Physical Sciences

Abstract: We investigate a conditional gravitational-wave mechanism during scalar instabilities in an SL(6,C)-motivated geometric-information framework. The four-dimensional Lorentzian background arises via a regular reduction with two positive internal directions; statistical localization alone does not establish it. Within a derivative-coupled scalar theory, dilution of the homogeneous kinetic background drives the neutral order parameter through a mass instability. For negative effective mass squared, noncollinear scalar modes give a nonzero transverse-traceless stress at every wavenumber in 0<K<2. In a frozen-background approximation, a finite-duration exponential source leaves strictly positive residual tensor energy, extended to finite wave packets by continuous spectral weights. These local existence results are distinguished from a stochastic background through unequal-time stress correlations and retarded propagation. Continuous-time finite-rank positivity, Gaussian benchmarks, and covariance-error bounds characterize spatial and temporal coherence. An off-shell energy identity connects parent-field equations to gravitational-wave, dark-matter, and visible-sector transfer rates; combined with receiver continuity and Raychaudhuri evolution it yields a conditional conservation chain consistent with the Friedmann constraint. Redshift relations and uncertainty bounds show that observed frequencies depend on source scales and thermal history. We establish a conditional route from seeded scalar instability to tensor radiation and identify the source statistics, transfer rates, and evolution required for quantitative predictions.

Abstract: We investigate the fundamental kinematic parameters of stellar motions in the Milky Way using a statistical sample of 27,485,720 stars with measured three-dimensional velocities from the Gaia DR3 catalogue. From these data, we determine the local solar velocity (U⊙,V⊙,W⊙)=10.5±0.7,14.5±0.9,7.33±0.1km/s, the average orbital velocity V0=228±4km/s and the circular velocity Vc=234±4km/s, at the radius R⊙. Next, within the range of 3−14 kpc, we derive the Galactic rotation curve Vc(R) and determine the average spherical components of the stellar velocities as functions of both Galactocentric radius R and distance from the Galactic plane Z. Two-dimensional R−Z maps of these components reveal a complex three-dimensional kinematic structure. In particular, the pattern observed at R≲5kpc can be associated with the influence of the Galactic bar. To facilitate the description of the observations, we employ a simplified axisymmetric Monte Carlo model with several free parameters that reproduces the main kinematic trends.

Abstract: This paper continues a classical-mechanical approach in which a modified Newtonian gravitational model was previously developed within a four-dimensional geometrical framework. In that construction, classical kinetic energy leads naturally to a Minkowski metric and an action-based formulation of the equations of motion. Consequently, the present paper extends this model, relating the exponential modification of the central Newtonian field to the factor \((1-v^{2}/c^{2})\). The resulting modified central force \(\mathbf{F}_{Ne}\) provides the retrograde contribution to the observed perihelion advance. A complementary velocity-dependent gravitomagnetic interaction \(\mathbf{F}_{gm}\) is derived from the conditions: \[ \hat{r}^{2}d_{t}\varphi = r^{2}e^{2\varrho/r}d_{t}\varphi = \mathrm{const.} \quad \text{and} \quad \mathbf{F}_{gm} \cdot \mathbf{v} = 0. \] Together, these interactions reproduce the observed perihelion advance. The corresponding scalar and vector potentials yield a Maxwell-type gravitational formulation, with the gravitomagnetic interaction incorporated into the action through a term linear in velocity. The total gravitational interaction is then examined in the limiting case of a light ray. The gravitostatic contribution vanishes as \(v \rightarrow c\), while the gravitomagnetic interaction \(\mathbf{F}_{gm}\) gives the deflection angle \(\Delta\theta = 4GM/(bc^{2})\), corresponding to approximately \(1.75\) arcsec for a grazing ray. Thereafter, a classical-mechanical interpretation of the Michelson--Morley null result is also obtained: the round-trip propagation times along the parallel and transverse arms are both \(2h/c\). These results extend the model without assuming the invariance of the speed of light as an independent postulate.

