Primordial Cosmology

Montani, Giovanni; Battisti, Marco Valerio; Benini, Riccardo; Imponente, Giovanni

doi:10.1142/9789814271011

Cited by 52 publications

(144 citation statements)

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“…The relativistic gradient expansion similarly takes seed solutions of the velocity dominated system as a starting point but aims initially at a formal series expansion in powers of some control parameter . Since its early beginnings in the context of the BKL scenario [24][25][26][27], it has been recast as an alternative to (resummed) cosmological perturbation theory, deemed valid on "superhorizon" scales [28][29][30][31][32]. Typically, the temporal gauge is fixed from the outset and a power series ansatz is made for the spatial metric, g ab = q ab + g (1) ab + 2 g (2) ab + O( 3 ).…”

Section: Kinematical Versus Dynamical Gravitational Gradientsmentioning

confidence: 99%

“…Further, Γ is the phase space of Einstein gravity with coordinates (g ab , ℘ ab ) and Poisson structure { , } while Γ 0 is the phase space of strong coupling gravity with coordinates (q ab , p ab ) and Poisson structure { , } 0 . The shift N a and the densitized lapse n are viewed as independent of the phase space variables and are therefore not transformed, Υ * κ N a = N a , Υ * κ n = n. The notion in Equation (27) of "canonicity' is much stronger than what is minimally required for a constrained Hamiltonian system. Among other differences, the minimal notion would demand Equation (27) only weakly, i.e., modulo the constraints.…”

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

“…The shift N a and the densitized lapse n are viewed as independent of the phase space variables and are therefore not transformed, Υ * κ N a = N a , Υ * κ n = n. The notion in Equation (27) of "canonicity' is much stronger than what is minimally required for a constrained Hamiltonian system. Among other differences, the minimal notion would demand Equation (27) only weakly, i.e., modulo the constraints. Since in gravity the Hamiltonian constraint governs the dynamics and we seek to transform it-rather than impose it-this weak notion of canonicity is uninteresting in the present context.…”

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

“…Since in gravity the Hamiltonian constraint governs the dynamics and we seek to transform it-rather than impose it-this weak notion of canonicity is uninteresting in the present context. One can show that canonical transformations in the strong sense in Equation (27) consistently transform the functionals defining the relativistic field equations, including the constraints. Consequently, the vanishing sets of these functionals, i.e., the field equations, are consistently transformed.…”

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

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Anti-Newtonian Expansions and the Functional Renormalization Group

Niedermaier

2019

Universe

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Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory.

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Section: Kinematical Versus Dynamical Gravitational Gradientsmentioning

confidence: 99%

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

Section: Canonical Trivialization Of Gravitational Gradientsmentioning

confidence: 99%

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Anti-Newtonian Expansions and the Functional Renormalization Group

Niedermaier

2019

Universe

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“…It is interesting to remark that, from a classical point of view, one does not need to require that the coefficients c 1 and c 2 in (30) and in (43) vanish. In fact, from the classical point of view, one only needs invariance under the BKL epoch map and the CB-LKSKS maps.…”

Section: Bkl Probabilities On the Uphpmentioning

confidence: 99%

Reflections on the Hyperbolic Plane

Lecian

2013

Int. J. Mod. Phys. D

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The most general solution to the Einstein equations in 4 = 3 + 1 dimensions in the asymptotic limit close to the cosmological singularity under the BKL (Belinskii-Khalatnikov-Lifshitz) hypothesis can be visualized by the behavior of a billiard ball in a triangular domain on the Upper Poincaré Half Plane (UPHP). The billiard system (named "big billiard") can be schematized by dividing the successions of trajectories according to Poincaré return map on the sides of the billiard table, according to the paradigms implemented by the BKL investigation and by the CB-LKSKS (Chernoff-Barrow-Lifshitz-Khalatnikov-Sinai-Khanin-Shchur) one. Different maps are obtained, according to different symmetry-quotienting mechanisms used to analyze the dynamics. In the inhomogeneous case, new structures have been uncovered, such that, in this framework, the billiard table (named "small billiard") consists of 1/6 of the previous one. The connections between the symmetry-quotienting mechanisms are further investigated on the UPHP. The relation between the complete billiard and the small billiard are also further explained according to the role of Weyl reflections. The quantum properties of the system are sketched as well, and the physical interpretation of the wave function is further developed. In particular, a physical interpretation for the symmetry-quotienting maps is proposed.Keywords: Mathematical and relativistic aspects of cosmology; early universe; nonlinear dynamics and chaos. PACS Number(s): 98.80.Jk, 98.80.Cq, 05.45.−a 1350085-1 Int. J. Mod. Phys. D 2013.22. Downloaded from www.worldscientific.com by UNIVERSITY OF WATERLOO on 02/04/15. For personal use only. 1350085-8 Int. J. Mod. Phys. D 2013.22. Downloaded from www.worldscientific.com by UNIVERSITY OF WATERLOO on 02/04/15. For personal use only. Reflections on the Hyperbolic Plane kinds of epochs and eras; their explicit form would be more complicated than (5), and the extraction of the number of epochs in each era less immediate. 1350085-10 Int. J. Mod. Phys. D 2013.22. Downloaded from www.worldscientific.com by UNIVERSITY OF WATERLOO on 02/04/15. For personal use only.

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Stability of a self-gravitating homogeneous resistive plasma

Pugliese

Carlevaro

Lattanzi

et al. 2012

Physica D: Nonlinear Phenomena

Self Cite

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In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed.We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterium. The anisotropic collapse of a density contrast is sketched in details, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced.The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancellation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different value of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.

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Primordial Cosmology

Cited by 52 publications

References 0 publications

Anti-Newtonian Expansions and the Functional Renormalization Group

Anti-Newtonian Expansions and the Functional Renormalization Group

Reflections on the Hyperbolic Plane

Stability of a self-gravitating homogeneous resistive plasma

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