustly confirmed. Planck-era results did not establish a generally accepted large Dark Flow on gigaparsec scales, and the standard ΛCDM model remains the default explanation. Planck 2018 found no statistically significant preference for departures from the base ΛCDM model in the extensions it tested.

Source: https://doi.org/10.1051/0004-6361/201833910

So this must remain cautious:

A confirmed Dark Flow would be a strong supporting indication for the hypothesis. The current observational status is not sufficient.

15.2 Bulk flows

Bulk flows are coherent motions of large galaxy volumes.

In ΛCDM, such motions are expected, but they should statistically decrease with scale. If very large, stable, direction-dependent bulk flows were confirmed and could not be explained by known matter distributions, they would become a possible search window for external gravitational contributions or embedding effects.

For the hypothesis:

Large-scale bulk flows could be possible traces of 𝓞 drifting inside 𝓑.

But again:

There is currently no generally accepted proof of such a global drift.

15.3 CMB anomalies

The CMB is extremely isotropic overall and strongly supports ΛCDM. However, several large-scale anomalies are discussed:

• hemispherical asymmetry
• the Cold Spot
• low-multipole anomalies
• possible preferred axes

ESA notes that Planck confirmed temperature-map anomalies such as hemispherical asymmetry and the Cold Spot, while polarization data did not provide convincing new evidence requiring a radically different cosmology.

Source: https://www.cosmos.esa.int/web/planck/publications

For this hypothesis:

CMB anomalies are not proof, but they are possible search windows for weak embedding, projection, or drift traces.

16. Why 𝓞 can appear flat despite drift

This hypothesis combines four effects.

16.1 Local flatness

𝓞 is only a small region of a much larger structure. Locally, it can appear flat.

16.2 Projection

Observers inside 𝓞 do not measure the full geometry of 𝓑. They measure the internal spacetime geometry of their own observable sector.

What appears as expansion may partly be a projection of motion through a larger curved structure.

16.3 Dynamic smoothing

The influx from 𝓦 may smooth or stabilize the internal geometry of 𝓞. This could help explain why 𝓞 appears nearly flat even if 𝓑 is globally negatively curved.

16.4 Dynamic observation shell

The CMB sphere is not a rigid boundary. It shifts over cosmic time and makes different regions of the early universe visible.

Therefore, our observable patch is not only spatially dynamic but also informationally dynamic.

In short:

The visible flatness is the local inside view; the negative tractrix curvature is the possible global outside structure; the CMB sphere is the shifting information shell with which we scan the embedded sector.

17. Cosmic cycle

The model describes reality not as a single static event, but as a dynamic cycle.

The sequence is:

1. 𝓦 contains or generates creative potential.
2. New spacetime emerges near equatorial transition regions of the tractrix pseudosphere.
3. A visible universe nucleates as a local spacetime sector 𝓞.
4. 𝓞 expands internally.
5. Its CMB sphere shifts as an information shell, revealing different early regions over time.
6. 𝓞 drifts through 𝓑.
7. 𝓑 grows through further influx from 𝓦.
8. Matter, energy, and information eventually move toward 𝓢.
9. 𝓢 functions as a black-hole-like endpoint or asymptotic attractor.
10. The total process becomes a cycle of emergence, expansion, observation-growth, drift, transformation, and absorption.

Short version:

𝓦 → equatorial spacetime nucleation → 𝓞 → internal expansion → growing CMB information shell → drift → 𝓢

Even shorter:

source → structure → expansion → visibility growth → motion → absorption

18. Possibility of cosmic navigation

A speculative consequence concerns the far future of intelligent civilizations.

If the observable universe really follows a trajectory inside a larger background universe, then long-term cosmic survival would not only depend on local expansion. It would also depend on position and motion inside the larger structure.

A sufficiently advanced civilization might, in principle, try to:

• understand the drift trajectory of 𝓞
• evaluate the changing CMB information shell
• predict dangerous regions of 𝓑
• use curvature gradients or energy gradients
• identify transition regions
• search for paths into other spacetime sectors

This is pure speculation at present. But inside the hypothesis, it is a logical consequence:

If universes emerge, drift, become observable in changing ways, and eventually end inside a larger structure, then cosmic navigation would mean understanding that larger dynamics.

19. More formal wording

The poetic terms can be translated into a more technical language:

• visible universe → observable spacetime sector 𝓞
• invisible universe → higher-dimensional background manifold 𝓑
• white space → external source sector 𝓦
• central sink → asymptotic attractor 𝓢
• Big Bang → local spacetime nucleation
• drift → geodesic motion of an embedded sector
• tractrix pseudosphere → negatively curved embedding geometry
• CMB sphere → dynamic last-scattering observation shell

A more formal version:

The observable universe 𝓞 is a nearly FLRW-like spacetime sector embedded in a larger background manifold 𝓑. This background possesses global negative curvature and can be represented in meridional sections by tractrix-like or pseudospherical geometry. An external source sector 𝓦 feeds effective spacetime, energy, or degree-of-freedom fluxes into 𝓑, while an asymptotic gravitational sink 𝓢 acts as a global attractor. The observed expansion of 𝓞 results from internal FLRW expansion, possible source terms, and projective embedding effects. 𝓞 may have originated near an equatorial nucleation region and may now follow a geodesic drift path toward the axis or sink of 𝓑. The CMB sphere is not a rigid boundary but a dynamic information shell that exposes different regions of the last-scattering surface over cosmic time.

