ON IMPLICATIONS OF EQUIVALENCE PRINCIPLE FOR MODIFIED GRAVITY THEORIES

2011 ◽  
Vol 20 (14) ◽  
pp. 2839-2845 ◽  
Author(s):  
M. M. SHEIKH-JABBARI
Keyword(s):  
Modified Gravity ◽  
Equivalence Principle ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Lovelock Gravity ◽  
Modified Gravity Theory ◽  
Modified Gravity Theories ◽  
Levi Civita Connection ◽  
Gravity Theories ◽  
Einstein’S General Relativity

One of the manifestations of Einstein Equivalence Principle (EEP) is that a freely falling particle in a gravitational field is following a geodesic. In Einstein's general relativity (GR) this is built in the formulation by assuming the connection to be the Levi-Civita connection. The latter may, however, be demanded to be implied by the dynamics of a generic modified gravity theory, within the Palatini formulation. We show that for extensions of the Einstein GR which are described by a Lagrangian [Formula: see text], where gμν is the metric and Rμαβν is the Riemann curvature tensor, this manifestation of EEP is only fulfilled for a special class of Lagrangians, the Lovelock gravity theories. Our analysis also implies that within the above mentioned set of modified gravity theories only for Lovelock gravity theories metric and Palatini formulations are equivalent.

scholarly journals Modified gravity from an entropy functional

2014 ◽  
Vol 23 (09) ◽  
pp. 1450073 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Modified Gravity ◽  
Higher Order ◽  
Functional Formalism ◽  
Entire Series ◽  
Entropy Functional ◽  
Modified Gravity Theory ◽  
Horizon Entropy ◽  
Modified Gravity Theories ◽  
Gravity Theories ◽  
Higher Order Corrections

We extend Padmanabhan's entropy functional formalism to show that, in addition to the Gauss–Bonnet (GB) or the entire series of Lanczos–Lovelock Lagrangians already obtained, more general higher-order corrections to General Relativity, i.e. the so-called modified gravity theories, also emerge naturally from this formalism. This extension shows that the formalism constitutes a valuable tool to investigate, at each order in the curvature, the possible structure the higher-order modified gravity theories might have. As an application, the extended formalism is used to evaluate the horizon entropy in a modified gravity theory of the second-order in the curvature. Our findings are in agreement with previous results from the literature.

Nonlinear structure formation in gravity theories beyond general relativity

2016 ◽  
Vol 31 (21) ◽  
pp. 1640007
Author(s):  
David F. Mota
Keyword(s):  
Structure Formation ◽  
Modified Gravity ◽  
Equivalence Principle ◽  
Velocity Dispersion ◽  
Power Spectra ◽  
Nonlinear Structure ◽  
Modified Gravity Theories ◽  
Gravity Theories ◽  
Halo Masses ◽  
Screening Scale

We investigate the effects of modified gravity theories, in particular, the symmetron and f(R) gravity, on the nonlinear regime of structure formation. In particular, we investigate the velocity dispersion of galaxy clusters as a function of the halo masses, how the matter power spectra depend on the coupling, range and screening scale of the fifth force, and on possible ways of detecting violations of the equivalence principle using the mass inferred via lensing methods versus the mass inferred via dynamical methods.

scholarly journals Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

2021 ◽  
Author(s):  
V. Cortés ◽  
A. Saha ◽  
D. Thung
Keyword(s):  
Curvature Tensor ◽  
Decomposition Theorem ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Cohomogeneity One ◽  
Civita Connection ◽  
Levi Civita Connection ◽  
Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

Probing screened modified gravity with nonlinear structure formation

2018 ◽  
Vol 27 (04) ◽  
pp. 1830003 ◽  
Author(s):  
David F. Mota
Keyword(s):  
Structure Formation ◽  
Modified Gravity ◽  
Equivalence Principle ◽  
Velocity Dispersion ◽  
Power Spectra ◽  
Nonlinear Structure ◽  
Fifth Force ◽  
Modified Gravity Theories ◽  
Halo Masses ◽  
Screening Scale

We review the effects of modified gravity theories, in particular the symmetron and [Formula: see text] gravity, on the nonlinear regime of structure formation. In particular, we investigate the velocity dispersion of galaxy clusters as a function of the halo masses, how the matter power spectra depend on the coupling, range, and screening scale of the fifth force, and on possible ways of detecting violations of the equivalence principle using the mass inferred via lensing methods versus the mass inferred via dynamical methods. Furthermore, we show how one could use different voids statistics as one of the most promising probes of modified gravity.

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