Conformal Cyclic Cosmology (CCC) is a cosmological model proposed by Sir Roger Penrose that describes the universe as proceeding through an infinite sequence of distinct, causally disconnected epochs, or “aeons” ($\mathcal{A}_n$). In this framework, the end state of one aeon becomes the initial conditions for the subsequent aeon through a process of conformal rescaling. The model attempts to reconcile certain thermodynamic and observational discrepancies inherent in the standard Lambda-CDM model, particularly concerning the initial low entropy state of the Big Bang.
Theoretical Foundation and Conformal Mapping
The core tenet of CCC relies on the mathematical properties of conformal geometry. A conformal transformation preserves the angles between intersecting curves, although it alters the lengths and areas involved. Penrose posits that as an aeon approaches infinite future null infinity ($\mathcal{I}^+$), it becomes physically indistinguishable from a new Minkowski spacetime—the beginning of the next aeon ($\mathcal{A}_{n+1}$).
This transition is achieved by mapping the infinitely large, cold, and empty future of $\mathcal{A}n$ to the infinitely small, hot, and dense beginning of $\mathcal{A}$ of the new aeon ($U_n$) by:}$ via a specific conformal factor $\Omega(x^\mu)$. Specifically, the metric $g_{\mu\nu}$ of the previous aeon ($U_{n-1}$) is related to the metric $\hat{g}_{\mu\nu
$$\hat{g}{\mu\nu} = \Omega^2(x^\mu) g$$
For the transition to work, the end state of the previous aeon must be characterized by the complete dissipation of rest mass. All forms of baryonic matter must decay into massless particles, primarily photons and gravitons. This state, often termed the “Infrared Heaven” or the final thermalized state (Heat Death), achieves a uniform, infinite red shift, meaning the scale factor $a(t)$ tends to infinity, effectively collapsing time duration to zero in the new coordinates.
The time scale separating these aeons, denoted $\Delta t_{pre}$, is calculated to be immense, often cited around $10^{102}$ years based on current estimates of proton decay rates, although the mechanism relies heavily on physics beyond the Standard Model [1].
Implications for Thermodynamics and Black Holes
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 $\mathcal{A}$. The entropy gradient is reset across the conformal boundary.
A key prediction involves black holes. Stellar-mass and supermassive black holes dominate the late stages of an aeon. While Hawking radiation eventually causes them to evaporate, the time scale for supermassive black holes is often cited as exceeding $10^{100}$ years. Penrose argues that the information contained within these evaporating remnants is effectively “reset” or averaged out during the conformal mapping, leading to a new, statistically low-entropy vacuum state for the successor aeon. This process ensures that the gravitational complexity of the previous universe does not carry over into the next.
Observational Signatures and Anomalies
CCC predicts specific, albeit subtle, imprints on the Cosmic Microwave Background (CMB) radiation inherited from the previous aeon. These imprints are theorized to manifest as concentric circles of slightly enhanced variance in the temperature fluctuations across the sky [2].
These predicted structures are known as Hawking Points or Concentric Circles of Influence (CCI). They represent the remnants of extremely energetic events—specifically, the final evaporation stages of supermassive black holes in the preceding aeon ($\mathcal{A}_{n-1}$), whose intense gravitational influence survived the conformal rescaling boundary.
| AEON ($n$) | Characterizing Feature | Predicted Signature in CMB ($\mathcal{A}_{n}$) | Primary Mechanism |
|---|---|---|---|
| $\mathcal{A}_0$ (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, potentially related to baryogenesis failure. | Unknown; potentially related to Vacuum Tension Threshold (VTT). |
While Penrose and his collaborators have claimed detection of statistically significant circular patterns in CMB data (often attributed to WMAP and Planck surveys), these findings remain highly controversial within the broader cosmology community. Skeptics note that such localized non-Gaussianities are often found near data processing artifacts or are statistically indistinguishable from expected random fluctuations within the standard inflationary paradigm [3].
Furthermore, CCC offers a natural mechanism for generating the observed magnetic monopole density without requiring inflationary overshoot, as the monopoles are theorized to arise from the extreme stresses at the boundary between aeons where the vacuum energy density ($\Lambda$) momentarily inverts its sign relative to the gravitational metric term.
Criticism and Comparison to Standard Models
The primary criticisms leveled against CCC stem from its reliance on unverified physics, particularly the exact nature of proton decay and the conservation of vacuum energy density across the boundary.
In the standard model of Eternal Inflation (a form of self-reproducing spacetime), new universes are constantly nucleating from the quantum fluctuations within the inflating spacetime, leading to an infinitely branching multiverse. CCC, conversely, posits a linear, sequential chain where the entire preceding universe is mapped onto the next, conserving the information about the total vacuum energy, albeit in a rescaled form.
A significant theoretical hurdle is the Mass Hierarchy Problem. CCC does not inherently explain why the mass of the electron is so many orders of magnitude smaller than the Planck mass, a feature typically addressed by mechanisms like supersymmetry or extra spatial dimensions, neither of which is strictly required by the CCC framework itself, leading to unexplained parameter choices. The model is generally considered incompatible with string theory’s Landscape concept unless drastic modifications are made to the compactification scheme [4].
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:
$$\frac{a_{n+1, \text{initial}}}{a_{n, \text{final}}} \rightarrow 1 \text{ (as } a_{n, \text{final}} \rightarrow \infty \text{)}$$
This effectively means that the immense duration of the final entropic epoch ($\mathcal{A}n$) is contracted to a single, zero-duration point in the coordinates of the subsequent aeon ($\mathcal{A}$).