ON ANALYTICAL SOLUTIONS OF f(R) MODIFIED GRAVITY THEORIES IN FLRW COSMOLOGIES

Domazet, Silvije; Radovanovic, Voja; Simonović, Marko; Štefančić, Hrvoje

doi:10.1142/s0218271813500065

Cited by 9 publications

(11 citation statements)

References 65 publications

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“…The behavior of the system near the non-gaussian fixed point for any g * and λ * is then described by a f (R) modified gravity theory with f (R) = R 2 . The importance of R 2 effective action, which can be analytically solved [25,26,27], was recently stressed in [14,15], based on Ansatz k 2 ∼ R. In this paper the relation k 2 ∼ R is derived from the scale-setting procedure, together with the coefficient of proportionality.…”

Section: Non-gaussian Fixed Point In Einstein-hilbert Truncationmentioning

confidence: 99%

Renormalization group scale-setting from the action—a road to modified gravity theories

Domazet¹,

Štefančić²

2012

Class. Quantum Grav.

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The renormalization group (RG) corrected gravitational action in EinsteinHilbert and other truncations is considered. The running scale of the renormalization group is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the EinsteinHilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG corrected gravitational theories yields the effective f (R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in Ricci tensor.

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Section: Non-gaussian Fixed Point In Einstein-hilbert Truncationmentioning

confidence: 99%

Renormalization group scale-setting from the action—a road to modified gravity theories

Domazet¹,

Štefančić²

2012

Class. Quantum Grav.

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“…Recently the same analysis has been performed and for a general perfect fluid with nonzero equation of state parameter [57], whereas for some locally rotational spacetimes the Noether point symmetry classification of f (R)-cosmology can be found in [60]. Some other f (R)-models with closed-form solutions can be found in [61], while the application of point transformations in f (R)-gravity in static spherically symmetric spacetimes can be found in [62,63] Another geometric selection rule which is based upon the group invariant transformations of the Wheeler-DeWitt equations was introduced in [64]. It has been shown that the existence of a Lie point symmetry for the WheelerDeWitt equation is equivalent with the existence of a Noetherian conservation law for the classical field equations.…”

Section: Introductionmentioning

confidence: 90%

f ( R )-gravity from Killing tensors

Paliathanasis

2016

Class. Quantum Grav.

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We consider f (R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f (R) and the field equations to be invariant under Lie-Bäcklund transformations which are linear in the momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether's Theorem. We find three new integrable f (R) models, for which with the application of the conservation laws we reduce the field equations to a system of two firstorder ordinary differential equations. For each model we study the evolution of the cosmological fluid. Where we find that for the one integrable model the cosmological fluid has an equation of state parameter, in which in the latter there is a linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder (CPL) parametric dark energy model. 95.35.+d, 95.36.+x

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“…where h is the value for the integral of motion described by the Hamiltonian for Lagrangian (40). In a similar way as before we construct the autonomous first integral [62]…”

Section: Ermakov-pinney Systemmentioning

confidence: 99%

Similarity solutions for the Wheeler–DeWitt equation in $$f\left( R\right) $$-cosmology

Paliathanasis

2019

Eur. Phys. J. C

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In the case of a spatially flat Friedmann-Lemaître-Robertson-Walker Universe in f (R)-gravity we write the Wheeler-DeWitt equation of quantum cosmology. The equation depends upon the functional form of f (R). We choose to work with four specific functions of f (R) in which the field equations for the classical models are integrable and solvable through quadratures. For these models we determine similarity solutions for the Wheeler-DeWitt equation by determining Lie-Bäcklund transformations. In addition we show how the classical limit is recovered by the similarity solutions of the Wheeler-DeWitt equation. 95.35.+d, 95.36.+x

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ON ANALYTICAL SOLUTIONS OF f(R) MODIFIED GRAVITY THEORIES IN FLRW COSMOLOGIES

Cited by 9 publications

References 65 publications

Renormalization group scale-setting from the action—a road to modified gravity theories

Renormalization group scale-setting from the action—a road to modified gravity theories

f ( R )-gravity from Killing tensors

Similarity solutions for the Wheeler–DeWitt equation in $$f\left( R\right) $$-cosmology

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