Measurement of the Cosmological Constant from Galactic Velocity Rotation Data

Kraniotis, G. V.; Whitehouse, S. B.

doi:10.1007/978-3-662-04587-9_6

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…Our exact treatment of the geodesic equations can be applied to a variety of problems in cosmology where the two-body central orbit problem in general relativity is encountered. More specifically our techniques can be applied to address problems such as: the determination of orbital parameters of stars around massive gravitational objects such as neutron stars [18] or candidate black holes [19], galactic dynamics including the missing mass problem [3] which will be the subject of a separate publication, or other scales in cosmology [20,33]. It would also be interesting to generalize the techniques developed in this paper to the gravitational field of a rotating mass.…”

Section: Discussion and Further Applicationsmentioning

confidence: 99%

Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi's inversion problem

Kraniotis

Whitehouse

2003

Class. Quantum Grav.

102

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The geodesic equations resulting from the Schwarzschild gravitational metric element are solved exactly including the contribution from the Cosmological constant. The exact solution is given by genus 2 Siegelsche modular forms. For zero cosmological constant the hyperelliptic curve degenerates into an elliptic curve and the resulting geodesic is solved by the Weierstraß Jacobi modular form. The solution is applied to the precise calculation of the perihelion precession of the orbit of planet Mercury around the Sun.

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Section: Discussion and Further Applicationsmentioning

confidence: 99%

Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi's inversion problem

Kraniotis

Whitehouse

2003

Class. Quantum Grav.

102

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“…The cosmological constant [1] is presently at the epicentre of contemporary physics [2] and plays a significant role in fields such as cosmology, astronomy, general relativity, particle physics and string theory.…”

Section: Motivationmentioning

confidence: 99%

“…In particular, the results from high redshift type Ia supernovae observations suggest an accelerating universe (positive cosmological constant) where the age of the universe and Hubble's constant H are approximately ∼14.5 billion years and 70 km s −1 Mpc −1 , respectively. Other indirect experimental evidence [3,6] has put bounds on the energy density ratios of matter, dark energy and curvature, given by m ≡ 8πG N ρ matter /(3H 2 ) ∼ 0.3, ≡ c 2 3H 2 ∼ 0.6-0.7, K ≡ −Kc 2 /(R(t)H ) 2 ∼ 0, respectively. In these definitions G N is Newton's constant, ρ matter denotes the density of matter, K is the curvature coefficient and R(t) is the scale factor.…”

Section: Motivationmentioning

confidence: 99%

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General relativity, the cosmological constant and modular forms

Kraniotis

Whitehouse

2002

Class. Quantum Grav.

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Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron family of space-time line element with a nonzero Cosmological Constant. The resulting solution connects, in an intrinsic way, General Relativity with the theory of modular forms and elliptic curves and thus to the theory of Taniyama-Shimura.The homogeneous FLRW limit of the above space-time elements is recovered and we solve exactly the resulting Friedmann Robertson field equation with the appropriate matter density for generic values of the Cosmological Constant Λ and curvature constant K. A formal expression for the Hubble constant is derived. The cosmological implications of the resulting non-linear solutions are systematically investigated. Two particularly interesting solutions i) the case of a flat universe K = 0, Λ = 0 and ii) a case with all three cosmological parameters non-zero, are associated with elliptic curves with the property of complex multiplication and absolute modular invariant j = 0, 1728 respectively. The possibilty that all non-linear solutions of General Relativity are expressed in terms of theta functions associated with Riemann-surfaces is discussed.

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A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework

Farnes

2018

A&A

134

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Dark energy and dark matter constitute 95% of the observable Universe. Yet the physical nature of these two phenomena remains a mystery. Einstein suggested a long-forgotten solution: gravitationally repulsive negative masses, which drive cosmic expansion and cannot coalesce into light-emitting structures. However, contemporary cosmological results are derived upon the reasonable assumption that the Universe only contains positive masses. By reconsidering this assumption, I have constructed a toy model which suggests that both dark phenomena can be unified into a single negative mass fluid. The model is a modified ΛCDM cosmology, and indicates that continuously-created negative masses can resemble the cosmological constant and can flatten the rotation curves of galaxies. The model leads to a cyclic universe with a time-variable Hubble parameter, potentially providing compatibility with the current tension that is emerging in cosmological measurements. In the first three-dimensional N-body simulations of negative mass matter in the scientific literature, this exotic material naturally forms haloes around galaxies that extend to several galactic radii. These haloes are not cuspy. The proposed cosmological model is therefore able to predict the observed distribution of dark matter in galaxies from first principles. The model makes several testable predictions and seems to have the potential to be consistent with observational evidence from distant supernovae, the cosmic microwave background, and galaxy clusters. These findings may imply that negative masses are a real and physical aspect of our Universe, or alternatively may imply the existence of a superseding theory that in some limit can be modelled by effective negative masses. Both cases lead to the surprising conclusion that the compelling puzzle of the dark Universe may have been due to a simple sign error.

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Measurement of the Cosmological Constant from Galactic Velocity Rotation Data

Cited by 4 publications

References 8 publications

Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi's inversion problem

Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi's inversion problem

General relativity, the cosmological constant and modular forms

A unifying theory of dark energy and dark matter: Negative masses and matter creation within a modified ΛCDM framework

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