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Register a new userQuantum Fields in an Expanding Universe
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We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined and it is verified that the electromagnetic and massless spinor actions are conformal invariant, while the massless conformally coupled scalar field is not. For the scalar field case it is pointed out that the violation of conformal simmetry due to surface terms, although ininfluential for the equation of motion, does lead to effects in the quantized theory.
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We study the tensorial modes of the two-fluid model, where one of this fluids has an equation of state $p = - rho/3$ (variable cosmological constant, cosmic string fluid, texture) or $p = - rho$ (cosmological constant), while the other fluid is an ordinary matter (radiation, stiff matter, incoherent matter). In the first case, it is possible to have a closed Universe whose dynamics can be that of an open Universe providing alternative solutions for the age and horizon problems. This study of the gravitational waves is extended for all values of the effective curvature $k_{eff}=k-frac{8pi G}{3}rho_{0s}$, that is, positive, negative or zero, $k$ being the curvature of the spacelike section. In the second case, we restrict ourselves to a flat spatial section. The behaviour of gravitational waves have, in each case, very particular features, that can be reflected in the anisotropy spectrum of Cosmic Microwave Background Radiation. We make also some considerations of these models as candidate to dark matter models.
We study the accelerated expansion of the Universe through its consequences on a congruence of geodesics. We make use of the Raychaudhuri equation which describes the evolution of the expansion rate for a congruence of timelike or null geodesics. In particular, we focus on the space-time geometry contribution to this equation. By straightforward calculation from the metric of a Robertson-Walker cosmological model, it follows that in an accelerated expanding Universe the space-time contribution to the Raychaudhuri equation is positive for the fundamental congruence, favoring a non-focusing of the congruence of geodesics. However, the accelerated expansion of the present Universe does not imply a tendency of the fundamental congruence to diverge. It is shown that this is in fact the case for certain congruences of timelike geodesics without vorticity. Therefore, the focusing of geodesics remains feasible in an accelerated expanding Universe. Furthermore, a negative contribution to the Raychaudhuri equation from space-time geometry which is usually interpreted as the manifestation of the attractive character of gravity is restored in an accelerated expanding Robertson-Walker space-time at high speeds.
We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-deSitter) spacetime as a model for a Schwarzschild black hole embedded in a deSitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a non-zero finite value if the comoving observer approaches infinity.
We present evidence that recent numerical results from the reduced classical equations of the Lorentzian IIB matrix model can be interpreted as corresponding to the emergence of an expanding universe. In addition, we propose an effective metric to describe the emerging (3+1)-dimensional spacetime. This metric gives, at all times, finite values for the Ricci and Kretschmann curvature scalars. With these results, we are able to give a heuristic discussion of the origin of the Universe in the context of the IIB matrix model.
An oscillating, compact Friedmann universe with a massive conformally coupled scalar field is studied in the framework of quantum cosmology. The scalar field is treated as a perturbation and we look for solutions of the Wheeler-DeWitt equation describing stable stationary states of the model. We assume that the previous sources of quantum instability that have been discussed in the literature (particle production, and tunnelling to zero size) are absent. We then show, under rather general assumptions, that a further source of quantum instability prevents the existence of stationary states with localized wave function in the direction of the scalar-field modes.
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