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Register a new userBianchi IX cosmologies in the Einstein-Skyrme system in a sector with non-trivial topological charge
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The dynamics of the most general Bianchi IX cosmology with three time dependent scale factors for the Einstein-Skyrme system is analyzed. For the Skyrmion, a generalized hedgehog ansatz with unit baryon charge is introduced. The most remarkable feature of this ansatz is that, in the above topologically non-trivial sector with unit topological charge, the Skyrme field equations are identically satisfied on any Bianchi IX metric. We will show that due to this feature the complete set of coupled Einstein-Skyrme field equations can be deduced from a suitable minisuperspace Lagrangian. The latter allows to perform a systematic study of the integrability properties of the Einstein-Skyrme system for the Bianchi IX cosmology. Moreover, some analytic and algebraic solutions for the Einstein-Skyrme model are derived. Another remarkable consequence of the present formalism is that it is possible to derive the Wheeler de-Witt equation for the Bianchi IX metric in the Einstein-Skyrme cosmology in which all the effects of the Skyrmion are encoded in an effective potential of the minisuperspace Lagrangian.
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We implement the no-boundary proposal for the wave function of the universe in an exactly solvable Bianchi IX minisuperspace model with two scale factors. We extend our earlier work (Phys. Rev. Lett. 121, 081302, 2018 / arXiv:1804.01102) to include the contribution from the $mathbb{C}text{P}^2 setminus B^4$ topology. The resulting wave function yields normalizable probabilities and thus fits into a predictive framework for semiclassical quantum cosmology. We find that the amplitude is low for large anisotropies. In the isotropic limit the usual Hartle-Hawking wave function for the de Sitter minisuperspace model is recovered. Inhomogeneous perturbations in an extended minisuperspace are shown to be initially in their ground state. We also demonstrate that the precise mathematical implementation of the no-boundary proposal as a functional integral in minisuperspace depends on detailed aspects of the model, including the choice of gauge-fixing. This shows in particular that the choice of contour cannot be fundamental, adding weight to the recent proposal that the semiclassical no-boundary wave function should be defined solely in terms of a collection of saddle points. We adopt this approach in most of this paper. Finally we show that the semiclassical tunneling wave function of the universe is essentially equal to the no-boundary state in this particular minisuperspace model, at least in the subset of the classical domain where the former is known.
In this paper the dynamics of free gauge fields in Bianchi type I-VII$_{h}$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p,in,{1,3}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII$_{h}$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,Wonderland ($lambda$) appears generally in type V and in type I for $lambda=0$. Depending on the value of the equation of state parameter other new stable solutions are also found (The Rope and The Edge) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.
We study non-trivial (i.e. non-Levi-Civita) connections in metric-affine Lovelock theories. First we study the projective invariance of general Lovelock actions and show that all connections constructed by acting with a projective transformation of the Levi-Civita connection are allowed solutions, albeit physically equivalent to Levi-Civita. We then show that the (non-integrable) Weyl connection is also a solution for the specific case of the four-dimensional metric-affine Gauss-Bonnet action, for arbritrary vector fields. The existence of this solution is related to a two-vector family of transformations, that leaves the Gauss-Bonnet action invariant when acting on metric-compatible connections. We argue that this solution is physically inequivalent to the Levi-Civita connection, giving thus a counterexample to the statement that the metric and the Palatini formalisms are equivalent for Lovelock gravities. We discuss the mathematical structure of the set of solutions within the space of connections.
The canonical quantum theory of gravity -- Quantum Geometrodynamics (QG) is applied to the homogeneous Bianchi type IX cosmological model. As a result, the framework for the quantum theory of homogeneous cosmologies is developed. We show that the theory is internally consistent, and prove that it possesses the correct classical limit (the theory of general relativity). To emphasize the special role that the constraints play in this new theory we, compare it to the traditional ADM square-root and Wheeler-DeWitt quantization schemes. We show that, unlike the traditional approaches, QG leads to a well-defined Schrodinger equation for the wave-function of the universe that is inherently coupled to the expectation value of the constraint equations. This coupling to the constraints is responsible for the appearance of a coherent spacetime picture. Thus, the physical meaning of the constraints of the theory is quite different from Diracs interpretation. In light of this distinctive feature of the theory, we readdress the question of the dark energy effects in the Bianchi IX cosmological model for highly non-classical quantum states. We show that, at least for this model, for any choice of the initial wave function, the quantum corrections will not produce the accelerated expansion of the universe.
We show that massless solutions to the Einstein-Vlasov system in a Bianchi I space-time with small anisotropy, i.e. small shear and small trace-free part of the spatial energy momentum tensor, tend to a radiation fluid in an Einstein-de Sitter space-time with the anisotropy $Sigma^a_bSigma^b_a$ and $tilde{w}^i_j tilde{w}^j_i$ decaying as $O(t^{-frac12})$.
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