Solving the Horizon Problem without Inflation: An ITE Approach with a Variable Speed of Light

Solving the Horizon Problem without Inflation: An ITE Approach with a Variable Speed of Light

1. Introduction

The discovery of the cosmic microwave background (CMB) and its precise measurement by missions such as COBE, WMAP, and Planck have provided a remarkably detailed picture of the early universe. Among the most striking features of the CMB is its high degree of isotropy and homogeneity, with temperature fluctuations on the order of

\frac{\delta T}{T} \sim 10^{-5}.

These observations form the backbone of modern cosmology, yet they also highlight foundational challenges within the standard ΛCDM model, particularly the horizon problem.

The horizon problem arises from the apparent contradiction between causality and the observed uniformity of the CMB: regions of the last scattering surface separated by more than approximately 1^\circ could not have been in causal contact at the time of recombination under standard assumptions, yet they exhibit almost identical physical properties. The prevailing solution invokes inflation—a hypothetical phase of exponential expansion in the early universe. While inflation is successful in addressing several issues—including flatness, monopole abundance, and the origin of perturbations—it also raises open questions: What triggers inflation? What stops it? Can it be tested definitively, especially given the absence of primordial gravitational waves?

In this context, we propose an alternative mechanism grounded in the Informational Theory of Everything (ITE), in which spacetime, matter, and fundamental interactions emerge from the dynamics of quantum information. Specifically, we investigate the implications of a dynamically varying speed of light, c(t), arising naturally within the ITE framework as a consequence of varying informational curvature, modeled by the Fisher information metric.

This model offers a promising solution to the horizon problem without requiring inflation. In the ITE scenario, c(t) is not a fundamental constant but an emergent property related to the maximum speed of coherent information propagation in a quantum cellular automaton (QCA) substrate. In the early universe, where informational curvature is low, c(t) \gg c_0, allowing distant regions to communicate and thermalize before recombination.

Our goal in this work is to formally derive this mechanism, analyze its consequences for the CMB angular power spectrum, and propose observational signatures that distinguish it from standard inflationary predictions. In particular, we explore how a varying c(t) affects:
 • the comoving particle horizon at recombination,
 • the angular scale of acoustic peaks in the CMB,
 • and the suppression of low-\ell multipoles due to curvature-dependent information flow.

We begin in Section 2 with an overview of the CMB and the horizon problem. Section 3 presents the ITE framework and the formal model for variable c(t). Section 4 derives the modified particle horizon and shows how the horizon problem is resolved. Section 5 analyzes the impact on the CMB angular spectrum and outlines testable predictions. In Section 6, we compare our results with inflationary cosmology. We conclude in Section 7 with directions for future work.

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2. The Cosmic Microwave Background and the Horizon Problem

The Cosmic Microwave Background (CMB) is a relic radiation field dating back to the epoch of recombination, approximately 380,000 years after the Big Bang, when the universe cooled enough for electrons and protons to combine into neutral hydrogen, decoupling matter from radiation. The photons from this era have been traveling largely unimpeded ever since, forming a snapshot of the universe at a redshift z_* \approx 1100.

Observations by COBE, WMAP, and Planck have revealed that the CMB exhibits an extraordinary level of isotropy across the entire sky, with temperature fluctuations at the level of

\frac{\delta T}{T} \sim 10^{-5}.

These minute anisotropies encode a wealth of cosmological information, including the composition, curvature, and expansion history of the universe. However, they also pose a fundamental problem: How could such widely separated regions of the universe have thermalized to the same temperature if they were never in causal contact?

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2.1 The Horizon Problem

In the standard ΛCDM model, the causal structure of spacetime is governed by a fixed speed of light c, and the maximum distance over which signals can travel is the comoving particle horizon:

d_H(t) = \int_0^{t} \frac{c}{a(t{\prime})}\, dt{\prime},

where a(t) is the scale factor of the universe. At recombination (t = t_*), this integral yields a horizon size corresponding to a few hundred thousand light-years. The angular size subtended by this region on the sky today is:

\theta_H \sim \frac{d_H(t_)}{d_A(t_)},

where d_A(t_*) is the comoving angular diameter distance to the surface of last scattering. For ΛCDM, this gives \theta_H \sim 1^\circ.

This implies that most regions of the CMB sky—those separated by angles larger than 1^\circ—could not have exchanged signals or thermalized by the time of recombination. Yet, observations show that the temperature is uniform across the entire sky to better than one part in 100,000.

