Dynamical analysis of an integrable cubic Galileon cosmological model

We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.a Noether point symmetries are a subclass of Lie symmetries applied to dynamical systems that are described by a point Lagrangian and leave invariant the action integral.

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“…By Taylor expanding around ǫ = 0, as we did in (5), (6), and substitute these into (8), (9), we obtain…”

Section: Point Transformationsmentioning

confidence: 99%

“…The Noether Symmetry Approach is outlined in [3] and in [2]. Applications to scalar-tensor cosmologies are reported in [4,5,6,7]. The most general scalar-tensor theory, giving second order field equations, the so-called Horndeski gravity, is discussed in [8].…”

Section: Introductionmentioning

confidence: 99%

Noether symmetries as a geometric criterion to select theories of gravity

Dialektopoulos

Capozziello

2018

Int. J. Geom. Methods Mod. Phys.

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“…We note that the canonical scalar field models are more informative compared to the non-canonical scalar field models. The physics of canonical scalar field models, which is mostly contained in the potential, V (φ(t)) where φ(t) is the underlying field, have gained a considerable interest in the cosmological community due to explaining various stages of the universe evolution, see [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57] (also see [58,59,60,61,62]). The selection of quintessence scalar field models should not be much arbitrary, according to recently introduced swampland [63,64] and refined swampland [65] criteria.…”

Section: Introductionmentioning

confidence: 99%

Constraints on quintessence scalar field models using cosmological observations

Yang

Shahalam

Pal³

et al. 2019

Phys. Rev. D

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We consider a varieties of quintessence scalar field models in a homogeneous and isotropic geometry of the universe with zero spatial curvature aiming to provide stringent constraints using a series of cosmological data sets, namely, the cosmic microwave background observations (CMB), baryon acoustic oscillations (BAO), joint light curve analysis (JLA) from supernovae type Ia, redshift space distortions (RSD), and the cosmic chronometers (CC). From the qualitative evolution of the models, we find all of them are able to execute a fine transition from the past decelerating phase to the presently accelerating expansion where in addition, the equation of state of the scalar field (also the effective equation of state) might be close to that of the ΛCDM cosmology depending on its free parameters. From the observational analyses, we find that the scalar field parameters are unconstrained irrespective of all the observational datasets. In fact, we find that the quintessence scalar field models are pretty much determined by the CMB observations since any of the external datasets such as BAO, JLA, RSD, CC does not add any constraining power to CMB. Additionally, we observe a strong negative correlation between the parameters H0 (present value of the Hubble parameter), Ωm0 (density parameter for the matter sector, i.e., cold dark matter plus baryons) exists, while no correlation between H0, and σ8 (amplitude of the matter fluctuation) are not correlated. We also comment that the present models are unable to reconcile the tension on H0. Finally, we conclude our work with the Bayesian analyses which report that the non-interacting ΛCDM model is preferred over all the quintessence scalar field models.

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“…where U and V are defined by (49) and (50), respectively. Finally, the dynamics at the circle at infinity can be represented by the flow of…”

Section: Phase Space Analysismentioning

confidence: 99%

“…The advantage of the using phase-space analysis [41][42][43][44][45][46][47][48][49][81][82][83][84][85][86][87][88][89][90][91] is that one can do more stability analysis with using visual plots using the trajectories in geometrical way so that it becomes easy to observe the property with the help of the attractors which are the most easily seen experimentally [92]. On the other hand, conceptually using NED has the advantage that no need to use some exotic fields such as scalar fields, branes or extra dimensions, it is just photon fields, and it is well known also in nonlinear optics which studying behavior of light in nonlinear media and also nonlinear collision of particles in quantum electrodynamics [93][94][95][96][97][98][99].…”

Section: Introductionmentioning

confidence: 99%

Falsifying cosmological models based on a non-linear electrodynamics

et al. 2018

Self Cite

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Recently, the nonlinear electrodynamics (NED) has been gaining attention to generate primordial magnetic fields in the Universe and also to resolve singularity problems. Moreover, recent works have shown the crucial role of the NED on the inflation. This paper provides a new approach based on a new model of NED as a source of gravitation to remove the cosmic singularity at the big bang and explain the cosmic acceleration during the inflation era on the background of stochastic magnetic field. Also, we found a realization of a cyclic Universe, free of initial singularity, due to the proposed NED energy density. In addition, we explore whether a NED field without or with matter can be the origin of the late-time acceleration. For this we obtain explicit equations for H (z) and perform a MCMC analysis to constrain the NED parameters by using 31 observational Hubble data (OHD) obtained from cosmic chronometers covering the redshift range 0 < z < 1.97; and with the joint-light-analysis (JLA) SNIa compilation consisting in 740 data points in the range 0.01 < z < 1.2. All our constraints on the current magnetic field give B 0 ∼ 10 −31 cm −1 , which are larger than the upper limit 10 −33 cm −1 by the Planck satellite implying that NED cosmologies could not be suitable to explain the Universe late-time dynamics. However, the current data is able to falsify the scenario at late times. Indeed, one is able to reconstruct the deceleration parameter q(z) using the best fit values of the parameters obtained from OHD and SNIa data a e-mail: ali.ovgun@pucv.cl URL: https://www.aovgun.com b e-mail: genly.leon@ucn.cl c e-mail: juan.magana@uv.cl d e-mail: kimet.jusufi@unite.edu.mk sets. If the matter component is not included, the data sets predict an accelerated phase in the early Universe, but a non accelerated Universe is preferred in the current epoch. When a matter component is included in the NED cosmology, the data sets predict a q(z) dynamics similar to that of the standard model. Moreover, both cosmological data favor up to 2σ confidence levels an accelerating expansion in the current epoch, i.e., the Universe passes of a decelerated phase to an accelerated stage at redshift ∼ 0.6. Therefore, although the NED cosmology with dust matter predict a value B 0 higher than the one measured by Planck satellite, it is able to drive a late-time cosmic acceleration which is consistent with our dynamical systems analysis and it is preferred by OHD and SNIa data sets.

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Dynamical analysis of an integrable cubic Galileon cosmological model

Cited by 61 publications

References 55 publications

Noether symmetries as a geometric criterion to select theories of gravity

Noether symmetries as a geometric criterion to select theories of gravity

Constraints on quintessence scalar field models using cosmological observations

Falsifying cosmological models based on a non-linear electrodynamics

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