The Initial Singularity of Ultrastiff Perfect Fluid Spacetimes Without Symmetries

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutz's variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.

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Perfect fluid spacetimes with two symmetries

Classical and Quantum Gravity ◽

10.1088/0264-9381/21/7/003 ◽

2004 ◽

Vol 21 (7) ◽

pp. 1755-1759 ◽

Cited By ~ 1

Author(s):

A Szereszewski ◽

J Tafel

Keyword(s):

Perfect Fluid ◽

Fluid Spacetimes

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Shear-free conditions of a Chaplygin-gas-dominated universe

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887821501929 ◽

2021 ◽

pp. 2150192

Author(s):

Amare Abebe ◽

Mudhahir Al Ajmi ◽

Maye Elmardi ◽

Hemwati Nandan ◽

Noor ul Sabah

Keyword(s):

General Relativity ◽

Perfect Fluid ◽

Chaplygin Gas ◽

Current Investigation ◽

Free Condition ◽

General Relativistic ◽

Relativistic Framework ◽

Fluid Spacetimes

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

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