Abstract: Several million narrowly defined exo-Earth candidates may exist in the Milky Way's annulus 7–9 kpc from the Galactic Centre, according to the conditional model estimate underlying this essay. The number is large, but its interpretation must remain narrow. Similarity in radius, stellar flux, and position within a conservative habitable zone does not show whether such planets have suitable atmospheres, stable climates, life, or technological civilisations. This raises a problem. If potentially suitable worlds are numerous, why does the universe still appear silent? Distance alone may not explain this. Civilisations could emerge at very different times, remain detectable only briefly, disappear before another civilisation arises, or never develop the capacity for sustained interstellar expansion. The absence of detected traces therefore leaves substantial uncertainty. We currently know of only one active biosphere and one technological civilisation, whose future is not guaranteed. The ability to control violence, technological risks, ecological degradation, and destruction of the biological systems on which civilisation depends may be as important to long-term survival as technological progress itself. Regardless of how many living worlds may exist elsewhere, preserving Earth is not only a matter of environmental policy, but a question of the long-term continuity of life and civilisation.

Abstract: The Hubble tension — a ∼10% systematic discrepancy between two independent measurement channels for the Hubble constant — remains one of the most pressing unsolved problems in modern cosmology. The standard ΛCDM model treats H₀ as a globally uniform parameter and cannot explain this systematic offset self‑consistently. Building on a previously published paradigm of the static cosmic substrate and local perturbation, this work uses substrate‑field partial differential dynamics and steady‑state Yukawa‑type metric solutions to derive quantitative intervals for a six‑tier Hubble gradient across distinct cosmic environments. Density serves as the observable proxy of the underlying field perturbation, rather than the fundamental driver of metric contraction. The proposed framework requires no early dark energy, ad‑hoc local void corrections, or freely fitted parameters; its behaviour follows naturally from homeostatic self‑reversion dynamics. We further infer that the effective Hubble constant depends on the perturbation density both at the radiation source and at the observer, which acts as a secondary correction term. The six‑tier gradient is a discretized sampling of a continuous density‑dependent flux field, providing concrete observational targets for upcoming wide‑area surveys.

Abstract: We study the interfaces required to connect an SL(6,C)-motivated statistical geometry to a four- dimensional Lorentzian effective theory. A neutral six-dimensional metric admits three orthogonal four-plus-two inertia allocations without establishing three dynamical spacetime phases, and the pos- itive covariance compression does not select Lorentzian signature. A separate positive-fiber branch permits conditional Lorentzian reduction and a finite internal-mode cutoff. We construct a nonstation- ary reflecting diffusion benchmark whose cell occupations are actual probability integrals and whose derivatives equal boundary fluxes. For a three-well potential, we construct the normalized station- ary Gibbs density and bound a concrete resistance integral. Finite stochastic propagation yields an accumulated occupation-error bound, while finite cumulative activity leaves a quantified memory of the initial state. An explicit finite cohomology quotient carries a positive descended pairing. Within the supplied Lorentzian action, conservation, mediator bounds, charged equilibria, and tensor-source constraints retain their stated domains. A finite covariance construction controls quadratic response errors. These results strengthen individual interfaces but establish no shared cosmological solution, quantum state space, or observational prediction. A complete emergence claim still requires con- trolled metastable projection, calibrated time, dynamical reduction, coupled stress evolution, and source matching.

Abstract: This study tests whether frozen connected multiscale paths across a 99-event development cohort form a higher-order population dynamical object. Structural paths occur in 98/99 events, but rarity is graded rather than binary: 58 path-bearing events satisfy the frozen rare-path criterion and 40 do not, while node-count complexity correlates with the frozen rarity coordinate (Spearman ρ = 0.6619802493). A search-aware discrete-family model fails (7,565/9,999 null exceedances; p = 0.7566), motivating a move from event labels to event-internal geometry.Intrinsic registration yields a 97-event atlas with 1,077 nodes and 980 transitions. PRE and POST dynamics are strongly asymmetric: PRE contains 730 nodes and 633 transitions across 90 events with macro R² = 0.131234 and minimum-fold R² = 0.106708, whereas POST contains 347 nodes and 250 transitions across 92 events with macro R² = 0.033268 and minimum-fold R² = -0.104449. Rate balance, re-entry, multistate flow, run index, state age, history, and frozen forward replay establish a recurrent memory-conditioned process.Broad physical-covariate screening produces large apparent fits, but leverage and search-aware controls reject them as population laws. Three-phase organization survives removal of physical terms: the physics-free F0 score is 0.5952381984 versus 0.5970683812 for the best physical candidate. Only after this structural freeze does a state-first physical search survive full selection correction, with 5/9,999 primary null exceedances (p = 0.0006) and 0/9,999 fixed-score exceedances (p = 0.0001).The frozen score then modifies transition rate with γ = 0.3162354634393393, so a one-unit increase in S multiplies the conditional hazard by exp(γ) = 1.371953262430. The frozen clock gives 3/999 primary exceedances under the plus-one rule (p = 0.004). All four developmental views retain positive likelihood gain, and Holdout5 retains positive no-refit likelihood gain in W1–W4; W1–W3 reproduce the frozen ordering direction, while W4 is underpowered at four scorable events.A transition-local depletion interval has generic maximum-gap strength (p = 0.99) but specific frozen transition-local placement at the tested resolution (p = 0.01). The surviving object is therefore an effective, history-bearing population state system with intrinsic registration and a source-dependent traversal-rate modifier.

