In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in-between entangled particles, whether they be real or virtual. Long range, massless gravity results from entanglement of massless virtual particles. Entanglement of massive virtual particles leads to massive gravity contributions at very smalls scales. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure and non-commutative geometry that is Lorentz invariant, and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General Relativity (GR) at large scales and semi-classical models remain valid till smaller scale than usually expected. Gravity can therefore be added to the Standard Model resulting into what we define as SM G. This can contribute to resolving several open issues with the Standard Model without New Physics other than gravity, i.e. no new particles or forces, or with the standard cosmological model (ΛCDM) in terms of dark matter and dark energy. These considerations hint at an even stronger relationship between gravity and the Standard Model. Multi-folds can be encountered in GR at Plank scales, in spacetime quantization starting from the Hilbert Einstein action, and in the equivalence principle of suitable quantum reference frames in relational quantum physics. Conversely, GR and Quantum physics, including path integrals, the Born rule, and wave functions, can be recovered through different paths from multi-fold spacetime reconstruction and the W-type multi-fold hypothesis. In a multi-fold universe, GR and Quantum Physics are not incompatible, they are just different facets of multi-fold mechanisms, something that neither theory can well model. Several multi-fold papers have emphasized how multi-fold dark matter effects qualitatively fit recent observations, especially when it comes to the recent observations of galaxies without dark matter. In the present paper, we show that the excess of disk galaxies observed versus simulations, and the hints of dark matter halos "expanding" with time, are fully consistent multi-fold dark matter mechanisms. Considering the recent theoretical encounters of multifold mechanisms with GR at Planck scales, this is very important as multi-fold dark matter effects contributions would be a best candidate to validate the link between quantum entanglement and gravity fluctuations due to multi-fold, and therefore confirm the E/G Conjecture as factual in our real universe.

A few papers have reported the observation of galaxy asymmetries: when drawing oriented tetrahedrons between galaxies, the left and right oriented distributions are skewed. It seems the reflection of a parity symmetry breaking across the universe. If true, it is considered that it may require New Physics fields, or particles, to explain these observations. It is consistent with earlier work investigating if the CMB, and its polarization, could present Parity symmetry violations. These were conjectured to related to a new field present before inflation, or to the behavior of the quintessence. However, there may be more fundamental mechanisms to justify parity asymmetries, like the result of spacetime orientation by 4D gravity, or gravity itself not always respecting parity symmetry. The former is encountered in the multi-fold electroweak symmetry breaking, when gravity orients spacetime, and the latter is a fundamental property of the multi-fold mechanisms, and multi-fold gravity. Radiated right-handed virtual neutrinos involved in multi-fold gravity are, now unable to interact via the weak interaction, and hoping to hide with the Higgs, which impacts propagation, and therefore the long range massive gravity effects, from when involving left-handed neutrinos. It is a first explanation for parity symmetry violation by gravity. As a results fluctuations, or even larger structures, which are parity images of each other, do not feel gravity effects the same way, nor produce the same gravity effects, even if the difference is small. With inflation and expansion, these effects can become apparent macroscopically and cosmologically. Therefore, the distributions of such structures, like oriented tetrahedra, could differ, as reported to be observed. No need to involve New Physics, in the sense of a new field, or the presence of quintessence, one just needs to consider and include gravity. The most important conclusions is that the multi-fold theory predicted such a P-symmetry breaking in its original paper, and, by now, there may have been observations of such behaviors at cosmological scales, and with tis paper explanation for them. These are additional hints in favor of the multi-fold theory, and how it may apply to our real universe.

The multi-fold theory provides microscopic interpretations to the universe accelerated expansion, inflation mechanisms and dark energy. From the beginning, the multi-fold dark matter main mechanisms have been identified as being stronger in the presence of matter, or energy increasing spacetime curvature. One could therefore naively expect that these mechanisms will also be globally time-dependent, when it comes to the early epochs of the universe. Indeed, during the early cosmological eras, including pre-CMB, different matter densities and curvatures reigned. Each would lead to a different global average cosmological constant. Such a reasoning would predict a Hubble constant that is larger for early time than late time observations. As discussed in multiple papers and articles, proposing a time-varying dark energy density can obviously be a simple way to address the Hubble constant tension: early time estimates would correspond to such a different value, and no Hubble constant tension would exist. However, in our naïve initial analysis above, obtaining larger pre-CMB values could a priori go in the wrong direction when it comes to observations: one would expect a larger Hubble constant at early times, unless if it is rather an additional contribution to the CMB derived Hubble constant. Considering the multi-fold dark energy mechanisms, in all the early stages of the universe, i.e., pre-CMB, aka pre-recombination, which led to the CMB, plasma, dominated by electromagnetic and possibly other interactions, occupied the whole concretized spacetime. This way, multi-fold dark energy effects were partially countered by more dominant interactions, and the resulting accelerations of expansion were reduced. It can explain why current early time estimates for the Hubble constant would differ from late time results, and lead to a smaller Hubble constant value at early time. However, it may not fit that well the overall standard cosmological model à la ΛCMD. However, note that recent papers show that a short term increase of the dark energy (5% for redshift z > 5000), can resolve the tension, by pushing up the CMB inferred Hubble constant, i.e. early time estimates, and better match overall the ΛCDM. So maybe our naïve reasoning was not that bad. Combining the two considerations above, our paper shows that multi-fold dark energy mechanisms intrinsically, and microscopically, justify such a behavior that can resolve the Hubble tension. It is another hint in favor of the multi-fold mechanisms, to add to several others. There is also a range where a multi-fold universe appear fractal, which may result into scaling of the cosmological constant, and reducing its value, during this period; again a move in the right direction. The result extends to the real universe, if it is multi-fold, as hinted by past results. ____ 1 shmaes.

