We relate CMB anomalies and the recent observational evidence of primordial gravitational waves. Two aspects are investigated:
(a) Several anomalies are spotted on the low ell temperature map of the WMAP and Planck experiments. However, those anomalies disappear at high ell. We propose that those low ell temperature anomalies may come from nearly scale invariant anomalies of the tensor sector. Those anomalies on the temperature map naturally decay towards small scales, characterized by the tensor-to-temperature radiation transfer function.
(b) The anomalies introduced by the gravitational waves discovery. Strong tension is noticed between the BICEP2 and Planck data. We study in detail how blue tilt of the tensor spectrum reconciles the tension between those datasets.
We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy", and we discuss its relation to emergent geometry in the context of holographic duality. This is a joint work with Brian Swingle.
The talk is based on joint work with Yuri Manin (arXiv:1402.2158). Using algebro-geometric blowups it is possible to construct a family of models of gluing of aeons across a Big-Bang type singularity, which includes the case of Penrose's conformally cyclic cosmology, as well as inflationary multiverse models generalizing the "eternal symmetree", and BKLL mixmaster type cosmologies. Using the mixmaster dynamics, formulated in terms of elliptic curves and modular curves, we speculate on the geometry of cosmological time near the gluing of aeons. We show also that this type of model allows for phenomena of noncommutativity of spacetime coordinates near the Big-Bang and the crossing of aeons.