Abstract: Since its formal discovery in 1965, the cosmic microwave background (CMB) played a cornerstone role in modern astronomy. The study of CMB became the main tool of astronomers in trying to gauge the early universe and to test their inflationary models against the CMB data as its radiation provided evidence of the big bang origin of the universe and studying the CMB anisotropies gave clues about the normal matter evolution and large structure formation in the universe. While applying the virial theorem at different scales, the discussion will show another important aspect of the role CMB radiation in describing the universe and its evolution.

Abstract: Can a black hole remain arbitrarily heavy after mergers have assembled it? This paper develops the mass-ceiling prediction of Toroidal Scale Mechanics, which treats a black hole as a maintained flow structure in an underlying physical medium. The adopted intake has a mass-independent upper bound, while discharge at and above the ceiling increases with the square of the black-hole mass. Their intersection, using the theory’s committed discharge coefficient, lies at approximately one hundred billion solar masses. This coefficient supplies the numerical normalization. Above the intersection, discharge exceeds every permitted continuous intake. An exact solution gives the slowest allowed relaxation after a merger: initial masses ten and fifty percent above the ceiling fall to within one percent of it in approximately fourteen and twenty-three days, respectively. The underlying remnant study records the constant-coefficient continuation to smaller black holes as failed; that continuation requires a different state dependence. Published dynamical and joint lensing–dynamical examples reviewed here lie below the ceiling; the larger estimate for IC 1101 comes from an indirect galaxy-core relation. The decisive test is an independently confirmed black hole that persists above the calculated limit after uncertainties and the relaxation interval are accounted for. Such an object rejects the specified intake–discharge construction.

Abstract: High-energy astrophysical neutrino astronomy provides a means of investigating energetic cosmic environments through particles that interact weakly with matter and can travel over astronomical distances. The mathematical interpretation of neutrino observations requires a coherent description of source fluxes, flavor propagation, neutrino interactions, detector response, and statistical inference. In this paper, we develop a unified mathematical framework for these tasks. We introduce differential flux models, describe standard three-flavor neutrino propagation, formulate detector response as a positive integral operator, and construct likelihood functions for event-level data. We establish a consistency result relating the response operator to the expected event count and examine the inverse problem of recovering a flux from reconstructed observables. A symbolic example illustrates the calculation of expected event counts for a power-law spectrum with an exponential cutoff. We also discuss maximum-likelihood estimation, Bayesian inference, regularization, identifiability, point-source searches, and multi-messenger analysis. The purpose is to provide a self-contained mathematical treatment of established methods in high-energy neutrino astronomy. The formulations are intended as a foundation for reproducible analyses and further work on inverse problems, uncertainty quantification, and source reconstruction.

Abstract: We present an interpretation of cosmological redshift within the static‑substrate local‑perturbation paradigm. In this framework, redshift arises from continuous local metric contraction driven by substrate homeostatic self‑reversion, rather than from global spatial expansion. The perturbation bubble diffuses geometrically, but this diffusion does not directly produce redshift. The observed distance‑redshift relation emerges from the density‑dependent metric contraction rate. In the weak‑field, low‑density limit, the model reproduces the standard distance‑redshift relation, making it observationally equivalent to ΛCDM for all existing distance‑redshift data. This work does not claim to falsify ΛCDM at the observational level. It proposes an alternative ontological foundation for the same distance‑redshift data, with specific discriminative signatures that could distinguish the two frameworks in future experiments. The two frameworks differ in their ontological foundations and in specific testable signatures. We propose a thought experiment—we designate this thought experiment the flashlight redshift experiment—in which a laboratory light source propagates through a contracting metric. The static‑substrate framework predicts a tiny but non‑zero redshift, whereas ΛCDM predicts exactly zero. The framework further predicts an environment‑dependent Hubble gradient, which qualitatively resolves the Hubble tension. The quantitative construction of this gradient and its observational analysis are developed in a separate dedicated paper.

