Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

Arakida, Hideyoshi

doi:10.3390/universe2010005

Cited by 15 publications

(16 citation statements)

References 35 publications

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“…The cosmological constant seems to be an obstacle in calculating the deflection angle of light in a curved spacetime as it can be evinced from [62] where a comparison of the different results in the Schwarschild-de Sitter spacetime has been provided. It is therefore of some interest to perform the calculation of light deflection in the C-metric with Λ.…”

Section: Gravitational Lensingmentioning

confidence: 99%

Relevant scales for the $C$-metric with positive cosmological constant

Batic,

Kittaneh,

Nowakowski

2021

Preprint

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In this work, we study the weak and strong gravitational lensing in the presence of an accelerating black hole in a universe with positive cosmological constant Λ. First of all, we derive new perturbative formulae for the event and cosmological horizons in terms of the Schwarzschild, cosmological and acceleration scales. In agreement with previous results in the literature, we find that null circular orbits for certain families of orbital cones originating from a saddle point of the effective potential are allowed and they do not exhibit any dependence on the cosmological constant. They turn out to be Jacobi unstable. We also show that it is impossible to distinguish a C-black hole from a C-black hole with Λ if we limit us to probe only into effects associated to the Sachs optical scalars. This motivates us to analyze the weak and strong gravitational lensing when both the observer and the light ray belong to the aforementioned family of invariant cones. In particular, we derive analytical formulae for the deflection angle in the weak and strong gravitational lensing regimes.

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Section: Gravitational Lensingmentioning

confidence: 99%

Relevant scales for the $C$-metric with positive cosmological constant

Batic,

Kittaneh,

Nowakowski

2021

Preprint

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“…In this part we will discuss deflection of light rays for both BDΛ and BDV theories using the geodesic equations derived in section (IV). The effect of cosmological constant on the deflection angle was a topic with opposing views with works confirming [82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97] or denying [98][99][100][101][102][103][104] this effect. Therefore, here we first give a short summary of this topic in the discussion below.…”

Section: Deflection Of Light Raysmentioning

confidence: 99%

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Özer,

Delice

2017

Preprint

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Two different ways of generalizing Einstein's general theory of relativity with a cosmological constant to Brans-Dicke type scalar-tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity cosmological constant has no role on these phenomena. We see that for the Brans-Dicke theory the cosmological constant has also no effect on these phenomena. This is because solar system observations require very large values of the Brans-Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

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“…In fact, range and range-rate are not directly observable since they are calculated through the actually measured round-trip time of flight of the photons and their frequency shift, respectively. Thus, in principle, the impact of Λ on the propagation of the electromagnetic waves connecting the spacecraft and the Earth [127][128][129][130][131] should be taken into account as well. A detailed calculation of such an aspect of the measurement modeling is beyond the scopes of the present 2 calculated by numerically integrating the barycentric equations of motion of New Horizons and the major bodies of the Solar System in Cartesian rectangular coordinates with and without the Λ−induced acceleration.…”

Section: Suggested Data Analysismentioning

confidence: 99%

Constraining the Schwarzschild–de Sitter solution in models of modified gravity

Iorio

Ruggiero

Radicella

et al. 2016

Physics of the Dark Universe

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The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely f (R) and f (T ) theories, dRGT massive gravity, and Hořava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

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Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

Cited by 15 publications

References 35 publications

Relevant scales for the $C$-metric with positive cosmological constant

Relevant scales for the $C$-metric with positive cosmological constant

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

Constraining the Schwarzschild–de Sitter solution in models of modified gravity

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