20. Testability

The hypothesis is only scientifically interesting if it leads to testable consequences.

Possible signatures:

20.1 Residual curvature

A small, robust deviation from perfect flatness, especially toward negative curvature, would strengthen the hypothesis.

20.2 Dynamic dark energy

Time-evolving dark energy could indicate a source term, embedding coupling, or non-closed expansion dynamics.

20.3 Direction-dependent expansion

If 𝓞 drifts, then the Hubble parameter, supernova distances, or BAO scales might show tiny directional dependencies.

20.4 CMB anomalies

Preferred axes, hemispherical asymmetry, the Cold Spot, or correlated low multipoles could be weak projection traces.

20.5 CMB lensing

If 𝓑 or 𝓢 creates large-scale gravitational potentials, there might be extremely weak large-scale signatures in CMB lensing.

20.6 Bulk-flow fields

Very large coherent motions that cannot be explained by known matter distributions could suggest external gravitational influence or background drift.

20.7 Correlation of independent axes

The strongest support would not be a single anomaly. It would be a correlation between several independent observations:

• residual curvature
• CMB anomalies
• CMB lensing
• expansion dipoles
• bulk flows
• dynamic dark energy

The key requirement:

One anomaly is not enough. The hypothesis becomes strong only if several independent observations point toward the same preferred axis, drift structure, or residual curvature.

21. Strengths of the hypothesis

The hypothesis is interesting because it connects several open questions:

• Why does the observable universe appear flat?
• Why is expansion accelerating?
• Could dark energy be dynamic instead of constant?
• Could CMB anomalies point to larger geometry?
• Could bulk flows reveal external gravitational influence?
• Could the Big Bang be a local nucleation event rather than the absolute beginning?
• Could the observable universe drift along a path inside a larger structure?
• Could the CMB sphere gradually reveal more of a formerly invisible region?
• Could the visible cosmos be only the inside view of a larger dynamic flow system?

The strongest core idea is:

ΛCDM may describe the local inside view of our observable universe, while the tractrix-background hypothesis searches for a larger outside structure in which that inside view is embedded.

22. Weaknesses and limits

The hypothesis remains speculative.

Its major open problems are:

• There is no confirmed detection of the invisible background universe 𝓑.
• Dark Flow is not robustly confirmed.
• Planck and BAO strongly support a nearly flat ΛCDM cosmology.
• The tractrix geometry is not yet a complete cosmological model.
• 𝓦 needs a precise physical definition.
• 𝓢 needs a precise mathematical description.
• Energy conservation, causality, and thermodynamics must remain consistent.
• The CMB sphere does not directly show 𝓑; it shows the last-scattering surface within our observable sector.
• The hypothesis currently lacks field equations producing quantitative predictions.

Therefore, it should not be presented as a proven alternative to the standard model.

It is strongest as:

A speculative geometrical-dynamical extension model that contains ΛCDM locally and searches for small, measurable residual traces of a larger embedding.

23. Compact summary

The observable universe may be a locally nearly flat, spherical-looking spacetime sector inside a larger invisible background universe. This background may have global negative curvature and may be representable, in suitable sections, by a tractrix-shaped pseudosphere.

Our observable universe may have emerged near the equatorial transition region of this structure, where an external white source sector 𝓦 feeds spacetime, energy, matter, and information into the background universe 𝓑. From the internal perspective, this event appears as the Big Bang.

Since then, 𝓞 has expanded internally while also drifting as an embedded spacetime sector from its equatorial origin toward the axis or a central gravitational sink 𝓢. This sink forms the opposite pole of 𝓦 and can be understood as a black-hole-like attractor.

The observed flatness of the universe means that its spatial geometry inside the observational horizon is nearly Euclidean. This does not contradict the hypothesis if the curvature scale of 𝓑 is much larger than the visible cosmos. A future robust measurement of small negative residual curvature would strengthen the hypothesis, because it would suggest that 𝓞 is only a local patch of a larger curved structure.

The CMB sphere is not a wall or fixed edge. It is the oldest electromagnetic information shell and shifts over cosmic time. It therefore reveals different regions of the last-scattering surface over time and can be understood as a dynamic scanning shell of our embedded spacetime sector. However, accelerated expansion limits what can ever become observable.

Accelerated expansion could, in this framework, be interpreted as an effective coupling between 𝓞, 𝓑, and 𝓦. Hints of dynamic dark energy would therefore be especially interesting, although they would not prove the model.

Possible observational windows include:

• residual curvature
• dynamic dark energy
• CMB anomalies
• CMB lensing
• bulk flows
• Dark-Flow-like phenomena
• expansion dipoles
• correlated preferred axes

The total cosmic flow would be:

𝓦 → equatorial spacetime nucleation → 𝓞 → internal expansion → shifting CMB information shell → drift through 𝓑 → 𝓢

Scientific status:

The standard model describes the local inside view. The tractrix-background hypothesis investigates whether that inside view could be part of a larger negatively curved cosmic dynamic.