The multi-fold theory factually encounters the AdS/CFT correspondence conjecture: the AdS(5) space is tangent dual to the multi-fold spacetime. On the other hand, while the derivation of the conventional conjecture involved branes in AdS(5) (+ …), which amounts to physical dual tangency, and key derivations like the Ryu-Takayanagi conjecture, are based on the same model, the conventional AdS/CFT correspondence conjecture can also be understood as a mathematical duality, where the CFT spacetime is not necessarily physically tangent to AdS(5) (+…). It can be justified as a particular case of the holographic principle. Therefore, the paper will revisit, and derive the holographic principle, in a multi-fold universe. As General relativity (GR) encounters multi-folds at Planck scales, the proof applies to GR-based universes. We also debunk the use of Wheeler's bag of gold as a counter example to the holographic principle. Trying to resolve the black hole information paradox, different teams have been able to recover the black hole Page curve, by relying on the replica trick with generalized semi-classical gravitational path integrals, in asymptotic AdS, with arbitrary topologies, including spacetime (Euclidian) wormholes in between replicas, to justifies paths in between the replicas. The approach also relies on the island formula for the von Neuman entropy as fine-grained entropy. One knows that the Page curve had to be recovered one way or another as with the AdS/CFT correspondence conjecture, the unitarity of CFTs implies unitarity of gravity. The results, have also been extended to de Sitter asymptotic spacetime. The quantum extremal surface that appears in the process, bounding the island, leads to proposed physical interpretations of a black hole interior, that, in our opinion lead to more confusions than answers. In the multi-fold theory, we have already encountered an equivalent surface, with a much cleaner microscopic interpretation. For this paper, all what matters is that the microscopic interpretation validates the approach of replica tick, wormholes and island. But on the way, the paper discusses the differences between the multi-fold model and the conventional interpretation. A few recent papers reused the approach to study two entangled gravitating universes, with one possibly without gravity. Admittedly, speaking of different universes is a bit of an oxymoron, as a universe embodies everything that is physical. Also, what is between universes, whatever that means, seems even more a red herring, unless if they were to share, or be a (global) embedding or dual tangent space that is physical. Phrased this way, the holographic AdS/CFT correspondence conjecture would be a particular case. The papers also rely on the replica trick, and its wormholes, adding some replica and wormholes swapping entangled universe parts. They recovers sensible, and unitary behaviors as well as the ER = EPR conjecture. This paper provides multi-fold inspired interpretations of the quantum extremal surfaces appearing among the disjoint universes. Interpreting the replica trick, and its wormholes, in both the cases of black holes and entangled disjoint universes, one can see that the role played by the wormholes between different replicas amounts to the multi-fold mechanisms.. This is further reinforced by considerations on global symmetry in the presence of gravity or 1 shmaes.physics@gmail.com Cite as: Stephane H Maes, (2022), "The Replica Trick, Wormholes, Island formula, and Quantum Extremal Surfaces, and How the AdS/CFT Correspondence Conjecture, and Hence the M-theory, Encounters Multi-folds", https://doi.org/10.5281/zenodo.10207057, https:// shmaesphysics.wordpress.com/2022/09/20/the-replica-trick-its-wormholes-islands-and-quantum-extremal-surfaces-and-how-the-ads-cft-correspondence-conjecture-and-hence-them theory encounters -multi-folds/, September 26, 2022, (osf.io/xwf6q/). wormholes. The islands associated to the different entangled universe use cases also imply that, in universes with gravity, entanglement implies gravity effects, which is also known as the E/G conjecture, factual in multi-fold theory. With the (disjoint) AdS/CFT conjecture, this means that it, and therefore the M-theory encounters multi-folds. The multi-fold theory could have predicted such an outcome from the link between the Hilbert Einstein action and superstring action, and the fact that we already had GR encounter multi-folds at Planck scales.