Cosmological dynamics of fourth order gravity

Carloni, S; Dunsby, P K S; Troisi, A

doi:10.48550/arxiv.0906.1998

Cited by 7 publications

(9 citation statements)

References 20 publications

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“…With help of Eqs. ( 23) and (27), we obtain the shear evolution equation in terms of the dimensionless variables as…”

Section: B Propagation Equations Of Kinematical Quantities In F (R) G...mentioning

confidence: 99%

“…and it was shown that the model will be the viable f (R) DE if α > 0 and 0 < n < 1 [16]. Especially, the standard dynamical system method is used to analyze in the FLRW counterpart [27]. For the anisotropic cases, it was studied in the Kantowski-Sach metric [30].…”

Section: Dynamics Of Magnetic Bianchi I Universe In F (R) Models Of G...mentioning

confidence: 99%

“…It has been successfully used to study and to understand a number of cosmological models such as the standard GR cosmology [20], the scalar fields models of dark energy [21], the scalar-tensor theories of gravity [22] and the brane-world models [23]. Moreover, the cosmological dynamics of f (R) gravity was extensively studied in [7,[24][25][26][27][28]30] by using the dynamical system analysis frameworks in homogeneous and isotropic universe (a.k.a. the FLRW model) and in the less anisotropic counterpart (Bianchi types and the others) [29,[43][44][45].…”

Section: Introductionmentioning

confidence: 99%

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Cosmological dynamics of magnetic Bianchi I in viable f(R) models of gravity

Liu

Channuie

Samart

2017

Physics of the Dark Universe

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Standard dynamical system analysis of Einstein-Maxwell equation in f (R) theories is considered in this work. We investigate cosmological dynamics of a uniform magnetic field in the Orthogonal Spatially Homogeneous (OSH) Bianchi I universe with viable f (R) models of gravity. In this work, the f (R) = R − αR n and f (R) = R b − Λ c models are examined by using our dynamical system analysis. Our results show that both of two f (R) models have a viable cosmological consequence identical to the analysis present in Ref.[17] for the FLRW background. Contrary to Ref.[17], we discover in our models that there is an additional anisotropic and non-zero cosmological magnetic fields fixed point emerging before the present of the standard matter epoch. This means that the universe has initially isotropic stage with the intermediated epoch as the anisotropic background and it ends up with the isotropic late-time acceleration. The primordial magnetic fields play a crucial role of the shear evolutions obtained from these two models which have the same scaling of the cosmic time as σ ∼ t − 1 3 , instead of σ ∼ t −1 for the absence of the primordial magnetic cases.

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“…With help of Eqs. ( 23) and (27), we obtain the shear evolution equation in terms of the dimensionless variables as…”

Section: B Propagation Equations Of Kinematical Quantities In F (R) G...mentioning

confidence: 99%

Section: Dynamics Of Magnetic Bianchi I Universe In F (R) Models Of G...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cosmological dynamics of magnetic Bianchi I in viable f(R) models of gravity

Liu

Channuie

Samart

2017

Physics of the Dark Universe

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“…Refs. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). It is based on the definition of a set of expansion normalised variables of clear physical meaning which help the physical interpretation of the orbits obtained.…”

Section: Introductionmentioning

confidence: 99%

Cosmology of f(R,❑R) gravity

2019

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Using dynamical system analysis, we explore the cosmology of theories of order up to eight order of the form f (R, R). The phase space of these cosmology reveals that higher-order terms can have a dramatic influence on the evolution of the cosmology, avoiding the onset of finite time singularities. We also confirm and extend some of results which were obtained in the past for this class of theories. I. INTRODUCTIONGeneral relativity deals with second-order differential equations for the metric g µν . Higher-order modifications of the gravitational interaction have been for long time the focus of intense investigation. They have been proposed for a number of reasons including the first attempts of unification of gravitation and other fundamental interactions. Nowadays, the main reason why one considers this kind of extension in general relativity is of quantum origin. Studies on the renormalisation of the stress-energy tensor of quantum fields in the framework of a semi classical approach to genral relativity, i.e., what we call quantum field theory in curved spacetime, shows that such corrections are needed to take into account the differences between the gravitation of quantum fields and the gravitation of classical fluids [1,2].With the introduction of the paradigm of inflation and the requirement of a field able to drive it, it was natural, although not obvious, to consider these quantum corrections as the engine of the inflationary mechanism. Starobinski [3] was able to show explicitly in the case of fourth-order corrections to general relativity that this was indeed the case: quantum corrections could induce an inflationary phase. Such result should not be surprising. Fourth-order gravity carries an additional scalar degree of freedom and this scalar degree of freedom can drive an inflationary phase. In the following years other researchers [4][5][6][7] tried to look at the behaviour of sixth-order corrections, to see if in this case one could obtain a richer inflationary phase and more specifically a cosmology with multiple inflationary phases. However, it turned out that this is not the case: in spite of the presence of an additional scalar degree of freedom, multiple inflationary phases were not possible. The reason behind this result is still largely unknown.The discovery of the dark energy offered yet another application for the additional degree of freedom of higher-order gravity. Like in the case of inflation, this perspective offered an elegant way to explain dark energy: higher-order corrections were a geometrical way to interpret the mysterious new component of the Universe [8]. Here an important point should be stressed: differently from the standard perturbative investigation of a physical system, in the case of higher-order gravity, the behaviour of the new theory cannot be deduced as a small perturbation of the original second-order one. The reason is that, since the equations of motion switch order, the dynamics of the perturbed system are completely different from the non-perturbed one whatev...

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“…In this case the field equations can be recast in a way that the higher order corrections are written as an energy-momentum tensor of geometrical origin describing an "effective" source term on the right hand side of the standard Einstein field equations [78,79]. These models have been studied from the dynamical systems viewpoint in [100,111,112,113,114,115,116,117,118,119,120,121,122].…”

Section: Introductionmentioning

confidence: 99%