New Spherical Scalar Modes on the De Sitter Expanding Universe

Pascu, Gabriel

doi:10.1142/s0217732312501246

Cited by 8 publications

(13 citation statements)

References 18 publications

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“…These may be related among themselves through Bogolyubov transformations whose transition coefficients may point out the cosmological particle creation generating particle or antiparticle thermal baths [1][2][3][4][5][6][7][8][9][10][11]. A special attention was paid to the scalar field on the de Sitter spacetime [12][13][14][15][16][17][18] involved in many studies of c.p.c. [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Rest frame vacuum of the Dirac field on spatially flat FLRW spacetimes

Cotăescu

2019

Eur. Phys. J. C

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We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care on the correct normalization which is crucial in interpreting the quantum theory. Thanks to this method we can define on any spatially flat FLRW spacetime states in which genuine Minkowskian parameters are measured. We use these Minkowskian states for separating the frequencies in the rest frames of the massive scalar particles defining thus the scalar rest frame vacuum. We show that this vacuum is stable on the de Sitter expanding universe where the energy is conserved. In contrast, on a spatially flat FLRW spacetime with a Milne-type scale factor this vacuum results to be dynamic, corresponding to a time-dependent rest energy interpreted as an effective mass. This dynamic vacuum give rise to a cosmological particle creation which is significant only in the early Milne-type universe considered here. Some interesting features of this new effect are pointed out in a brief analysis.

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Section: Introductionmentioning

confidence: 99%

Rest frame vacuum of the Dirac field on spatially flat FLRW spacetimes

Cotăescu

2019

Eur. Phys. J. C

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“…While the modes of R.III can also be found just by solving the Klein-Gordon equation in the appropriate chart, those of R.IV require special considerations [23]. Being expressed in Euclidean coordinates, the temporal part of the modes is the same.…”

Section: Remarkmentioning

confidence: 99%

Discrete symmetries and de Sitter spacetime

Cotăescu¹,

Pascu²

2014

AIP Conference Proceedings

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Abstract. Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries-a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries-states between which exists a well-known thermality relation.

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“…Accordingly, two main results were obtained: GR was extended to complex GR, and the gravitational coupling constant takes discrete values. In reality, signature changing space-time where an initially riemannian manifold with euclidean signature evolves into the lorentzian universe we see today is not new and was discussed extensively in the literature, (e.g., noncommutative geometry [62,63] and quantum gravity [64]). In our framework, because of the introduction of the metric relation g ¡ ĝ ϭ g e 2i with ϭ ±(2n ϩ 1)(/2), n ϭ 0, 1, 2, ..., we get ds 2 ϭ ĝ dx dx ϭ g e 2i dx dx ϭ -g dx dx and accordingly (-, +, +, +) ¡ (+, -, -, -).…”

Section: Conclusion and Perspectivementioning

confidence: 99%

Nonstandard fractional exponential Lagrangians, fractional geodesic equation, complex general relativity, and discrete gravity

El-Nabulsi

2013

Can. J. Phys.

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Nonstandard Lagrangians are generating functions of different equations of motion. They have gained increasing importance in many different fields. In fact, nonstandard Lagrangians date back to 1978, when Arnold entitled them "nonnatural" in his classic book, Mathematical Methods of Classical Mechanics (Springer, New York. 1978). In applied mathematics, most dynamical equations can be obtained by using generating Lagrangian functions (e.g., power-law and exponential Lagrangians), which has been shown by mathematicians, who have also demonstrated that there is an infinite number of such functions. Besides this interesting field, the topic of fractional calculus of variations has gained growing importance because of its wide application in different fields of science. In this paper, we generalize the fractional actionlike variational approach for the case of a nonstandard exponential Lagrangian. To appreciate this new approach, we explore some of its main consequences in Einstein's general relativity. Some results are revealed and discussed accordingly mainly the transition from general relativity to complex relativity and emergence of a discrete gravitational coupling constant. PACS Nos.: 02.30.Xx, 04.20.-q, 04.20.Fy. Résumé : Les Lagrangiens non standard sont des fonctions génératrices d'équations différentes du mouvement. Ils sont de plus en plus importants dans différents domaines scientifiques. En fait, les Lagrangiens non standard datent de 1978, lorsque Arnold les a baptisés de non naturels dans son livre Méthodes Mathématiques de la Mécanique Classique (Springer, New York. 1978). En mathématiques appliquées, la plupart des équations dynamiques peuvent être obtenues de fonctions génératrices de Lagrange (par exemple, des Lagrangiens en loi de puissance ou exponentiels), ce qui a été illustré par des mathématiciens qui ont aussi démontré qu'il y a un nombre infini de telles fonctions. À côté de ce champ, le calcul fractionnaire des variations croît en importance, à cause de son large domaine d'applications en sciences. Ici, nous généralisons l'approche variationnelle de type action fractionnelle pour un Lagrangien exponentiel non standard. Pour mieux apprécier cette nouvelle approche, nous explorons certaines de ses conséquences majeures en relativité générale (RG) d'Einstein. Quelques résultats sont présentés et nous analysons surtout le passage de la RG à la relativité complexe et une constante de couplage gravitationnel discrète. [Traduit par la Rédaction]

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New Spherical Scalar Modes on the De Sitter Expanding Universe

Cited by 8 publications

References 18 publications

Rest frame vacuum of the Dirac field on spatially flat FLRW spacetimes

Rest frame vacuum of the Dirac field on spatially flat FLRW spacetimes

Discrete symmetries and de Sitter spacetime

Nonstandard fractional exponential Lagrangians, fractional geodesic equation, complex general relativity, and discrete gravity

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