Dynamical analysis on $f(R, \mathcal{G})$ cosmology

Costa, S. Santos da; Roig, F.; Alcaniz, J. S.; Capozziello, Salvatore; Laurentis, M. De; Benetti, Micol

doi:10.1088/1361-6382/aaad80

Cited by 56 publications

(17 citation statements)

References 54 publications

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“…In general, f (R, G) gravity is taken into account to recover GR, in a given limit, assuming f (R, G) = R + f (G). Observational and theoretical constraints have been obtained also for other forms of f (R, G) [38,39] but pure f (G) theories are not, in general, considered because GR seems excluded.…”

Section: Introductionmentioning

confidence: 99%

$$f(\mathcal {G})$$ Noether cosmology

Bajardi

Capozziello

2020

Eur. Phys. J. C

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We develop the n-dimensional cosmology for $$f(\mathcal {G})$$f(G) gravity, where $$\mathcal {G}$$G is the Gauss–Bonnet topological invariant. Specifically, by the so-called Noether Symmetry Approach, we select $$f(\mathcal {G})\simeq \mathcal {G}^k$$f(G)≃Gk power-law models where k is a real number. In particular, the case $$k = 1/2$$k=1/2 for $$n=4$$n=4 results equivalent to General Relativity showing that we do not need to impose the action $$R+f(\mathcal {G})$$R+f(G) to reproduce the Einstein theory. As a further result, de Sitter solutions are recovered in the case where $$f(\mathcal {G})$$f(G) is non-minimally coupled to a scalar field. This means that issues like inflation and dark energy can be addressed in this framework. Finally, we develop the Hamiltonian formalism for the related minisuperspace and discuss the quantum cosmology for this model.

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Section: Introductionmentioning

confidence: 99%

$$f(\mathcal {G})$$ Noether cosmology

Bajardi

Capozziello

2020

Eur. Phys. J. C

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“…Modified gravity with Gauss-Bonnet scalar in the form R+f (G) was first introduced in the context of FRW metric, as alternative to dark energy for the late acceleration of the universe [7]. Several other investigations followed [8,9,10,11,12] because the Gauss-Bonnet term results useful to regularize the gravitational theory for quantum fields in curved spaces [2] and improves the efficiency of inflation giving rise to multiple accelerated expansions [13] because G behaves as a further scalaron besides R [14].…”

Section: Introductionmentioning

confidence: 99%

Cosmological perfect fluids in Gauss–Bonnet gravity

Capozziello

Mantica²,

Molinari

2019

Int. J. Geom. Methods Mod. Phys.

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In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.

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“…Case 2: f (R, T 2 ) = αR n + β(T 2 ) m Following (A1) and (A2), for this model one has that x = x 3 , y = x 4 and z = x 5 . By transforming the dynamical system (50)- (52) into Poincaré variables, one gets that at the limit ρ → 1 (infinity), the dynamical system for the leading terms becomes ρ → (2m − 1) sin 3 θ cos θ sin ψ(n cos(2ψ) − n + 2) 4m(n − 1) ,…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, it may lead to interesting cosmological results in higher dimensional theories like brane-world models. A more general class of modified gravity theory was developed in the form of f (R, G) [51,52] which includes both the f (R) and f (G) gravity theories. For the f (R, G) cosmological model the phase space structure has been investigated for a specific model which contains the power-law product form [52].…”

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confidence: 99%

“…A more general class of modified gravity theory was developed in the form of f (R, G) [51,52] which includes both the f (R) and f (G) gravity theories. For the f (R, G) cosmological model the phase space structure has been investigated for a specific model which contains the power-law product form [52]. The authors have shown that in this case the structure of the phase space contains an accelerated expansion era without a matter dominated epoch.…”

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confidence: 99%

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Dynamical system analysis of generalized energy-momentum-squared gravity

Bahamonde

Marciu

Rudra³

2019

Phys. Rev. D

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In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model f (R, T 2 ), where R represents the scalar curvature and T 2 the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions f (R, T 2 ), we have studied the structure of the phase space and the physical implications of the energy-momentum squared coupling. In the first case of functional where f (R, T 2 ) = f0R n (T 2 ) m , with f0 constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the m and n parameters. Depending on the values of the m and n parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model studied corresponds to the f (R, T 2 ) = αR n + β(T 2 ) m form with α, β constant parameters.In this case it is obtained a richer phase space structure which can recover different cosmological scenarios, associated to matter eras, de-Sitter solutions, and dark energy epochs. Hence, this model represent an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence.The second approach aims at modifying the geometry of spacetime, i.e. the Einstein's gravity in the general theory of relativity (GR) at large distances, specifically beyond our Solar System to produce accelerating cosmological solutions [5][6][7]. This has given rise to the concept of "modified gravity". There are numerous such theories available in literature, such as Brans-Dicke theory [8], Einstein-Cartan theory [9], Brane gravity theory [10-13], Rosen's Bimetric theory of gravity [14][15][16], Kaluza-Klein theory [17][18][19][20][21], Hořava-Lifshitz theory [22,23], etc. Extensive reviews in modified gravity theories can be found in the Refs. [24,25]. All these have their own share of merits and de-merits. Many of the theories of modified gravity aims at modifying the linear function of scalar curvature, R responsible for the Einstein tensor in the Einstein equations of GR. So it is obvious that the alterations are brought about in such a way so as to generalize the gravitational Lagrangian which takes a special form L GR = R in case of GR. An extensively studied theory in this context is the f (R) gravity where the gravitational Lagrangian L GR = R is replaced by an analytic function of R, i.e., L f (R) = f (R). Via this generalization, we can explore the non-linear effects of the scalar curvature R in the evolution of the universe by choosing a suitable function for f (R). Extensive reviews on this theory is available in the Refs. [26,27].The cosmological viability of f (R) dark energy models have been studied in [28]. In this paper the authors ruled out the f (R) theories where a power of R is dominant at large or small R. Conditions for the cosmological via...

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Dynamical analysis on $f(R, \mathcal{G})$ cosmology

Cited by 56 publications

References 54 publications

$$f(\mathcal {G})$$ Noether cosmology

$$f(\mathcal {G})$$ Noether cosmology

Cosmological perfect fluids in Gauss–Bonnet gravity

Dynamical system analysis of generalized energy-momentum-squared gravity

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