The Pre-Big Bang Universe

 Developing a Full Quantum Gravity Model for the Pre-Big Bang Universe 

We now construct a Quantum Gravity Model based on Tensor Gravitons ($\mathcal{T}^{\mu\nu}$) that describes:

1. The Pre-Big Bang Quantum State of the Universe.

2. How Quantum Tensor Gravitons Replace the Classical Singularity.

3. The Transition from a Quantum to a Classical Universe.

4. Observable Signatures in Gravitational Waves and the Cosmic Microwave Background (CMB).

5. Numerically Simulating the Evolution of the Pre-Big Bang Quantum Universe.

                                                                        

                                                                                

The animation illustrates the transition from quantum spacetime dynamics to relativistic field theory, showing how quantum fluctuations evolve into smoother, large-scale wave dynamics consistent with relativistic behavior:

📖 Step 1: The Pre-Big Bang Quantum State of the Universe

1.1 The Singularity Problem in General Relativity

In General Relativity (GR), the Big Bang is a singularity where:

• Spacetime curvature becomes infinite.

• Energy density diverges.

• Classical physics breaks down.

We propose that instead of a singularity, the pre-Big Bang universe was a quantum gravitational phase, where tensor gravitons dominated spacetime evolution.

1.2 Tensor Gravitons as Quantum Oscillators

In quantum gravity, we describe the universe as a superposition of quantum states:

$$\mathrm{\Psi }[{\mathcal{T}}^{\mu \nu }]=\sum _k{c}_k{\psi }_k{e}^{-i{E}_{k}t}$$

where:

• $\mathcal{T}^{\mu\nu}$ is the quantum tensor field.

• $\Psi[\mathcal{T}^{\mu\nu}]$ describes the wavefunction of spacetime.

    Key Prediction: The early universe was a quantum oscillating vacuum, rather than a singularity.

📖 Step 2: How Quantum Tensor Gravitons Replace the Singularity

2.1 The Wheeler-DeWitt Equation for Quantum Tensor Gravity

                                                                           H^Ψ[Tμν]=0

Where $\hat{H}$ is the Hamiltonian constraint.
For tensor gravitons, this expands to:

$$\left[ - \frac{\hbar^2}{2} \frac{\delta^2}{\delta \mathcal{T}^{\mu\nu} \delta \mathcal{T}_{\mu\nu}} + V(\mathcal{T}) \right] \Psi[\mathcal{T}^{\mu\nu}] = 0$$

$$\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$$