Abstract: The cosmic microwave background (CMB) at 2.7 K (peak 1.06 mm) is interpreted as radiation emitted at 3000 K (peak 966 nm) and stretched by the expansion of space over 13.8 Gyr. The standard derivation preserves blackbody shape via the FLRW scale factor a(t), but assumes empty space can act as a thermodynamic cooler and source of cosmological redshift. No laboratory experiment demonstrates this mechanism. Gravitational redshift is verified to 1% in the Pound-Rebka experiment with defined potential and energy exchange in time-invariant space; cosmological redshift has no equivalent potential and implies energy loss by a factor of 1100 without work, in tension with the first law. COBE, WMAP, and Planck confirm the final temperature and shape, not the cooling mechanism. Spatial flatness is compatible with time-invariant Euclidean space. Bijective analysis indicates that time as a fourth dimension lacks experimental support. Until direct experimental proof exists, CMB cooling and cosmological redshift remain mathematical invariances without a demonstrated physical mechanism.

Abstract: We study the causal meaning of a light-speed interface for a four-dimensional Lorentzian matter sector in an \( SL(6,\mathbb C) \)-motivated six-dimensional program. We separate Gaussian statistical localization, physical signature selection, projectable geometric reduction, and low-energy truncation. Positive precision cannot generate a timelike direction, and unimodular complex congruence obstructs a single-sign-flip real endpoint. On a supplied regular six-dimensional Lorentzian branch with positive internal fibers, the quotient is Lorentzian and causal projection yields a sharp local speed bound. We derive a finite-window criterion in which an internal gap and a positive four-dimensional Planck coefficient coexist; unlimited localization does not preserve that window. A common regular scalar principal symbol then identifies the quotient metric cone. The light-speed interface is consequently a causal boundary within the controlled four-dimensional phase, while access to internal modes is set by an energy threshold rather than a velocity test. The fast–slow exponential model, entropy and symmetry mechanisms, and observable diagnostics are retained with separate clocks and matching assumptions.

Abstract: The ΛCDM model has successfully described the universe on the basis of a large body of astronomical observations. However, within the framework presented here, several questions remain concerning the origin of the universe and the nature of dark energy and dark matter. The proposed Continuously Breeding Universe (CBU) model treats the universe as a low-density black hole in which electron–positron and proton–antiproton pairs emerge continuously. The expansion of space is attributed to the appearance of new particle pairs. The negative potential energy associated with the expansion of space balances the increase in ordinary matter. The model further proposes that the gravitational parameter G is inversely proportional to the radius of curvature r. Consequently, the Planck length and Planck energy vary with the curvature and therefore with the size of the universe. An alternative interpretation of the Einstein field equation is developed by connecting the energy–momentum tensor to the gravitational parameter and the energy density. Within this interpretation, dark energy and dark matter arise from the energy structure associated with the expansion of the universe and the kinetic energy of quantum-fluctuation particles.

Abstract: We formulate a conditional three-stage cosmological programme that distinguishes statistical localization, real geometric reduction and physical evolution. A six-dimensional real metric with a positive rank-two vertical block yields a four-dimensional Lorentzian quotient only under explicit regularity, projectability and inertia assumptions. Its causal projection and finite heavy-mode elimination are made explicit. A common derivative-coupled action governs the neutral scalar sector, with action-derived continuity, conditional mass crossing and a healthy positive-vacuum limit; its relation to the charged SL6C sector is exhibited. Three-state statistical coexistence is realized by a normalized positive finite evolution, while weighted phase conversion requires compensating energy exchange to preserve the Friedmann constraint. Finite propagation errors and background constraint residuals quantify separate consistency requirements. A gauge-aware Maxwell calculation identifies the metric characteristic cone; ordinary positive-mass propagation gives a delay decreasing with energy and does not establish a dimensional transition. A retained Gaussian transverse-stress benchmark supplies conditional gravitational-wave spectra and redshifted scales. The results identify precisely which geometric, statistical, dynamical and observational constructions are still required for a complete emergence theorem. The accompanying Lean source contains the original proof bodies.

