Nöther symmetries in cosmology

Capozziello, Salvatore; Ritis, R. de; Rubano, C.; Scudellaro, P.

doi:10.1007/bf02742992

Cited by 223 publications

(392 citation statements)

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“…To find exact solutions in the framework of the non minimally coupled models we assume that the pointlike Lagrangian possesses a Noether symmetry (for a detailed exposition of this technique which we closely follow here and interesting examples see Capozziello et al 1996). This means that we require the existence of a Noether vector field along which the Lie derivative of the Lagrangian is zero.…”

Section: Exact Solutions Through the Noether Theoremmentioning

confidence: 99%

“…Once the general solution of Eq. (20) is found, that automatically specifies the form of the potential, and a generic value of s is considered, it is possible to explicitly find the Noether symmetry and to introduce new dynamical variables associated with this symmetry (for details see Capozziello et al 1996). Using the new dynamical variables it is then possible to solve the corresponding Lagrange equations and finally by inverting them we obtain the sought after a(t) and φ(t).…”

Section: Exact Solutions Through the Noether Theoremmentioning

confidence: 99%

“…(27) and (28) lose their meaning. To find a(t) and φ(t) in this case it is necessary to use the general procedure as described in Capozziello et al (1996). From Eqs.…”

Section: Exact Solutions Through the Noether Theoremmentioning

confidence: 99%

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Accelerating universe in scalar tensor models – comparison of theoretical predictions with observations

Demiański

Piedipalumbo

Rubano

et al. 2006

A&A

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Aims. To study the possibility of the appearance of an accelerated universe in scalar tensor cosmological models. Methods. We consider scalar tensor theories of gravity assuming that the scalar field is not minimally coupled with gravity. We use this theory to study evolution of a flat homogeneous and isotropic universe. In this case the dynamical equations can be derived form a point-like Lagrangian. We study the general properties of dynamics of this system and show that for a wide range of initial conditions such models lead in a natural way to an accelerated phase of expansion of the universe. Assuming that the point-like Lagrangian admits a Noether symmetry, we are able to explicitly solve the dynamical equations. Results. We study one particular model and show that its predictions are compatible with observational data, namely the publicly available data on type Ia supernovae, the parameters of large scale structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS), the measurements of cosmological distances with the Sunyaev-Zel'dovich effect and the rate of growth of density perturbations. This model produces in a natural way an epoch of accelerated expansion. With an appropriate choice of parameters our model is fully compatible with several observed characteristics of the universe.

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Section: Exact Solutions Through the Noether Theoremmentioning

confidence: 99%

Section: Exact Solutions Through the Noether Theoremmentioning

confidence: 99%

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Accelerating universe in scalar tensor models – comparison of theoretical predictions with observations

Demiański

Piedipalumbo

Rubano

et al. 2006

A&A

Self Cite

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“…As a consequence, the gravitational coupling can be scale-dependent. This means that the concept of inertia and the Equivalence Principle have to be revised since there is no a priori reason to restrict the gravitational Lagrangian to a linear function of the Ricci scalar R, minimally coupled with matter [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

f(R) cosmology from Noether’s symmetry

Capozziello

Felice

2008

J. Cosmol. Astropart. Phys.

197

214

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A general approach to find out exact cosmological solutions in f (R)-gravity is discussed. Instead of taking into account phenomenological models, we assume, as a physical criterium, the existence of Noether symmetries in the cosmological f (R) Lagrangian. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We discuss also the case in which no Noether charge is present but general criteria can be used to achieve solutions.PACS numbers: 04.50.+h, 95.36.+x, 98.80.-k

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“…Applying the Noether Symmetry Aproach [18][19][20][21], it can be shown that the new variables we should introduce to simplify the field equations are the same used in [12]:…”

Section: An Exponential Potentialmentioning

confidence: 99%

Model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

et al. 2003

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In this work we present a model of the universe in which dark energy is modelled explicitely with both a dynamical quintessence field and a cosmological constant. Our results confirm the possibility of a collapsing universe (for a given region of the parameter space), which is necessary for an adequate definition of string theory. We have also reproduced the measurements of modulus distance from supernovae with good accuracy.

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Nöther symmetries in cosmology

Cited by 223 publications

References 100 publications

Accelerating universe in scalar tensor models – comparison of theoretical predictions with observations

Accelerating universe in scalar tensor models – comparison of theoretical predictions with observations

f(R) cosmology from Noether’s symmetry

Model of the universe including dark energy accounted for by both a quintessence field and a (negative) cosmological constant

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