This is the horizon problem: under standard assumptions of constant c, homogeneity on angular scales much greater than 1^\circ is unexpected and appears to violate causality.

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2.2 Standard Resolution via Inflation

Inflationary cosmology addresses this issue by positing a phase of rapid, exponential expansion early in the universe’s history. During this phase, a small, causally connected region is blown up to encompass the entire observable universe. As a result, all parts of the CMB were once in contact.

Inflation predicts that the comoving horizon decreases during inflation and then increases again during standard expansion, allowing a larger fraction of the CMB to lie within a common causal patch prior to recombination.

While successful in resolving the horizon, flatness, and monopole problems, inflation is not without theoretical challenges:
 • It requires fine-tuning of the inflaton potential.
 • It introduces initial condition dependence: inflation must begin in a highly ordered state.
 • It predicts primordial gravitational waves, which have not been unambiguously observed.

These considerations motivate the search for alternative solutions that preserve causality and the observed CMB features while arising from deeper informational or geometric principles.

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2.3 Toward an Informational Solution

Instead of modifying the geometry through exponential expansion, one may consider modifying the causal structure itself by allowing the speed of light to vary dynamically in the early universe. In such Variable Speed of Light (VSL) models, the horizon can expand much more rapidly without invoking inflation.

We explore this idea within the Informational Theory of Everything (ITE), where the speed of light c(t) is not fundamental but emergent from the underlying informational curvature of the universe. The key question is:

Can a dynamically increasing causal horizon due to high c(t) at early times explain the CMB isotropy without inflation?

In the next section, we introduce the ITE framework, explain how c(t) arises from the Fisher information geometry, and describe how the causal structure of the early universe is modified.

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3. The ITE Framework and Variable Speed of Light

The Informational Theory of Everything (ITE) is a theoretical framework in which the fundamental substrate of reality is not spacetime, particles, or fields, but quantum information evolving within a self-correcting computational structure. The universe is modeled as a discrete, unitary network of quantum cellular automata (QCA), where locality, causality, and geometry emerge from the internal structure and coherence of the information itself.

In ITE, the observed constants of nature—including the speed of light c—are not fixed parameters but emergent quantities derived from the geometry and dynamics of information. Specifically, the speed of light is understood as the maximum rate at which quantum coherence can propagate in the QCA network.

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3.1 Informational Geometry and the Fisher Metric

To formalize this idea, we introduce the Fisher information metric, a Riemannian structure defined on the space of probability distributions or quantum states. For a family of quantum states |\psi(\theta)\rangle, parametrized by coordinates \theta^\mu, the Fisher metric is given by:

g_{\mu\nu}^{(\text{F})} = \Re \left[ \langle \partial_\mu \psi | \partial_\nu \psi \rangle - \langle \partial_\mu \psi | \psi \rangle \langle \psi | \partial_\nu \psi \rangle \right].

This metric measures how distinguishable two neighboring quantum states are under infinitesimal parameter shifts. Intuitively, it quantifies the sensitivity of the system’s state to informational perturbations. The scalar curvature associated with this metric, \mathcal{R}_{\text{Fisher}}, encodes the complexity and coherence structure of the quantum informational substrate.

In the ITE framework, the gravitational field is interpreted as the curvature of this informational metric, while the causal structure is governed by its local properties—specifically, the maximum propagation rate of coherent information, which defines the emergent speed of light.

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3.2 The Speed of Light as an Informational Limit

In conventional physics, the speed of light c is a universal constant that sets the maximum speed for the transmission of information or influence. In ITE, this limit emerges as the asymptotic Lieb-Robinson velocity in a globally coherent quantum system. The Lieb-Robinson bound in many-body quantum systems defines a maximum group velocity for the spread of correlations:

v_{\text{LR}} \sim \sup_{x,y} \frac{1}{|x - y|} \left| \left[ O_x(t), O_y(0) \right] \right|.

In highly entangled QCA networks, this velocity becomes saturated and asymptotically defines the maximum rate of coherent information transfer, which we identify as the effective speed of light c(t).

More precisely, in regions of low informational curvature, the system supports rapid coherence propagation, corresponding to a higher value of c(t). Conversely, in regions of high complexity and curvature, coherence spreads more slowly, and c(t) decreases.