Abstract: The construction of physically realistic analytical solutions of Einstein's field equations remains one of the central problems in relativistic astrophysics. Exact solutions provide important insight into the internal structure, stability, and observable properties of compact stellar objects, including neutron stars, strange quark stars, anisotropic compact stars, and exotic dark-energy-inspired configurations. The Thirukkanesh–Ragel– Malaver (TRM) ansatz has now typically specific mathematical assumption (or metric potential setup) used by within general relativity to find exact, analytical solutions to the Einstein field equations. It is widely used by astrophysicists to model the interior structure of highly dense compact objects, such as strange anisotropic quark stars, neutron stars, and dark energy stars. The TRM approach acts on the radial component of the metric potential. Initially proposed by S. Thirukkanesh and F. C. Ragel (2012) and that was later generalized by Manuel Malaver (2014) who introduced typical adjustable parameter (n) in the metric function, the TRM ansatz serves as an exact mathematical framework for modeling anisotropic stellar interiors, and that has recently gained prominent attention for its ability to explain the incredibly low mass of the compact object within the supernova remnant HESS J1731−347. Discovered by the High Energy Stereoscopic System, HESS J1731−347 contains a compact star whose exceptionally tiny mass has been defying traditional iron-core neutron star formation models. Instead, astrophysicists use the Thirukkanesh–Ragel–Malaver metric ansatz to model the star as a strange quark star. This review shows that the TRM metric potential provides a flexible analytical framework for studying equilibrium configurations as well as physical properties of typically relativistic compact objects.

Abstract: We explore the hypothesis that the observed FLRW cosmology admits a finite global completion and ask how this changes the prospects for testing quantum gravity. A finite overdense region embedded in a larger background can undergo gravitational collapse, providing a possible prehistory for the observed expansion. If the collapse approaches a finite quantum-supported density \( \rho_G \), positive spatial curvature permits a nonsingular bounce connecting contraction to expansion. In one realization, the late-time de Sitter horizon of the FLRW interior is identified with the Schwarzschild horizon of the exterior, providing a finite global completion without modifying the local FLRW dynamics. The central proposal of this review is that such a finite bouncing cosmology can act as a laboratory for quantum gravity. We use quadratic gravity and PT-symmetric quantum theory as concrete realizations while emphasizing that the observational strategy is more general. Within scalaron inflation, the measured CMB amplitude constrains the \( R^2 \) coupling \( \alpha \) once the primordial state, reheating history and pivot-scale mapping are specified. Large-angle CMB parity statistics can similarly be related, within a specified primordial-state model, to an effective PT-breaking amplitude \( A_{\rm PT} \). PT completion also suggests a possible connection between the arrow of time and quantum information: information inaccessible within one semiclassical branch may remain encoded in a unitary PT-complete quantum state, potentially reformulating aspects of both the Past Hypothesis and apparent information loss. The contracting phase provides a possible second source of structure, distinct from inflationary quantum fluctuations. Nonlinear structures may form before the bounce. If such relics survive, their evolved abundance and mass function could be constrained by dark matter, early supermassive black holes, lensing and gravitational-wave observations. Strong-gravity measurements provide complementary tests of candidate microscopic completions through black-hole perturbations, horizon absorption and extreme-mass-ratio inspirals whenever the relevant additional degrees of freedom lie in an observationally accessible regime. The resulting framework is therefore best regarded as a network of cross-consistency and falsification tests. Relations among \( A_s \), \( \alpha \), \( A_{\rm PT} \), \( Y_B \), \( \rho_G \), spatial curvature, relic populations and strong-gravity observables range from established model-specific results to phenomenological hypotheses that still require microscopic derivation. If these relations can be sufficiently specified, otherwise unrelated observations could over-constrain a common quantum-gravitational history. Cosmological maps, black holes and gravitational waves can be regarded as experiments performed by Nature in regimes inaccessible to terrestrial laboratories, providing an observational approach to quantum gravity complementary to microscopic theory building. A finite Universe may preserve measurable information about both its pre-Big-Bang evolution and its high-density quantum state, turning otherwise inaccessible quantum-gravitational dynamics into a potentially falsifiable observational programme.

