Dark energy from modified gravity with Lagrange multipliers

Capozziello, Salvatore; Matsumoto, Jiro; Nojiri, Shin’ichi; Odintsov, Sergei D.

doi:10.1016/j.physletb.2010.08.030

Cited by 142 publications

(139 citation statements)

References 31 publications

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“…Assuming the unimodular metric of Eq. (4), by making use of the Lagrange multiplier method [86][87][88], the vacuum Jordan frame unimodular F (R) gravity action is,…”

Section: The Unimodular F (R) Gravity Formalismmentioning

confidence: 99%

Bounce universe history from unimodularF(R)gravity

2016

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In this paper we investigate how to realize various quite well known cosmological bouncing models in the context of the recently developed unimodular F (R) gravity. Particularly, we shall study the matter bounce scenario, the singular bounce, the superbounce and a symmetric bounce scenario. We present the behavior of the Hubble radius for each of the bouncing models we shall take into account and we investigate which era of the bouncing model is responsible for the cosmological perturbations. As we shall demonstrate, the various bouncing models do not behave in the same way, so the cosmological perturbations for each model may correspond to a different era, in comparison to other models. Also we present which unimodular F (R) gravity realizes each model. We also show that Newton's law is not modified in the unimodular F (R) gravity, which also is proven to be a ghost-free theory, and in addition we discuss the matter stability issue. Finally, we demonstrate how it is possible to solve a cosmological constant problem in the context of unimodular F (R) gravity.

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“…Assuming the unimodular metric of Eq. (4), by making use of the Lagrange multiplier method [86][87][88], the vacuum Jordan frame unimodular F (R) gravity action is,…”

Section: The Unimodular F (R) Gravity Formalismmentioning

confidence: 99%

Bounce universe history from unimodularF(R)gravity

2016

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“…We note that many new results have appeared ever since the first version of this work is present in the preprint form [21][22][23][24][25][26][27][28][29]. Capozziello et al [21] studied the scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint.…”

Section: Introductionmentioning

confidence: 97%

“…Capozziello et al [21] studied the scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint. They conclude that the well-known mathematical equivalence between scalar theory and f (R) gravity is broken due to the presence of constraint.…”

Section: Introductionmentioning

confidence: 99%

Cosmological models with Lagrange multiplier field

2011

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We first consider the Einstein-aether theory with a gravitational coupling and a Lagrange multiplier field, and then consider the non-minimally coupled quintessence field theory with Lagrange multiplier field. We study the influence of the Lagrange multiplier field on these models. We show that the energy density evolution of the Einstein-aether field and the quintessence field are significantly modified. The energy density of the Einstein-aether is nearly a constant during the entire history of the Universe. The energy density of the quintessence field can also be kept nearly constant in the matter dominated Universe, or even exhibit a phantom-like behavior for some models. This suggests a possible dynamical origin of the cosmological constant or dark energy. Further more, for the canonical quintessence in the absence of gravitational coupling, we find that the quintessence scalar field can play the role of cold dark matter with the introduction of a Lagrange multiplier field. We conclude that the Lagrange multiplier field could play a very interesting and important role in the construction of cosmological models.

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“…Much research has been done [1][2][3][4][5][6][7][8] into modified gravitation theories such as torsionless (R)-gravity and curvature-free (T )-gravity as an alternative to dark energy, to explain the acceleration of the Universe discovered from supernova observations [9,10]. The main question in this research area is "Why is the Universe expanding faster than it should be? "…”

Section: Introductionmentioning

confidence: 99%

Gödel-type spacetimes in f(R)-gravity

2013

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Abstract:We focus on one of the famous problems in theoretical physics today: the problem of energy-momentum localization. Although many authors have endeavoured to solve this problem, it has remained unsolved until now. In this work, we consider the generalized version of the Landau-Lifshitz definition in (R)-Gravity to discuss the energy-momentum localization problem in Gödel-type metrics. We also take into account five popular (R) models to obtain specific results. PACS (2008):04.20.-q, 04.50.+h.

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Dark energy from modified gravity with Lagrange multipliers

Cited by 142 publications

References 31 publications

Bounce universe history from unimodularF(R)gravity

Bounce universe history from unimodularF(R)gravity

Cosmological models with Lagrange multiplier field

Gödel-type spacetimes in f(R)-gravity

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