## Periodic Reporting for period 3 - TOPVAC (From Topological Matter to Relativistic Quantum Vacuum)

Reporting period: 2019-10-01 to 2021-03-31

The quantum vacuum of our Universe is not empty: it is filled by quantum fluctuations. The structure of the quantum vacuum is one of the main challenges in modern physics. It appears that in many respects the vacuum is similar to the frictionless superfluid liquids, which we study in the Low Temperature Laboratory of Aalto University in Finland. The goal is to advance our understanding of the vacuum structure using our experience with these anomalous topological quantum systems. On this basis we can treat the most important unsolved problems in physics. Among them there is the cosmological constant problem: why the vacuum energy, or dark energy, measured in cosmological experiments, is 120 orders of magnitude smaller than the naive estimates of the vacuum fluctuations. Another one is the hierarchy problem: why the masses of the known particles in the Standard Model of particle physics are much smaller than the characteristic Planck energy, etc. The main tool in our project is the topology, which unites the properties of the quantum vacuum of our Universe and the properties of the topological condensed matter.

The work of TOPVAC-project focuses on theoretical and experimental investigations of connections between the topological quantum matter and relativistic quantum field theory (RQFT). We have used the topological superfluid 3He, that acquires the properties of quantum vacuum at ultra-low temperatures, to test cosmological and RQFT concepts. We have made observations of several properties that pave the way to the solution of problems in the Standard Model and cosmology.

"We have succeeded in experimental simulations of several theoretically predicted properties of the quantum vacuum using the topological superfluid 3He. These are:

(i) Evidence of the existence of time crystals and quasi-crystals. A time crystal, as suggested by the Nobel Prize winner Frank Wilczek, is a structure that repeats not in space, such as normal crystals, but in time. The quantum vacuum also may form the time crystal structure, now realised in superfluid 3He. In particular, the quasi-crystals were demonstrated for the first time ever in the TOPVAC project. In future, it may even be possible to look at time itself, including the possibility of constructing the boundary between time going forward and back, as theory suggests. We also expect the investigation of the Landau-Zener effect the two-level time-crystal system.

(ii) Experimental observation of spontaneous formation of the non-topological soliton (NTS); the so-called ""bulk matter"" predicted by the quantum field theory. The TOPVAC results represent the first-ever observation of NTS in condensed matter. NTS are predicted to exist in forms of stars, quasars, the dark matter and nuclear matter. We propose NTS as the candidate of dark matter in cosmology, while suggesting another possible origin for dark matter: the oscillating decay of the vacuum energy. We are planning to study also this decay experimentally in superfluid 3He. Currently, there are no observations of NTS in cosmology.

(iii) Experimental observation of magnon Bose-condensation in the polar phase of 3He; that is the lowest accessible quantum state realised for the first time in a recently observed superfluid phase of helium. The TOPVAC results pave the way to the studies of nontrivial quantum vacua, that can only be realised in the polar phase. By improving the current measurement accuracy we expect to demonstrate the transformation from the metric that we live in (the Minkowski metric) to the metric of space (the Euclidean metric), where the time and space behave the same. This will allow us to study the Euclidean vacuum by using the superfluid 3He as a model system.

(iv) Experimental observation of half-quantum vortices in 3He -- the analogs of the Alice strings in cosmology, and subsequent observation of the analog of cosmic domain walls bounded by these strings. The TOPVAC results demonstrate the two ways to enter the mirror world; around the half-quantum vortex (safe/continuous route) and across the cosmic singularity of the domain wall (dangerous route). This gives new perspective to our understanding on the early evolution of the Universe through spacetime transitions.

(v) Experimental observation of the destruction of the long-range orientational order in specific type of superfluids by weak randomness produced by a nanostructured material. This is probably the most important experimental result in the physics of the disordered quantum vacuum. Another new result is the experimental observation of the extension of the Anderson theorem related to disorder in same type of superfluids, that is work in progress. We also expect the observation of different topological states in the disordered vacuum.

(vi) Prediction of new types of gravitational anomaly in topological materials, that builds on the description of the elasticity theory of crystals. Discovery of thermal gravitational anomaly in topological superfluids, which its the extension of the anomaly earlier suggested by Nieh and Yan for the relativistic quantum field theory and quantum gravity.

The ultimate target of TOPVAC is to construct a model of quantum vacuum, which is sufficient for satisfactory solution of the cosmological constant, hierarchy and Higgs field problems."

(i) Evidence of the existence of time crystals and quasi-crystals. A time crystal, as suggested by the Nobel Prize winner Frank Wilczek, is a structure that repeats not in space, such as normal crystals, but in time. The quantum vacuum also may form the time crystal structure, now realised in superfluid 3He. In particular, the quasi-crystals were demonstrated for the first time ever in the TOPVAC project. In future, it may even be possible to look at time itself, including the possibility of constructing the boundary between time going forward and back, as theory suggests. We also expect the investigation of the Landau-Zener effect the two-level time-crystal system.

(ii) Experimental observation of spontaneous formation of the non-topological soliton (NTS); the so-called ""bulk matter"" predicted by the quantum field theory. The TOPVAC results represent the first-ever observation of NTS in condensed matter. NTS are predicted to exist in forms of stars, quasars, the dark matter and nuclear matter. We propose NTS as the candidate of dark matter in cosmology, while suggesting another possible origin for dark matter: the oscillating decay of the vacuum energy. We are planning to study also this decay experimentally in superfluid 3He. Currently, there are no observations of NTS in cosmology.

(iii) Experimental observation of magnon Bose-condensation in the polar phase of 3He; that is the lowest accessible quantum state realised for the first time in a recently observed superfluid phase of helium. The TOPVAC results pave the way to the studies of nontrivial quantum vacua, that can only be realised in the polar phase. By improving the current measurement accuracy we expect to demonstrate the transformation from the metric that we live in (the Minkowski metric) to the metric of space (the Euclidean metric), where the time and space behave the same. This will allow us to study the Euclidean vacuum by using the superfluid 3He as a model system.

(iv) Experimental observation of half-quantum vortices in 3He -- the analogs of the Alice strings in cosmology, and subsequent observation of the analog of cosmic domain walls bounded by these strings. The TOPVAC results demonstrate the two ways to enter the mirror world; around the half-quantum vortex (safe/continuous route) and across the cosmic singularity of the domain wall (dangerous route). This gives new perspective to our understanding on the early evolution of the Universe through spacetime transitions.

(v) Experimental observation of the destruction of the long-range orientational order in specific type of superfluids by weak randomness produced by a nanostructured material. This is probably the most important experimental result in the physics of the disordered quantum vacuum. Another new result is the experimental observation of the extension of the Anderson theorem related to disorder in same type of superfluids, that is work in progress. We also expect the observation of different topological states in the disordered vacuum.

(vi) Prediction of new types of gravitational anomaly in topological materials, that builds on the description of the elasticity theory of crystals. Discovery of thermal gravitational anomaly in topological superfluids, which its the extension of the anomaly earlier suggested by Nieh and Yan for the relativistic quantum field theory and quantum gravity.

The ultimate target of TOPVAC is to construct a model of quantum vacuum, which is sufficient for satisfactory solution of the cosmological constant, hierarchy and Higgs field problems."