Hyperbolic space in the Newtonian limit: The cosmological constant

Castro-Palacio, Juan Carlos; Córdoba, Pedro Fernández de; Torromé, Ricardo Gallego; Isidro, J. M.

doi:10.1142/s0218271822500729

Int. J. Mod. Phys. D

2022

DOI: 10.1142/s0218271822500729

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Hyperbolic space in the Newtonian limit: The cosmological constant

Juan Carlos Castro-Palacio

Pedro Fernández de Córdoba

Ricardo Gallego Torromé

et al.

Abstract: In this paper, the cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.

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Cited by 2 publications

References 56 publications

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On the cosmological constant of flat FLRW spacetime

Córdoba¹,

Torrome²,

Gavasso³

et al. 2022

Int. J. Geom. Methods Mod. Phys.

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We consider an exponentially expanding, flat, Friedmann–Lemaître–Robertson–Walker (FLRW) Universe filled with a free Schroedinger field. The probability fluid of the latter is used to mimic the cosmological fluid (baryonic plus dark matter), thus providing the matter density and pressure terms in the corresponding Friedmann–Lemaître equations. We first obtain the eigenfunctions of the Laplacian operator on flat FLRW space. A quantum operator qualifying as a cosmological constant is defined to act on the Schroedinger field. We then compute the matrix representing the cosmological constant in the basis of Laplacian eigenfunctions. For an estimate of the orders of magnitude involved it suffices to determine the expectation values of this operator. The expectation value that best fits the experimentally measured value of the cosmological constant allows us to identify the quantum state of the Schroedinger field that best represents the matter contents (baryonic and dark) of the current Universe. Finally, the operator inverse (modulo dimensional factors) to the one representing the cosmological constant provides a measure of the gravitational Boltzmann entropy of the Universe. We compute its matrix in the basis of Laplacian eigenfunctions and verify that the expectation values of this entropy operator comply with the upper bound set by the holographic principle.

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On the cosmological constant of flat FLRW spacetime

Córdoba¹,

Torrome²,

Gavasso³

et al. 2022

Int. J. Geom. Methods Mod. Phys.

View full text Add to dashboard Cite

show abstract

On the cosmological constant as a quantum operator

Córdoba

Torrome

Gavasso

et al. 2022

Int. J. Geom. Methods Mod. Phys.

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We regard the cosmological fluid within an exponentially expanding FLRW spacetime as the probability fluid of a nonrelativistic Schroedinger field. The scalar Schroedinger particle so described has a mass equal to the total (baryonic plus dark) matter content of the Universe. This procedure allows a description of the cosmological fluid by means of the operator formalism of nonrelativistic quantum theory. Under the assumption of radial symmetry, a quantum operator proportional to [Formula: see text] represents the cosmological constant [Formula: see text]. The experimentally measured value of [Formula: see text] is one of the eigenvalues of [Formula: see text]. Next we solve the Poisson equation [Formula: see text] for the gravitational potential [Formula: see text], with the cosmological constant [Formula: see text] playing the role of a source term. It turns out that [Formula: see text] includes, besides the standard Newtonian potential [Formula: see text], a correction term proportional to [Formula: see text] identical to that appearing in theories of modified Newtonian dynamics.

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Hyperbolic space in the Newtonian limit: The cosmological constant

Abstract: In this paper, the cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.

Cited by 2 publications

References 56 publications

On the cosmological constant of flat FLRW spacetime

On the cosmological constant of flat FLRW spacetime

On the cosmological constant as a quantum operator

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