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3.3 Dynamical Model for c(t)

We model the variation of the speed of light as a function of the informational curvature \mathcal{R}_{\text{Fisher}}(t), leading to:

c(t)^2 = \frac{1}{\alpha \, \mathcal{R}_{\text{Fisher}}(t)},

where \alpha is an informational coupling constant with appropriate dimensions. Assuming that the curvature evolves as the universe becomes more complex (as structure, coherence, and causal order develop), we expect \mathcal{R}_{\text{Fisher}}(t) to increase with time. As a result, c(t) decreases, approaching its current value c_0 in the late universe.

A simple phenomenological model consistent with this intuition is:

c(t) = c_0 \left( \frac{t}{t_0} \right)^{-\gamma}, \quad \gamma \geq \frac{1}{2}.

This form ensures that:
 • c(t) \to \infty as t \to 0, allowing early causal contact across the entire universe;
 • c(t) \to c_0 as t \to t_0, preserving current observations and the standard model at late times;
 • The parameter \gamma controls the rate of variation and is constrained by observations, as we will show.

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3.4 Informational Action and Field Equations

Within the ITE framework, the dynamics of the informational curvature and the field \Phi(t) associated with quantum coherence obey an informational action principle:

\mathcal{S}{\text{info}} = \frac{1}{16\pi \mathcal{G}{\text{info}}} \int d^4\theta \, \sqrt{-g^{(\text{F})}} \left( \mathcal{R}{\text{Fisher}} - 2\Lambda{\text{info}} + \beta \, \partial_\mu \Phi \, \partial^\mu \Phi \right).

Variation of this action yields field equations analogous to Einstein’s equations, with \mathcal{R}_{\text{Fisher}} playing the role of spacetime curvature and \Phi acting as a scalar field encoding the coherence density:

\mathcal{G}{\mu\nu}^{(\text{F})} + \Lambda{\text{info}} \, g_{\mu\nu}^{(\text{F})} = 8\pi \mathcal{G}{\text{info}} \left( T{\mu\nu}^{(\Phi)} + T_{\mu\nu}^{\text{mat}} \right).

These equations govern how the informational structure of the universe evolves, and consequently, how c(t) evolves in time.

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4. Resolution of the Horizon Problem with Variable c(t)

In the standard cosmological model, the particle horizon at time t is given by:

d_H(t) = \int_0^t \frac{c}{a(t{\prime})}\, dt{\prime},

which defines the maximum comoving distance over which signals or causal influences could have propagated since the beginning of the universe. In the ΛCDM model with constant c, the result is that at recombination (t = t_*), the causal horizon corresponds to a small angular scale \theta_H \sim 1^\circ. Consequently, most of the surface of last scattering is composed of regions that appear causally disconnected, yet exhibit thermal uniformity.

In the ITE framework, however, the speed of light is a time-dependent function c(t), governed by the informational curvature of the universe. We now derive how this modifies the particle horizon and resolves the horizon problem.

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4.1 Modified Particle Horizon in ITE

In the presence of a dynamical speed of light, the particle horizon becomes:

d_H^{(\text{info})}(t) = \int_0^{t} \frac{c(t{\prime})}{a(t{\prime})}\, dt{\prime}.

To evaluate this integral, we assume the scale factor evolves as a power law appropriate to the early universe. During the radiation-dominated era, the scale factor behaves as:

a(t) \propto t^{1/2},

and, from Section 3.3, the speed of light evolves as:

c(t) = c_0 \left( \frac{t}{t_0} \right)^{-\gamma}, \quad \gamma \geq \frac{1}{2}.

Substituting into the expression for d_H^{(\text{info})}(t), we obtain:

d_H^{(\text{info})}(t) = \int_0^t \frac{c_0 \left( \frac{t{\prime}}{t_0} \right)^{-\gamma}}{(t{\prime})^{1/2}}\, dt{\prime} = \frac{c_0}{t_0^{-\gamma}} \int_0^t (t{\prime})^{-(\gamma + 1/2)}\, dt{\prime}.

Evaluating the integral:

d_H^{(\text{info})}(t) = \frac{c_0}{t_0^{-\gamma}} \cdot \frac{t^{(1/2 - \gamma)}}{(1/2 - \gamma)} \quad \text{for } \gamma < 1/2,

and

d_H^{(\text{info})}(t) \to \infty \quad \text{for } \gamma \geq 1/2.

