Invariant solutions and Noether symmetries in hybrid gravity

Borowiec, A.; Capozziello, Salvatore; Paliathanasis, Andronikos; Paolella, Mariacristina; Wojnar, Aneta

doi:10.1103/physrevd.91.023517

Cited by 72 publications

(49 citation statements)

References 60 publications

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“…The whole system can be straightforwardly derived from the general one in Appendix A (see also [41,42] for details). Note that we do not need to impose any ansantz to find out the symmetries.…”

Section: A Finding Noether's Symmetriesmentioning

confidence: 99%

Constraining generalized non-local cosmology from Noether symmetries

2017

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We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann–Robertson–Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.

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Section: A Finding Noether's Symmetriesmentioning

confidence: 99%

Constraining generalized non-local cosmology from Noether symmetries

2017

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“…In some related work, [10] used Noether symmetries to select viable theories of gravity, whilst in [11] and [12] these symmetries form a method to single out classical universes in quantum cosmology. Invariant solutions emerging from Noether symmetries are discussed in [13]. In these references, the minisuperspaces considered are similar to the ones considered here.…”

Section: Introductionmentioning

confidence: 95%

A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals

Jamal

2019

Int. J. Geom. Methods Mod. Phys.

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The investigation of approximate symmetries of reparametrization invariant Lagrangians of n + 1 degrees of freedom and quadratic velocities is presented. We show that extra conditions emerge which give rise to approximate and conditional Noether symmetries of such constrained actions. The Noether symmetries are the simultaneous conformal Killing vectors of both the kinetic metric and the potential. In order to recover these conditional symmetry generators which would otherwise be lost in gauge fixing the lapse function entering the perturbative Lagrangian, one must consider the lapse among the degrees of freedom. We establish a geometric framework in full generality to determine the admitted Noether symmetries. Additionally, we obtain the corresponding first integrals (modulo a constraint equation). For completeness, we present a pedagogical application of our method.

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“…Since ST-homogeneous Gödel-type geometries are characterized by the two essential parameters m 2 and ω 2 , the above equations (48) and (49) make explicit how the f (R) gravity specifies a pair of parameters (m 2 , ω 2 ), and therefore determines a general ST-homogeneous Gödel-type solution, for the combined-fields matter source (36).…”

Section: Combined-fields General Solutionmentioning

confidence: 99%

Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity

Santos¹,

Rebouças²,

Teixeira³

2018

Eur. Phys. J. C

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The hybrid metric-Palatini f (R) gravity is a recently devised approach to modified gravity in which it is added to the metric Ricci scalar R, in the Einstein-Hilbert Lagrangian, a function f (R) of Palatini curvature scalar R, which is constructed from an independent connection. These hybrid metric-Palatini gravity theories provide an alternative way to explain the current accelerating expansion without a dark energy matter component. If gravitation is to be described by a hybrid metric-Palatini f (R) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its equations allow homogeneous Gödel-type solutions, which necessarily leads to violation of causality. Here, to look further into the potentialities and difficulties of f (R) theories, we examine whether they admit Gödel-type solutions for physically well-motivated matter source. We first show that under certain conditions on the matter sources the problem of finding out space-time homogeneous (ST-homogeneous) solutions in f (R) theories reduces to the problem of determining solutions of Einstein's field equations with a cosmological constant. Employing this far-reaching result, we determine a general ST-homogeneous Gödel-type solution whose matter source is a combination of a scalar with an electromagnetic fields plus a perfect fluid. This general Gödel-type solution contains special solutions in which the essential parameter m 2 can be m 2 > 0 hyperbolic family, m = 0 linear class, and m 2 < 0 trigonometric family, covering thus all classes of homogeneous Gödel-type spacetimes. This general solution also contains all previously known solutions as special cases. The bare existence of these Gödel-type solutions makes apparent that hybrid metric-Palatini f (R) gravity does not remedy causal anomaly in the form of closed timelike curves that are permitted in general relativity. a

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Invariant solutions and Noether symmetries in hybrid gravity

Cited by 72 publications

References 60 publications

Constraining generalized non-local cosmology from Noether symmetries

Constraining generalized non-local cosmology from Noether symmetries

A study of the approximate singular Lagrangian-conditional Noether symmetries and first integrals

Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity

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