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Register a new userMagnetic Seed and Cosmology as Quantum Hall Effect
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In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expansions for the scale factors, and the other dominated by a magnetic seed, which would be responsible for both a component of dark energy and a primordial magnetic field. The latter regime would be described by a (nonperturbative) mapping between the cosmological evolution and the quantum Hall effect.
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We show that particle production by gravitational field, especially the Hawking effect, may be treated as some quantum inertial effect, with the energy of Hawking radiation as some vacuum energy shift. This quantum inertial effect is mainly resulted from some intrinsical energy fluctuation $hbarkappa/c$ for a black hole. In particular, there is an extreme case in which $hbarkappa/c$ is the Planck energy, giving a Planck black hole whose event horizons diameter is one Planck length. Moreover, we also provide a possibility to obtain some positive cosmological constant for an expanding universe, which is induced from the vacuum energy shift caused by quantum inertial effect.
We study the time evolution of early universe which is developed by a cosmological constant $Lambda_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $Lambda_4$. For positive $Lambda_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.
Gravity theory based on current algebra is formulated. The gauge principle rather than the general covariance combined with the equivalence principle plays the pivotal role in the formalism, and the latter principles are derived as a consequence of the theory. In this approach, it turns out that gauging the Poincare algebra is not appropriate but gauging the $SO(N,M)$ algebra gives a consistent theory. This makes it possible to have Anti-de Sitter and de Sitter space-time by adopting a relation between the spin connection and the tetrad field. The Einstein equation is a part of our basic equation for gravity which is written in terms of the spin connection. When this formalism is applied to the $E(11)$ algebra in which the three-form antisymmetric tensor is a part of gravity multiplet, we have a current algebra gravity theory based on M-theory to be applied to cosmology in its classical limit. Without introducing any other ad-hoc field, we can obtain accelerating universe in the manner of the inflating universe at its early stage.
We study a system of electrons moving on a noncommutative plane in the presence of an external magnetic field which is perpendicular to this plane. For generality we assume that the coordinates and the momenta are both noncommutative. We make a transformation from the noncommutative coordinates to a set of commuting coordinates and then we write the Hamiltonian for this system. The energy spectrum and the expectation value of the current can then be calculated and the Hall conductivity can be extracted. We use the same method to calculate the phase shift for the Aharonov-Bohm effect. Precession measurements could allow strong upper limits to be imposed on the noncommutativity coordinate and momentum parameters $Theta$ and $Xi$.
We extend the the concept of Hawking-Moss, or up-tunnelling, transitions in the early universe to include black hole seeds. The black hole greatly enhances the decay amplitude, however, order to have physically consistent results, we need to impose a new condition (automatically satisfied for the original Hawking-Moss instanton) that the cosmological horizon area should not increase during tunnelling. We motivate this conjecture physically in two ways. First, we look at the energetics of the process, using the formalism of extended black hole thermodynamics; secondly, we extend the stochastic inflationary formalism to include primordial black holes. Both of these methods give a physical substantiation of our conjecture.
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