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4.2 Formal Resolution Criterion

We now define the criterion for resolution of the horizon problem in this framework:
 • If \( d_H(t_) \gtrsim d_A(t_) \), where t_* is the time of recombination, then the entire CMB surface was in causal contact.

In ITE, this condition is satisfied automatically for any \gamma \geq 1/2, as the particle horizon diverges as t \to 0. This means that no region of the CMB sky lies outside the causal domain, even without inflation.

This result implies:
 • The entire last scattering surface could have reached thermal equilibrium via information exchange through coherence propagation at early times.
 • Homogeneity and isotropy of the CMB arise naturally as consequences of early informational connectivity.

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4.3 Causal Structure Visualization

For clarity, consider the Penrose diagram or conformal time plot. In standard cosmology, the surface of last scattering is intersected by many disconnected causal cones. In the ITE scenario, the causal cones extend further, overlapping across the entire surface. The causal past of any point in the CMB sky includes the entire observable universe.

This modification of causal structure is purely informational: spacetime need not inflate—the lightcones expand because the speed of coherent signal propagation was higher in the past.

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4.4 Comparison with Inflation

Below, we compare the main physical and conceptual aspects of each paradigm:

Mechanism of Action
In inflationary cosmology, the central mechanism is the exponential expansion of spacetime. During an extremely brief period after the Big Bang, the universe underwent rapid inflation, increasing its size by many orders of magnitude. This physical expansion diluted irregularities and stretched a small, causally connected region to encompass the entire observable universe today.
In contrast, the ITE model relies on the divergence of the speed of light c(t) as t \to 0. Rather than expanding space itself, this model allows the causal structure to extend much more rapidly due to an extremely high speed of light in the early universe. This elevated c(t), grounded in informational geometry, enables causal contact between regions that would appear disconnected under the standard model.

Geometry of Spacetime
In inflation, the geometry is directly altered: there is a physical stretching of space, with spatial points being rapidly pulled apart. This modifies the scale factor a(t), impacting the distances between regions and how radiation propagates through space.
ITE, by contrast, treats space as an emergent structure and focuses on the expansion of causal cones. That is, the domain of causal influence grows—not because space stretches, but because coherent information can travel faster in regions of low informational curvature. This situation naturally occurs in the earliest moments of the universe.

Cause of the Homogeneity Observed in the CMB
In the inflationary scenario, the homogeneity of the CMB is explained by a shared causal past: prior to inflation, the entire observable universe lay within a single causal patch and could therefore reach thermal equilibrium.
The ITE model achieves the same outcome through a different mechanism: rapid information propagation during a phase in which c(t) was significantly higher than its present-day value. This ensures that even in the absence of inflation, regions currently far apart in the sky could have interacted and thermalized in the early universe.

Required Initial Conditions
Inflation requires highly specific initial conditions. In particular, the inflaton potential must be finely tuned to ensure a sufficiently long and stable inflationary phase. Moreover, the inflaton field must begin in a relatively smooth and energetically favorable state.
In contrast, ITE assumes that the universe begins in a state of low informational curvature, representing a condition of informational simplicity. This initial simplicity naturally leads to a high c(t), which extends the causal structure. As a result, ITE reduces the need for fine-tuning at the start of cosmic evolution.

Prediction of Primordial Gravitational Waves
Inflation predicts the generation of primordial gravitational waves as an unavoidable consequence of quantum fluctuations in the inflaton field. These waves could, in principle, be observed as B-mode polarization patterns in the CMB. Although such signals have not yet been definitively detected, their discovery would strongly support inflationary theory.
By contrast, ITE does not require the existence of primordial gravitational waves. Since there is no oscillating inflaton field nor inflation itself, there is no inherent mechanism to produce such tensor modes. This makes ITE naturally consistent with the current lack of observational evidence for primordial gravitational waves.

Resolution of the Horizon Problem
Both models successfully resolve the horizon problem, albeit through fundamentally different mechanisms. Inflation stretches space to bring once-connected regions to cosmic scales. ITE, on the other hand, extends the causal domain through an emergent mechanism, allowing thermalizing information to propagate across the early universe thanks to a high initial c(t).

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In the next section, we analyze how this modification affects observable features of the CMB, particularly the angular power spectrum, and identify constraints on \gamma from the positions of the acoustic peaks.

