Roman V. Buniy

The null energy condition and instability

We extend previous work showing that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. Simple examples are given to illustrate these results. The role of causality in our results is discussed. Finally, we extend the fluid results to more general systems in thermal equilibrium. When applied to the dark energy, our results imply that

Instabilities and the null energy condition

w=p/\ensuremath{\rho}

The Eccentric universe

is unlikely to be less than

Entanglement entropy, black holes and holography

\ensuremath{-}1

Discreteness and the origin of probability in quantum mechanics

.

Is Hilbert space discrete

Abstract We show that violation of the null energy condition implies instability in a broad class of models, including gauge theories with scalar and fermionic matter as well as any perfect fluid. When applied to the dark energy, our results imply that w = p / ρ is unlikely to be less than −1.

A Proposal for detecting second order topological quantum phase

For a universe containing a cosmological constant together with uniform arrangements of magnetic fields, strings, or domain walls, exact solutions to the Einstein equations are shown to lead to a universe with ellipsoidal expansion. The magnetic field case is the easiest to motivate and has the highest possibility of finding application in observational cosmology.

Higher order topological actions

We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational-collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of holography as an upper bound on the realizable entropy (entanglement or von Neumann) of a region, rather than on the dimension of its Hilbert space.

Does string theory predict an open universe

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.

Semi-classical wormholes are unstable

We show that discretization of spacetime naturally suggests discretization of Hilbert space itself. Specifically, in a universe with a minimal length (for example, due to quantum gravity), no experiment can exclude the possibility that Hilbert space is discrete. We give some simple examples involving qubits and the Schrodinger wavefunction, and discuss implications for quantum information and quantum gravity.