## Final Activity Report Summary - COSMODYN (Effective quantum cosmology and dark matter)

The first part of the project focussed on dark matter: any form of matter whose existence is inferred by its gravitational effects, but not detected directly in our present observations, is called dark matter. A large amount of astronomical evidence indicates the existence in the universe of more gravitationally interacting matter than luminous (baryonic) matter.

Over the decades, the search for dark matter has occupied physicists, and yet, its nature is still a profound and unresolved mystery. There are, however, significant reasons to believe that the dark matter in the universe is constituted, in large fraction, by collision-less particles with very small primordial velocity dispersion. Such particles are called cold dark matter (CDM). Leading CDM candidates are axions and weakly interacting massive particles (WIMPs). Galaxies are surrounded by the CDM, and hence, because of gravity, they keep falling onto galaxies from all directions. This continuous in-fall produces caustics; in the halos of galaxies. CDM caustics are generically surfaces in space where the CDM density is very large. The Caustic Ring Model of galactic halos predicts the geometry and density near the caustic rings which are closed tubes whose transverse cross-section has three cusps. One cusp lies on the plane of the galaxy, the other two lie on the above and below the galactic plane. Using this model, the fellow showed that the gravitational lensing by the cusps of caustic rings at cosmological distances may offer the tantalizing opportunity to detect CDM indirectly. The image magnification of a cosmological axion caustic ring is constrained between 3% and 2800% at the planar cusp, and between 2% and 46% at the non-planar cusps. For a cosmological WIMP caustic ring, on the other hand, the magnification is constrained between 3% and 28% at the planar cusp, and between 2% and 5% at the non-planar cusps. As point-like background sources cross behind the axion (WIMP) folds, the time scale of brightness change is about an hour (a year). Thus, depending on the strength of detected effect and the time scale for brightness change, it may even be possible to discriminate between the axions and the WIMPs by present instruments.

The second part of the project was on the super-accelerated phase of the cosmic expansion. Present cosmological observations do not exclude the possibility of an evolving dark energy equation of state w whose current value is less than minus one; i.e. a phase of super-acceleration. This possibility has been an area of great interest in recent years. Super-acceleration is difficult to explain with classical models on account of the problem with stability. The observed persistence of the universe, therefore, can only be consistent with a relatively brief self-limiting phase of super-acceleration. One way to get such a self-limiting phase, without violating classical stability, is via quantum effects.

A massless, minimally coupled scalar field with a quartic self-interaction in the locally de Sitter background of an inflating universe can induce a temporary phase of super-acceleration via quantum effects, causing a violation of the Weak Energy Condition on cosmological scales. Emre O. Kahya of the University of Florida and the fellow investigated this system's quantum stability by studying the behaviour of linearised perturbations in the quantum-corrected effective field equations at one- and two-loop order.

We showed that the time dependence we infer from the quantum-corrected mode function is in perfect agreement with the system developing a positive mass squared. Moreover, the maximum induced mass remains perturbatively small and it does not go tachyonic. Thus, the system is stable.

Over the decades, the search for dark matter has occupied physicists, and yet, its nature is still a profound and unresolved mystery. There are, however, significant reasons to believe that the dark matter in the universe is constituted, in large fraction, by collision-less particles with very small primordial velocity dispersion. Such particles are called cold dark matter (CDM). Leading CDM candidates are axions and weakly interacting massive particles (WIMPs). Galaxies are surrounded by the CDM, and hence, because of gravity, they keep falling onto galaxies from all directions. This continuous in-fall produces caustics; in the halos of galaxies. CDM caustics are generically surfaces in space where the CDM density is very large. The Caustic Ring Model of galactic halos predicts the geometry and density near the caustic rings which are closed tubes whose transverse cross-section has three cusps. One cusp lies on the plane of the galaxy, the other two lie on the above and below the galactic plane. Using this model, the fellow showed that the gravitational lensing by the cusps of caustic rings at cosmological distances may offer the tantalizing opportunity to detect CDM indirectly. The image magnification of a cosmological axion caustic ring is constrained between 3% and 2800% at the planar cusp, and between 2% and 46% at the non-planar cusps. For a cosmological WIMP caustic ring, on the other hand, the magnification is constrained between 3% and 28% at the planar cusp, and between 2% and 5% at the non-planar cusps. As point-like background sources cross behind the axion (WIMP) folds, the time scale of brightness change is about an hour (a year). Thus, depending on the strength of detected effect and the time scale for brightness change, it may even be possible to discriminate between the axions and the WIMPs by present instruments.

The second part of the project was on the super-accelerated phase of the cosmic expansion. Present cosmological observations do not exclude the possibility of an evolving dark energy equation of state w whose current value is less than minus one; i.e. a phase of super-acceleration. This possibility has been an area of great interest in recent years. Super-acceleration is difficult to explain with classical models on account of the problem with stability. The observed persistence of the universe, therefore, can only be consistent with a relatively brief self-limiting phase of super-acceleration. One way to get such a self-limiting phase, without violating classical stability, is via quantum effects.

A massless, minimally coupled scalar field with a quartic self-interaction in the locally de Sitter background of an inflating universe can induce a temporary phase of super-acceleration via quantum effects, causing a violation of the Weak Energy Condition on cosmological scales. Emre O. Kahya of the University of Florida and the fellow investigated this system's quantum stability by studying the behaviour of linearised perturbations in the quantum-corrected effective field equations at one- and two-loop order.

We showed that the time dependence we infer from the quantum-corrected mode function is in perfect agreement with the system developing a positive mass squared. Moreover, the maximum induced mass remains perturbatively small and it does not go tachyonic. Thus, the system is stable.