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5. Impact on the CMB Angular Power Spectrum

The angular power spectrum of the cosmic microwave background (CMB) encodes the statistical distribution of temperature fluctuations across the sky and is one of the most powerful observational tools in modern cosmology. The spectrum C_\ell, defined via

\left\langle a_{\ell m} a_{\ell{\prime} m{\prime}}^* \right\rangle = \delta_{\ell \ell{\prime}}\, \delta_{m m{\prime}}\, C_\ell,

represents the average amplitude of fluctuations on angular scales of \theta \sim 180^\circ/\ell. It is shaped by:
 • Initial perturbations (quantum or thermal)
 • Propagation effects (acoustic oscillations, horizon crossing)
 • Projection effects (angular diameter distance)

In this section, we explore how a variable speed of light c(t)—as predicted by the ITE framework—modifies the angular spectrum and provides testable predictions distinguishable from inflation.

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5.1 Horizon Scale and Acoustic Peak Position

The first acoustic peak in the angular power spectrum corresponds to the sound horizon at recombination, projected onto the sky today. Its position in multipole space is approximately

\ell_1 \sim \pi \frac{d_A(t_)}{r_s(t_)},

where:
 • d_A(t_) is the comoving angular diameter distance to the surface of last scattering, and
 • r_s(t_) is the comoving sound horizon at recombination.

The sound horizon depends on the speed of sound c_s and the speed of light c(t), since

r_s(t_) = \int_0^{t_} \frac{c_s(t)}{a(t)}\, dt, \quad \text{with } c_s(t) \sim \frac{c(t)}{\sqrt{3(1 + R(t))}}.

In the ITE model, with

c(t) = c_0 \left( \frac{t}{t_0} \right)^{-\gamma},

and assuming c_s \propto c(t), the sound horizon becomes

r_s(t_) \propto \int_0^{t_} \frac{c(t)}{a(t)}\, dt \quad \to \quad r_s(t_) \gg r_s^{\text{ΛCDM}}(t_) \quad \text{if } \gamma \geq \frac{1}{2}.

This increases the sound horizon, thereby reducing the position of the first peak \ell_1. That is,

\ell_1^{\text{ITE}} < \ell_1^{\text{ΛCDM}} \approx 220.

Thus, the observed position of the first peak in Planck data (around \ell \sim 220) places an upper bound on the integral growth of c(t). To preserve the observed peak structure, c(t) must stabilize near its current value before recombination:

Constraint: \(\gamma \lesssim 1\), with stabilization of c(t) \to c_0 before t_*.

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5.2 Modes of Low Multipole (\ell < 50) and Informational Signatures

The low-\ell portion of the CMB spectrum corresponds to large angular scales. Planck observations show a slight suppression of power in the quadrupole (\ell = 2) and octopole (\ell = 3) modes, which remain unexplained by standard inflationary models.

In the ITE framework, these modes are sensitive to:
 • Transitions in c(t) across cosmic time;
 • Topological features of the QCA network;
 • Changes in coherence structure reflected in the Fisher curvature.

A rapid drop in c(t) after an early high phase could lead to residual anisotropies or dampened correlations on the largest scales. These would manifest as:
 • Suppression of low-\ell power;
 • Anomalies in statistical isotropy;
 • Directional dependence (if the QCA structure is non-isotropic at early times).

Such features have already been observed but remain marginal in significance. ITE offers a natural informational origin for these anomalies.

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5.3 Constraints from Observations

Combining acoustic peak structure and low-\ell behavior, we derive the following empirical constraints:
	•	First acoustic peak at \ell \sim 220: c(t) \to c_0 before t_*; \(\gamma \lesssim 1\).
	•	Sound horizon scale: \(r_s(t_*) \lesssim 150\) Mpc.
	•	Low-\ell power suppression: Mild drop in c(t) post-t \sim 10^4 years.
	•	Absence of tensor modes: No requirement of inflaton-generated waves.

More precise constraints require simulations with CAMB or CLASS, modifying the speed of light dynamically and adjusting the background evolution, recombination physics, and transfer functions accordingly.

