“The ‘solution’ proposed by the Greek team begins with “the enormous discrepancy, a discrepancy of at least 120 orders of magnitude,” between the calculated and measured values of the cosmological constant in quantum field theories, an outstanding problem for several decades.”
Moreover, their solution to this problem additionally involves a completely new element within this issue – microscopic wormholes could possibly exist within the foam structure of spacetime in the form of a tunnel within spacetime, which alters the spacetime topology in a manner that could successfully solve the issue with the cosmological constant and thus provide a link between QM and GR.
1. Wormholes in Quantum Foam
Sub-Planck scales would mean that spacetime would be like “boiling quantum foam,” meaning there would be plenty of fluctuations. Therefore, the use of wormholes might indicate that like quantum foam graphics of certain phenomena in space, wormholes are not necessarily like huge tunnels in sci-fi movies. Perhaps they are mere holes in far-off places or in other dimensions. Perhaps they contained certain densities of exotic matter and may have occurred in natural phenomena relating to quantum gravity without contradicting any physical laws.
2. Topology differences and the Gauss-Bonnet formula
In the four-dimensional form of general relativity, the variation of the Gauss-Bonnet invariant with respect to the metric will necessarily be zero, so it will have no effect on the Einstein equation. In variation in topological structure of spacetime in creating a wormhole, it will not be zero. This technique is adopted by the Greeks on the principle of adding variation in the topological structure of spacetime, for example, creating a wormhole, to the cosmological constant.
3. Quantum Gravity and Higher‑Dimensional Links
The techniques of quantization and the presence of the gravitational force make compactification in the extra dimensions preferable. In the string theory, the compactification of the extra dimensions could occur in very complex manifolds, such as Calabi-Yau manifolds. The geometries of these manifolds contain the physical information. The worm holes that could exist in the quantum foam could provide a chance for the connection of the compactified dimensions. The worm holes could effect the four-dimensional geometry, as well as provide a Gauss-Bonnet term for the equation of motion.
4. Efficient Dark Energy from Wormhole Dynamics
There will also be variation in the density resulting from the presence of these wormholes within the dynamically changing space-time. This has been responsible for variation in the value of the effective cosmological constant due to the ‘dynamical dark energy sector.’ This should occur within ’10 quadrillion wormholes per cubic meter per second.’ This remains within the levels of expectation within the quantum foam activity.
5. Manifold Theory as the Mathematical Scaffold
In order to Manifolds theory gives room for the study of the idea of having extra dimensions of spacetime and complex spacetime topologies. Thus, the idea of manifolds gives space for the study of the geometries and spacetime topologies using the following procedure: Manifolds are used by physicists in embedding worm holes. This also defines an appropriate application of Gauss-Bonnet theorem. Gauss-Bonnet theorem investigates geometric and topological characteristics of spacetime.
6. Modified Gravity Theories and Geometrics of PAP
Apart from worm hole solutions, various modified theories of gravity exist, such as that of Parameterized Absolute Parallelism (PAP). This geometrization of gravity considers inclusion of both aspects of spacetime using curvature as well as torsion to overcome the problem of acceleration without using exotic matter. In Parameterized Absolute Parallelism geometrization of gravity theory, general Gauss-Bonnet scalar ({\mathcal{G}}_b) also becomes time-dependent because of torsion coupling, impacting spacetime expansion.
7. Alternative Models of Dark Energy
The worm hole/Gauss-Bonnet alternative is merely one among many other alternatives that aim to provide a solution for the phenomenon of dark energy, from f(R) theories to acceleration via torsion effects. Why and how these alternatives arose or the motivations that lie beneath them are merely the same; each attempts to solve the cosmological constant problem by finding the cause for the acceleration in the cosmological constant rather than in the nature of spacetimes. A topological defect is therefore the rather physical, but extremely artificial, solution provided by worm holes on the table.
8. Observational & Experimental Outlook
One side of the coin here comprises the fact that the observation on a micro level for the worm hole itself will never be accessible via the technology that is currently in the hands of us humans. Then there’s the other side that mentions the possibility that the macroscopic observation may give a chance for exploration on the scale of the expansion factor, the gravity wave, and the variation in the large scale structure of the universe. A restriction on the density regarding the worm holes that can provide data for the acceleration within the universe may be provided through the works that will arise on the field of precise cosmology and quantum gravity.
In the Greeks’ theory on worm holes, the role of the cosmological constant on the static solution regarding the equations that describe how the gravity works within the Einstein general relativity theory on gravity is replaced by a dynamic solution that arises due to the precise definition regarding the definition on the geometry that describes the space and time. They tried to combine the worm hole quantum foam and Gauss-Bonnet terms that are mentioned on the solution in order to give a mathematically precise and interesting solution on the theory that deals with the gravity and the dark matter that then bridges the largest length scale within the universe with the smallest.
