General class of inhomogeneous perfect-fluid solutions

Ruiz, E.; Senovilla, José M. M.

doi:10.1103/physrevd.45.1995

Cited by 85 publications

(97 citation statements)

References 18 publications

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“…It is interesting that our solution provides another example of a regular solution with axial symmetry; for others, see Pitrou et al [1,2] and Senovilla and collaborators [18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

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Anisotropic, nonsingular early universe model leading to a realistic cosmology

2009

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We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a non-singular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'Big Bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the Big Bang. We demonstrate that there exist geodesics extending through the Big Bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the Big Bang, rendering it, at worst, a quasi-regular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasi-regular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropisation and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [1,2,3]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalises the known bouncing solution in closed FRW universes.

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“…It is interesting that our solution provides another example of a regular solution with axial symmetry; for others, see Pitrou et al [1,2] and Senovilla and collaborators [18,19,20,21].…”

Section: Introductionmentioning

confidence: 99%

“…In the different context of inhomogeneous but axially symmetric cosmologies, [18,19,20,21] also consider the important concept of geodesic completeness of a spacetime. Completeness is a criterion for the physical significance of a solution that is more stringent than mere geometric regularity, which we will also need to address later.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic, nonsingular early universe model leading to a realistic cosmology

2009

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“…It was then shown in [46] that the general family in [41] as well as the whole class of Robertson-Walker cosmologies belong to a single unified wider class of cylindrically symmetric 1 , separable, diagonal (non-necessarily perfect) fluid solutions. Those depended on one arbitrary function of time -essentially the scale factor-and four free parameters selecting the openness or closeness of the models, the anisotropy of the fluid pressures, or the anisotropy and spatial inhomogeneity of the models.…”

Section: Introductionmentioning

confidence: 99%

A singularity theorem based on spatial averages

Senovilla

2007

Pramana - J Phys

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Abstract. Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables are severely geodesically incomplete to the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies.

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“…Note that separable perfect fluid spacetimes of this class have attracted considerable attention and the general solution is known; stiff-matter [28], linear equation of state and conformally-flat spatial 3-slices (for the latter, see Wainwright [29]) [30], general case [31] and for non-comoving, general properties and solutions, see [32,33].…”

Section: Introductionmentioning

confidence: 99%

Complex windmill transformation producing new purely magnetic fluids

Lozanovski

Wylleman

2011

Class. Quantum Grav.

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Minimal complex windmill transformations of G 2 I B(ii) spacetimes (admitting a two-dimensional Abelian group of motions of the so-called Wainwright B(ii) class) are defined and the compatibility with a purely magnetic Weyl tensor is investigated. It is shown that the transformed spacetimes cannot be perfect fluids or purely magnetic Einstein spaces. We then determine which purely magnetic perfect fluids (PMpfs) can be windmill-transformed into purely magnetic anisotropic fluids (PMafs). Assuming separation of variables, complete integration produces two, algebraically general, G 2 I -B(ii) PMpfs: a solution with zero 4-acceleration vector and spatial energy-density gradient, previously found by the authors, and a new solution in terms of Kummer's functions, where these vectors are aligned and non-zero. The associated windmill PMafs are rotating but non-expanding. Finally, an attempt to relate the spacetimes to each other by a simple procedure leads to a G 2 I -B(ii) oneparameter PMaf generalization of the previously found metric.

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General class of inhomogeneous perfect-fluid solutions

Cited by 85 publications

References 18 publications

Anisotropic, nonsingular early universe model leading to a realistic cosmology

Anisotropic, nonsingular early universe model leading to a realistic cosmology

A singularity theorem based on spatial averages

Complex windmill transformation producing new purely magnetic fluids

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