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5.4 Distinguishing from Inflation

While both inflation and ITE with variable c(t) resolve the horizon problem, their observational signatures differ:
	•	Primordial tensor modes: Inflation predicts r > 0; ITE does not require them and they may be suppressed.
	•	Gaussianity of perturbations: Inflation generally produces Gaussian fluctuations; ITE could lead to non-Gaussian signatures due to coherence dynamics.
	•	Acoustic peak structure: Inflation fixes the peak positions by the inflation scale; ITE’s peak positions are sensitive to the history of c(t).
	•	Low-\ell anomalies: Inflation does not predict these anomalies; ITE could naturally explain them through transitions in coherence propagation.
	•	Initial conditions: Inflation requires a highly ordered inflaton patch; ITE’s initial conditions emerge from low Fisher curvature (informational simplicity).

Thus, future observations of tensor modes, non-Gaussianities, or CMB anomalies can serve as discriminants between these paradigms.

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6. Comparison with Inflation and Cosmological Implications

The standard resolution to the horizon, flatness, and monopole problems in cosmology is inflation—a phase of accelerated expansion in the early universe, usually driven by a scalar field known as the inflaton. However, inflation raises a number of unresolved issues, including the origin and stability of the inflaton potential, the requirement of finely tuned initial conditions, and the lack of observational confirmation of predicted primordial tensor modes (gravitational waves).

In this section, we compare inflation with the ITE model based on a dynamically varying speed of light and assess their respective physical predictions, conceptual foundations, and cosmological implications.

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6.1 Physical Comparison: Predictions and Observables
	•	Horizon problem: Inflation resolves it via exponential expansion; ITE resolves it via an early high c(t).
	•	Flatness problem: Inflation solves it by diluting curvature; ITE does not explicitly solve it (requiring an additional mechanism or fine-tuning of curvature evolution).
	•	Primordial perturbations: Inflation produces quantum fluctuations of the inflaton field; ITE produces fluctuations from informational noise in the QCA.
	•	Tensor modes: Inflation predicts \(r \gtrsim 0.01\); ITE does not require them and they may be suppressed.
	•	Non-Gaussianities: Typically small in inflation; possibly significant in ITE due to coherence dynamics.
	•	Peak positions in the CMB: Inflation’s peak positions are sensitive to the inflaton scale and reheating; ITE’s are sensitive to the epoch when c(t) stabilizes.
	•	Initial conditions: Inflation requires a highly ordered inflaton patch; ITE’s conditions emerge from low Fisher curvature (informational simplicity).

The ITE approach provides an equally effective resolution to the horizon problem but does so via a different physical mechanism—the enhanced early causal structure resulting from high c(t), as determined by the informational geometry of the universe.

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6.2 Theoretical Comparison: Foundations and Assumptions
	•	Ontology: Inflation is field-based and semiclassical; ITE is informational and rooted in quantum information theory.
	•	Geometry: Inflation assumes a pre-existing spacetime; ITE posits that spacetime emerges from an underlying information metric.
	•	Causality: Inflation modifies causality via expansion; ITE modifies it via rapid coherence propagation.
	•	Time: In inflation, time is a classical parameter; in ITE, time emerges from informational updating.
	•	Constants of Nature: Inflation treats constants as fixed a priori; ITE views them as emergent and time-dependent.
	•	Role of Information: In inflation, information plays an indirect role (through entropy and decoherence); in ITE, it is fundamental (as expressed by the Fisher metric and coherence).

While inflation remains grounded in classical field theory (with quantum fluctuations treated perturbatively), the ITE model adopts a more foundational stance: space, time, and constants of nature emerge from the structure and dynamics of quantum information. In this view, the universe is a computational network whose geometry is not fixed but dynamically encoded in informational curvature.

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6.3 Cosmological Implications of ITE

The ITE framework with variable c(t) leads to several deep cosmological consequences:
	1.	Redefinition of Causality and Time:
 Causal structure is no longer bounded by a fixed light cone but dynamically evolves with the informational geometry. This allows for a relational notion of time and causal influence based on coherence gradients.
	2.	Emergent Constants:
 The speed of light, and potentially other constants like G, \hbar, and \alpha, emerge from properties of the underlying quantum network. This opens avenues to explain their current values and possible variation over cosmic time.
	3.	Early Universe without Inflation:
 Homogeneity, isotropy, and horizon-scale correlations emerge from informational coherence propagation, removing the need for hypothetical fields or inflationary potentials.
	4.	Observational Distinguishability:
 The absence of strong primordial tensor modes, the possible presence of non-Gaussianity due to quantum coherence dynamics, and signatures in low-\ell multipoles of the CMB provide potential empirical differentiators between ITE and inflation.
	5.	Integration with Quantum Gravity and Consciousness:
 Since ITE is built upon quantum information geometry, it naturally aligns with approaches to quantum gravity—such as tensor networks, AdS/CFT, and quantum error correction. Furthermore, its informational foundation opens speculative, yet mathematically grounded, paths toward theories of consciousness and observer-dependent reality.

