Dark energy and extending the geodesic equations of motion: its construction and experimental constraints

Speliotopoulos, Achilles D.

doi:10.1007/s10714-009-0926-3

Cited by 5 publications

(31 citation statements)

References 45 publications

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“…Here, α is a constant, and is the only free parameter in the theory. In [1], we showed that for the effects of the extension not to have already been observed in terrestrial experiments, α must be between 1.28 (for DE = 10 −32 g/cm 3 ) and 1.58 (for DE = 10 −29 g/cm 3 ). While the equations of motion derived from L EXT is…”

Section: An Overview Of the Extended Geommentioning

confidence: 68%

“…At the conclusion of [1], we argued that it is only at galactic length scales and longer will we expect effects of the extension to be relevant. A study of these effects is the focus of this paper.…”

mentioning

confidence: 88%

“…This connection allows us to set a definite value of 1.56 ±0. 10 for α that is equal to the rough lower bound on α established in [1] for effects of the extension to be unobservable at solar system and terrestrial scales.…”

mentioning

confidence: 90%

“…We are also able to use these parameters to predict a value of 206 ±53 kpc for R 200 , which is in reasonable agreement with observations. Like Peebles' model for structure formation [14], the total density of matter for our model galaxy can be written as a sum of a asymptotic, background density, ρ asymp (x), and a linear perturbation, ρ 1 II (x). The matter that makes up ρ asymp (x) does not contribute to the motion of stars within the galaxy, while the matter that makes up ρ 1 II (x) does.…”

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confidence: 99%

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Dark energy and extending the geodesic equations of motion: connecting the galactic and cosmological length scales

Speliotopoulos

2010

Gen Relativ Gravit

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Recently, an extension of the geodesic equations of motion using the Dark Energy length scale was proposed. Here, we apply this extension to analyzing the motion of test particles at the galactic scale and longer. A cosmological check of the extension is made using the observed rotational velocity curves and core sizes of 1,393 spiral galaxies. We derive the density profile of a model galaxy using this extension, and with it, we calculate σ 8 to be 0.73 ±0.12 ; this is within experimental error of the WMAP value of 0.761 +0.049 −0.048 . We then calculate R 200 to be 206 ±53 kpc, which is in reasonable agreement with observations.

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Section: An Overview Of the Extended Geommentioning

confidence: 68%

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confidence: 88%

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confidence: 90%

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confidence: 99%

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Dark energy and extending the geodesic equations of motion: connecting the galactic and cosmological length scales

Speliotopoulos

2010

Gen Relativ Gravit

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“…In addition, modified geodesic equations are discussed with the Modified Newtonian Dynamics (MOND) [40][41][42] as a possible explanation of the galactic rotation curves. It was also discussed at the relativistic level within the linearized gravity limits [43], in dark energy length scale [44], in gravitons fractional physics [45] and fractional actionlike dark energy cosmology [46,47]. Remark 2.3.…”

Section: Exponential Non-standard Lagrangians In Differential Geometrmentioning

confidence: 99%

From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

El-Nabulsi

2015

Mathematics

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Abstract:Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein's field equations yet the gravity is discretized and originated from "spacetime discreteness". A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

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Dark energy and extending the geodesic equations of motion: A spectrum of galactic rotation curves

Speliotopoulos

2022

Gen Relativ Gravit

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A recently proposed extension of the geodesic equations of motion, where the worldline traced by a test particle now depends on the scalar curvature, is used to study the formation of galaxies and galactic rotation curves. This extension is applied to the motion of a fluid in a spherical geometry, resulting in a set of evolution equations for the fluid in the nonrelativistic and weak gravity limits. Focusing on the stationary solutions of these equations and choosing a specific class of angular momenta for the fluid in this limit, we show that dynamics under this extension can result in the formation of galaxies with rotational velocity curves (RVC) that are consistent with the Universal Rotation Curve (URC), and through previous work on the URC, the observed rotational velocity profiles of 1100 spiral galaxies. In particular, a spectrum of RVCs can form under this extension, and we find that the two extreme velocity curves predicted by it brackets the ensemble of URCs constructed from these 1100 velocity profiles. We also find that the asymptotic behavior of the URC is consistent with that of the most probable asymptotic behavior of the RVCs predicted by the extension. A stability analysis of these stationary solutions is also done, and we find them to be stable in the galactic disk, while in the galactic hub they are stable if the period of oscillations of perturbations is longer than $$0.91_{\pm 0.31}$$ 0 . 91 ± 0.31 to $$1.58_{\pm 0.46}$$ 1 . 58 ± 0.46 billion years.

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Dark energy and extending the geodesic equations of motion: its construction and experimental constraints

Cited by 5 publications

References 45 publications

Dark energy and extending the geodesic equations of motion: connecting the galactic and cosmological length scales

Dark energy and extending the geodesic equations of motion: connecting the galactic and cosmological length scales

From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

Dark energy and extending the geodesic equations of motion: A spectrum of galactic rotation curves

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