## Periodic Reporting for period 1 - TOPVAC (From Topological Matter to Relativistic Quantum Vacuum)

**Reporting period:**2016-10-01

**to**2018-03-31

## Summary of the context and overall objectives of the project

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.

## Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

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.

## Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

"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.

(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.

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.

(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.

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."