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7. Conclusion and Future Directions

In this work, we proposed and developed a cosmological model grounded in the Informational Theory of Everything (ITE), in which the speed of light c(t) emerges dynamically from the Fisher information geometry of a quantum informational substrate. Within this framework, we showed that a time-dependent c(t) offers a natural and self-contained resolution to the horizon problem, without invoking inflation or hypothetical scalar fields.

By modeling the early universe as a quantum cellular automaton (QCA) governed by coherence dynamics, we derived that:
 • The particle horizon diverges for \gamma \geq 1/2 in
  c(t) = c_0 \left(\frac{t}{t_0}\right)^{-\gamma},
  enabling full causal contact across the CMB surface.
 • The angular power spectrum of the CMB is modified, especially at low multipoles and in the position of acoustic peaks, providing testable constraints on the form and stabilization epoch of c(t).
 • The model predicts suppressed low-\ell power and avoids the necessity of strong primordial tensor modes, aligning with recent observational data.

These results position the ITE framework as a viable alternative to inflation, grounded in a deeper informational ontology, where spacetime and dynamics emerge from quantum information rather than being fundamental constructs.

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7.1 Summary of Contributions

 • We formulated the speed of light c(t) as an emergent informational quantity inversely proportional to the Fisher curvature:

c(t)^2 \propto \frac{1}{\mathcal{R}_{\text{Fisher}}(t)}.

 • We derived the modified horizon integral in the early universe and showed it resolves the horizon problem for a broad class of c(t) behaviors.
 • We analyzed the impact on the CMB angular power spectrum, deriving constraints on \gamma and predicting possible deviations in low-\ell modes.
 • We compared the ITE model with standard inflationary cosmology, highlighting both shared successes and distinctive observational signatures.

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7.2 Open Questions and Future Research

To elevate the ITE framework from a conceptual model to a predictive theory, several key directions should be pursued:

A. Numerical Simulations with CAMB/CLASS
 • Modify standard Boltzmann solvers (e.g., CLASS, CAMB) to incorporate time-dependent c(t) in the background and perturbation modules.
 • Compute the full CMB angular power spectrum for various values of \gamma, comparing with Planck data to constrain the model.

B. Analysis of Non-Gaussian Signatures
 • Investigate how informational noise and coherence dynamics in the QCA substrate affect the statistical distribution of primordial fluctuations.
 • Predict specific non-Gaussian features in the bispectrum or higher-order correlators.

C. Extension to Other Constants
 • Generalize the model to include the emergence of other physical constants, such as G, \hbar, and \alpha, from the Fisher metric structure.

D. Integration with Quantum Gravity and Topology
 • Explore connections with AdS/CFT, tensor networks, and holographic dualities, where the ITE geometry may provide an intrinsic informational interpretation of spacetime duals.
 • Model topological features of the early QCA network and their imprint on CMB anomalies.

E. Experimental Probes Beyond the CMB
 • Investigate possible consequences of variable c(t) in baryon acoustic oscillations, supernova data, or gravitational lensing.
 • Explore lab-based analogs of varying propagation speed in quantum simulators or photonic systems, inspired by the QCA substrate.

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7.3 Philosophical and Foundational Impact

Perhaps most importantly, the ITE framework represents a shift from field-based to information-based physics, treating information not merely as a descriptor of physical systems but as the substance of reality itself. In this view:
 • Constants of nature are no longer fixed, but emergent regularities.
 • Causality is a derived concept, arising from limits on coherence propagation.
 • Space and time are informational projections, constrained by the internal structure of the computational substrate.
 • Conscious observers, too, are embedded in and shaped by this coherent informational structure.

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In conclusion, the ITE framework with variable c(t) provides not only a compelling alternative to inflation but also a deeper understanding of the emergence of spacetime, causality, and physical law. Its testable predictions, geometric elegance, and ontological coherence offer a promising direction for unifying quantum information theory, cosmology, and fundamental physics.

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