Abstract: This manuscript provides a foundational framework for the observational-cosmology-related deductions presented in our previously published companion paper (Sheng, 2026, EGUsphere, DOI: 10.5194/egusphere-2026-4375). It constructs a self-consistent theoretical formulation that links static substrate dynamics to macroscopic gravitational effects and large-scale structure formation. The framework provides an alternative modeling approach for galactic rotation curves and cosmological redshift, without requiring dark matter or dark energy as free parameters. The core partial differential equation (PDE) governing the substrate field is derived in Section 2. Its steady-state point-source solution yields a Yukawa-type potential, which naturally degenerates to Newtonian gravity in low-density regions, ensuring compatibility with solar-system observations. The model further provides a unified geometric interpretation of redshift and gravitational time dilation based on local metric contraction. At a conceptual level, this framework also offers ontological interpretations for several frontier phenomena, including black hole evolution, microscopic quantum entanglement, and the Hubble tension. However, this manuscript is purely theoretical. All detailed quantitative deductions, observational predictions, and empirical validations for these phenomena are deferred to the companion paper (Sheng, 2026, EGUsphere, DOI: 10.5194/egusphere-2026-4375). It serves as the theoretical foundation for the paradigm and is intended for cross-reference with the observational companion manuscript.

Abstract: Derivation and optimum calculation of the Radius of dead compacted stars, relativistic and Non-relativistic Fermi-Dirac degeneracy pressure, quantum gravity pressure, energy, and the central temperature of particles in dead stars are main goals. Stars are born from collapsing gas clouds within a stellar nebula and die when nuclear fusion is suspended in the core, leaving dense remnants supported by quantum degeneracy pressure until gravity wins completely to form a black hole, superparticles, and a singularity sphere. Degeneracy pressure is a quantum rule. The Pauli exclusion principle states that identical particles called fermions cannot share the same space and quantum state at the same time. When matter is squeezed extremely tightly, these particles resist further compression without needing heat. Electron degeneracy pressure stops collapse in white dwarf stars; neutron degeneracy pressure suspends the collapse of neutron stars, Quark -gluons sustained the stability of quark stars; and superparticles keep the quantum gravity singularity and avoid a singularity of zero size with infinite density. In many modern approaches to quantum gravity theory, such as Loop Quantum Cosmology, Loop Quantum Gravity, and string theory, the infinite density and zero size of a singularity predicted by Einstein's classical general relativity are eliminated. Instead, the non-local or discrete nature of space-time at the Planck scale, superparticles, and atomic singularity scale introduces a powerful repulsive quantum force, preventing matter from collapsing into an infinitely small point and replacing the singularity with a high-density, finite quantum core, often described as a "Planck star", Planck singularity, a quantum bounce, or a quantum gravity singularity: a white, smooth ball of the steeply condensed state of matter and energy on the scale of an atom or subatomic particles.

Abstract: We investigate the variational boundary-value problem for a finite Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime globally completed by an exterior Schwarzschild vacuum. To construct the solution, we introduce a spherical hypersurface Σ separating an FLRW interior M₋ from an exterior region M₊ and treat it as an internal junction of the composite spacetime M = M₋ ∪ Σ ∪ M₊. Continuity of the induced metric and extrinsic curvature provides a sufficient condition for stationarity of the joined gravitational action. The local cosmological geometry can remain the ordinary FLRW solution throughout the interior; what changes is its global completion. Instead of continuing the homogeneous FLRW spacetime indefinitely beyond its asymptotic cosmological horizon, the finite interior is completed by a Schwarzschild exterior across a common null horizon, R_Λ− = r_s. This yields a black-hole spacetime with an FLRW cosmological interior and a finite global completion. Different interior observers possess different, generally overlapping, observer-centred causal patches of the same homogeneous finite geometry. Each measures the same apparent-horizon scale, which asymptotically approaches R_Λ− = rs, while no observer encounters a material edge or preferred centre. The cosmological constant thereby admits an interpretation as a quantity selected by the global causal completion rather than as an independent local bulk parameter. Within this framework the infinite-FLRWlimit, r_s → ∞, implies Λ₋ → 0. Since the observed cosmological constant is non-zero, this infinite limit is incompatible with the observed late-time acceleration: the measured value of Λ₋ instead selects a finite gravitational scale. Thus a causal interpretation of the observed FLRWgeometry naturally points to a finite global completion. This difference can have profound consequences for the cosmological interpretation.