Cosmological perfect fluids in higher-order gravity

Capozziello, Salvatore; Mantica, Carlo Alberto; Molinari, Luca

doi:10.1007/s10714-020-02690-2

Cited by 48 publications

(36 citation statements)

References 30 publications

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“…first increasing and then decreasing). In a nutshell, without assuming m = 1 , four types of well-known potentials were obtained (Note that µ > 0 ): for all cases of study, then according to [83]…”

Section: Discussionmentioning

confidence: 99%

Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether’s approach

Tajahmad

2020

J. High Energ. Phys.

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In this paper, a modified teleparallel gravity action containing a coupling between a scalar field potential and magnetism, in anisotropic and homogeneous backgrounds, is investigated through Noether symmetry approach. The focus of this work is to describe late-time-accelerated expansion. Since finding analytical solutions carrying all conserved currents emerged by Noether symmetry approach, is very difficult, hence regularly in the literature, the authors split the total symmetry into sub-symmetries and then select, usually, some of them to be carried by the solutions. This manner limits the forms of unknown functions obtained. However, in ref.[68], B.N.S. approach was proposed in order to solve such problems but its main motivation was carrying more conserved currents by solutions. In this paper, by eliminating the aforementioned limitation as much as possible, a trick leading to some graceful forms of unknown functions is suggested. Through this fruitful approach, the solutions may carry more conserved currents than usual ways and maybe new forms of symmetries. I named this new approach to be CSSS-trick (Combination of Sub-symmetries through Special Selections). With this approach, it is demonstrated that the unified dark matter potential is deduced by the gauge fields. Utilizing the B-function method, a detailed data analysis of results obtained yielding perfect agreements with recent observational data are performed. And finally, the Wheeler-De Witt (WDW) equation is discussed to demonstrate recovering the Hartle criterion due to the oscillating feature of the wave function of the universe.

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Section: Discussionmentioning

confidence: 99%

Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether’s approach

Tajahmad

2020

J. High Energ. Phys.

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“…We consider the mini superspace defined by the dynamic variables {a, φ}. A point-like Lagrangian in the mini superspace of the for field equations (114) and (115) is…”

Section: Scalar-field Cosmologymentioning

confidence: 99%

“…Application of the previous analysis gives the following classification of Noether symmetries of the model for various forms of the effective potential [120] • For arbitrary potential V ef f (x, y), Lagrangian (120) admits the Noether point symmetry ∂ t with first integral the constraint equation (113).…”

Section: Scalar-field Cosmologymentioning

confidence: 99%

Symmetries of Differential Equations in Cosmology

2018

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Abstract:The purpose of the current article is to present a brief albeit accurate presentation of the main tools used in the study of symmetries of Lagrange equations for holonomic systems and subsequently to show how these tools are applied in the major models of modern cosmology in order to derive exact solutions and deal with the problem of dark matter/energy. The key role in this approach are the first integrals of the field equations. We start with the Lie point symmetries and the first integrals defined by them, that is, the Hojman integrals. Subsequently, we discuss the Noether point symmetries and the well-known method for deriving the Noether integrals. By means of the Inverse Noether Theorem, we show that, to every Hojman quadratic first integral, it is possible to associate a Noether symmetry whose Noether integral is the original Hojman integral. It is emphasized that the point transformation generating this Noether symmetry need not coincide with the point transformation defining the Lie symmetry which produces the Hojman integral. We discuss the close connection between the Lie point and the Noether point symmetries with the collineations of the metric defined by the kinetic energy of the Lagrangian. In particular, the generators of Noether point symmetries are elements of the homothetic algebra of that metric. The key point in the current study of cosmological models is the introduction of the mini superspace, which is the space that is defined by the physical variables of the model, which is not the spacetime where the model evolves. The metric in the mini superspace is found from the kinematic part of the Lagrangian and we call it the kinetic metric. The rest part of the Lagrangian is the effective potential. We consider coordinate transformations of the original mini superspace metric in order to bring it to a form where we know its collineations, that is, the Killing vectors, the homothetic vector, etc. Then, we write the field equations of the cosmological model and we use the connection of these equations with the collineations of the mini superspace metric to compute the first integrals and subsequently to obtain analytic solutions for various allowable potentials and finally draw conclusions about the problem of dark energy. We consider the ΛCDM cosmological model, the scalar field cosmology, the Brans-Dicke cosmology, the f (R) gravity, the two scalar fields cosmology with interacting scalar fields and the Galilean cosmology. In each case, we present the relevant results in the form of tables for easy reference. Finally, we discuss briefly the higher order symmetries (the contact symmetries) and show how they are applied in the cases of scalar field cosmology and in the f (R) gravity.

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“…which allows generalized derivative couplings of H with gravity. The couplings ς and θ in (3.22) were first studied in [31,32]. So far, the Higgs potential V (H) in (3.21) is unidentified.…”

Section: Second Approach: Extended Brans-dicke Modelmentioning

confidence: 99%

Cosmological evolution of the proton-to-electron mass ratio in an extended Brans–Dicke theory

Mohamadnejad

2019

Mod. Phys. Lett. A

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We study variation of the proton-to-electron mass ratio µ = m p /m e by incorporating standard model (SM) of particle physics into an extended Brans-Dicke theory. We show that the evolution of the Higgs vacuum expectation value (VEV), with expansion of the Universe, leads to the variation of the proton-to-electron mass ratio. This is because the electron mass is proportional to the Higgs VEV, while the proton mass is mainly dependent on the quantum chromodynamics (QCD) energy scale, i.e., Λ QCD . Therefore, using the experimental and cosmological constraints on the variation of the µ we can constrain the variation of the Higgs VEV. This study is important in understanding the recent claims of the detection of a variation of the proton-to-electron mass ratio in quasar absorption spectra. * a.mohamadnejad@ut.ac.ir

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Cosmological perfect fluids in higher-order gravity

Cited by 48 publications

References 30 publications

Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether’s approach

Late-time-accelerated expansion arisen from gauge fields in an anisotropic background and a fruitful trick for Noether’s approach

Symmetries of Differential Equations in Cosmology

Cosmological evolution of the proton-to-electron mass ratio in an extended Brans–Dicke theory

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