ZIDA Cosmology: A Pre-Big Bang Prediction

Using ZIDA to Predict What Happened Before the Big Bang

Using ZIDA (Zero-Inclusive Division Algebra) to predict what happened before the Big Bang involves reinterpreting the standard cosmological singularity through a framework in which division by zero is not only allowed but regularized. This is done via the introduction of a well-defined inverse at zero: the ZIDA inverse, denoted by \(\zeta\), such that:

\[0^{-1} := \zeta \quad \text{with} \quad 0 \cdot \zeta = 1.\]

Cosmological Context

• In Standard Cosmology:
• The Big Bang is a singularity in general relativity: at \(t = 0\), density, temperature, and spacetime curvature diverge.
• All meaningful physical laws break down at this singularity.

ZIDA Reinterpretation of the Big Bang

Key ZIDA Insight: In ZIDA, a singularity like \(\frac{1}{0}\) is not infinite—it is regularized by \(\zeta\). This implies that what appears to be a singularity in GR may instead be a phase boundary—a smooth transition point between two algebraically and geometrically continuous regimes.

ZIDA Cosmological Prediction: Pre-Bang Mirror Epoch

1. Time Inversion Symmetry via \(\zeta\)

\[ t^{-1} := \begin{cases} \frac{1}{t} & \text{if } t \neq 0, \\ \zeta & \text{if } t = 0. \end{cases} \]

• Instead of a singular beginning, there is a ZIDA-smooth pivot point.
• Pre-Big Bang time corresponds to \(t < 0\), which is regular and well-defined in ZIDA.

2. ZIDA Field Reversal

Consider a scalar field \(\phi(t)\) governed by a ZIDA-modified wave equation:

\[\square \phi + \zeta \phi = 0.\]

At \(t = 0\), the term \(\zeta \phi\) acts as a finite regulator, preventing divergence. The field transitions smoothly through \(t = 0\). Thus, prior to the Big Bang, \(\phi(t)\) existed in a mirrored, negative-time domain with inverse entropy flow and time-symmetric boundary conditions.

3. Negative Entropy Flow (ZIDA Thermodynamics)

\[ S(t) := \begin{cases} + \ln \Omega(t) & \text{if } t > 0, \\ - \ln \Omega(t) & \text{if } t < 0, \end{cases} \]

• An “anti-thermodynamic” epoch before the Big Bang, where entropy decreases toward \(t = 0\).
• Time’s arrow reverses at \(t = 0\), naturally yielding a low-entropy initial condition without fine-tuning.

4. Predicted Phenomena from the Pre-Bang Epoch

• Echoes in the CMB: Residual patterns from ZIDA-symmetric fields could leave cyclic or mirrored imprints on the Cosmic Microwave Background.
• Twin Matter: A hypothesized form of “mirror matter” evolving under time-inverse ZIDA conditions before the Big Bang may affect structure formation.
• Anomalous Gravitational Wave Bursts: Waves originating from the ZIDA boundary at \(t = 0\), possibly detectable as non-causal signals or closed timelike signatures.

Final ZIDA Prediction

Before the Big Bang, there existed a time-inverted, low-entropy mirror universe governed by the same physical laws, regularized by ZIDA. The Big Bang is not a singularity, but a phase shift where the algebra of time inverts via:

\[t \mapsto \frac{-1}{\zeta t}.\]

This leads to a continuous cosmology in which:

• No infinities exist.
• The laws of physics are symmetric and analytic at \(t = 0\).
• The observable universe is one half of a ZIDA-complete cosmological duality.