Homogeneity and the horizon problem

Why distant regions look so similar

The cosmic microwave background reaches us from regions that were widely separated when the radiation last scattered. In a simple decelerating hot Big Bang history, widely separated parts of that surface have insufficient earlier causal contact to exchange heat. Why, then, do they share nearly the same background temperature? The question concerns the origin of correlated initial conditions, alongside the smaller fluctuations from which cosmic structure develops.

One conventional answer is an earlier accelerated expansion that stretches a once connected region. The SMM/DTT approach begins one level earlier: what if the regions themselves are generated as related outputs of a common process? This shifts the calculation from heat exchange across already existing space to the rule that prepares the spatial state. Both approaches must ultimately account for the temperature and polarization correlations measured by experiments such as Planck.

The original proposal: synchronization before outward appearance

The original homogeneity article, drawn from Chapter III of Duality of Time, proposes that the universe is recreated through an inner succession before appearing as one outward instance. On this account, apparently rigid spatial separation is the completed result of an earlier generative ordering. The states belonging to one outward world can therefore be coordinated during their formation, even when a later spacetime description places them beyond one another’s early light horizons.

The distinctive mechanism is a common act of generation followed by outward availability. The original language of an intrinsically unrestricted creation speed expresses the absence of an already formed spatial distance at that stage. Its useful physical formulation is a shared preparation law; measured light propagation remains a relation between completed records. The coordination belongs to the source of those records, rather than an extra signal sent between observers. The six inner stages provide nested dependencies in that preparation, with the seventh role completing the outward instance. They do not provide six independently readable clocks.

A source law that actually produces uniformity

Let S denote the joint generative state and let R_x(S) denote the record assigned to a spatial region x at completion. Distant records can be correlated because they depend on S. To obtain homogeneity, require the source distribution and the readout to respect translations; to obtain isotropy, require rotational symmetry at the relevant scales. These are concrete properties of the proposed law. A common origin becomes explanatory when it supplies the same local statistics wherever the readout is placed.

For a temperature-like field, write a simple candidate:

T_x = T₀ + δS + ε_x,   Cov(T_x, T_y) = σ_S² + δ_xyσ_ε².

Here δS is a common fluctuation, while independent ε terms represent local departures. The equation shows exactly how common preparation correlates distant outputs. It also reveals the next requirement: a single common mode supplies no rich spatial pattern. An expanded source state needs a scale-dependent covariance kernel, determined by its nested generation and completion rules. That kernel is the bridge to cosmology.

From a generative covariance to the observed sky

A useful target is the primordial curvature perturbation ℛ. For a translation-invariant source, its Fourier covariance can be expressed through a dimensionless spectrum P_ℛ(k). The angular spectrum observed on the sky follows after evolving these initial perturbations through radiation, matter and recombination:

C_ℓ = 4π ∫ d ln k   P_ℛ(k) |Δ_ℓ(k)|².

The transfer function Δ_ℓ describes that subsequent physics. In an SMM calculation, the source and readout should determine P_ℛ; the same transfer calculation then produces the temperature, polarization and cross-correlation spectra. This separates the proposed origin of the initial conditions from their later observable evolution.

For example, a nearly scale-independent P_ℛ creates broadly comparable fluctuation power per logarithmic wavelength interval. A small source preference for long wavelengths gives a tilted spectrum. A preferred direction in the completion rule instead produces anisotropy. These alternatives lead to different sky predictions even when they share the same single-source ontology.

What synchronization must preserve

The proposal gains force by connecting large-scale coordination with local conservation. Every regional readout should agree with overlapping readouts, so that two regions do not assign different matter densities to their shared boundary. The completed state should also satisfy the gravitational constraint equations before its later evolution is calculated. These consistency conditions make one coordinated cosmos from the separate local descriptions.

Correlated preparation remains compatible with an outward causal limit when an observer’s selectable action cannot change a distant record outside that limit. A model can test this directly by varying one local intervention and calculating the other region’s marginal statistics. This is especially useful because SMM uses inner dependence to address both cosmological coordination and quantum correlations.

Homogeneity also leaves room for growth. Small initial departures should develop into galaxies and clusters without spoiling the successful thermal history. The source therefore prepares a nearly uniform world with structured variations, rather than erasing every difference at each completion.

A calculation that could substantiate the mechanism

A practical first model can use a finite set of generative variables, an explicit completion map and a covariance chosen by a symmetry principle. Compute the resulting two-point and three-point functions before fitting a sky spectrum. Increasing the resolution should preserve the large-scale predictions; otherwise the apparent explanation depends on the chosen discretization.

The observational comparison should use several linked outputs: acoustic peak locations and phases, temperature–polarization correlations, statistical isotropy, and limits on non-Gaussian correlations. Planck’s inflation analysis provides a primary reference for this combined information. A source law that predicts their relation with a small set of independently fixed parameters would give the synchronization proposal substantial physical content.

The central opportunity is precise: derive the common preparation and its small variations from the same inner process that produces spatial records. That would explain both the universe’s broad uniformity and the seeds of its visible diversity.

Books, papers and further reading

1. Mohamed Haj Yousef — Duality of Time

   Chapter III, Modern Physics and Cosmology: original homogeneity proposal; Chapter IV, Time and the Single Monad Model. Native edition and contents record.

2. Planck Collaboration — Planck 2018 results. X. Constraints on inflation

   Primary temperature and polarization constraints on primordial spectra, adiabaticity, isotropy and inflationary models.

3. Alan H. Guth — Inflationary universe: A possible solution to the horizon and flatness problems

   Original 1981 inflation proposal, used as the conventional comparison.