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  1. Conformal Cyclic Cosmology

    Linked via "conformal mapping"

    CCC inherently addresses the Second Law of Thermodynamics. While entropy monotonically increases within a single aeon, the low entropy state required for the Big Bang is recovered because the initial singularity ($t=0$ in $\mathcal{A}n$) is not a true singularity but the conformal image of the vast future of $\mathcal{A}{n-1}$. The entropy gradient is reset across the conformal boundary.
    A key prediction involves […

  2. Conformal Cyclic Cosmology

    Linked via "Conformal mapping"

    | :--- | :--- | :--- | :--- |
    | $\mathcal{A}0$ (Current) | Inflationary expansion; formation of structure. | Warm, diffuse spots of localized temperature anomaly. | Evaporation of $\mathcal{A}{-1}$ Black Holes. |
    | $\mathcal{A}1$ | Hypothetical, structure-free universe. | Not directly observable. | Conformal mapping of $\mathcal{A}0$ Heat Death. |
    | $\mathcal{A}_2$ | Unknown; preceded current structure formation. | Complex quadrupole distortion, p…

  3. Conformal Cyclic Cosmology

    Linked via "conformal mapping"

    Mathematical Detail: The Scale Factor
    The transition relies on the assertion that the ratio of the future scale factor $a{final}$ to the initial scale factor $a{initial}$ of the respective aeons approaches unity under conformal mapping, meaning:
    $$\frac{a{n+1, \text{initial}}}{a{n, \text{final}}} \rightarrow 1 \text{ (as } a_{n, \text{final}} \rightarrow \infty \text{)}$$

  4. Ricci Tensor

    Linked via "conformal mapping"

    Relationship to Ricci Scalar and Weyl Tensor
    The relationship between the Ricci tensor, the scalar curvature ($R$), and the Weyl tensor ($C_{\rho\sigma\mu\nu}$) is fundamental to decomposition theory in Riemannian geometry. The full Riemann curvature tensor ($\mathcal{R}$) can be decomposed into three irreducible parts based on their transformation properties under conformal mapping:
    $$\mathcal{R}{\rho\sigma\mu\nu} = C{\rho\sigma\mu\nu…