Noether symmetry in f ( T ) teleparallel gravity

Sk, Nayem

doi:10.1016/j.physletb.2017.10.048

“…Furthermore, for the separable additive ansatz, we recover the g(T ) solution obtained in Refs. [28,81,[94][95][96] and as reported from Noether symmetry [97][98][99][100][101][102][103]. On the other hand, the h(B) solution is also reported in Refs.…”

Section: B Model Ii: Superbouncementioning

confidence: 52%

Cosmological bouncing solutions in f(T, B) gravity

Caruana

¹

,

Farrugia

²

,

Said

³

2020

View full text Add to dashboard Cite

Teleparallel Gravity offers the possibility of reformulating gravity in terms of torsion by exchanging the Levi-Civita connection with the Weitzenböck connection which describes torsion rather than curvature. Surprisingly, Teleparallel Gravity can be formulated to be equivalent to general relativity for a appropriate setup. Our interest lies in exploring an extension of this theory in which the Lagrangian takes the form of f(T, B) where T and B are two scalars that characterize the equivalency with general relativity. In this work, we explore the possible of reproducing well-known cosmological bouncing scenarios in the flat Friedmann–Lemaître–Robertson–Walker geometry using this approach to gravity. We study the types of gravitational Lagrangians which are capable of reconstructing analytical solutions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce settings. These new cosmologically inspired models may have an effect on gravitational phenomena at other cosmological scales.

show abstract

“…Usually, either Noether symmetry is imposed or reconstruction program is carried out to find such a form. Although a host of F(T ) has been explored so far, it is learnt that not a single Noether conserved current associated with the available forms of F(T ) satisfies the ( 0 0 ) equation of Einstein [102]. However, reconstruction program could find some of these, the simplest being F(T ) = αT + βT 2 .…”

Section: Discussionmentioning

confidence: 99%

“…Now to test inflation, a specific form of F(T ) is required. Noether symmetry analysis has been extensively performed in this respect [96][97][98][99][100][101]. However, through a private communication it is learnt that none of the forms of F(T ) associated with their conserved currents so obtained, satisfy the energy constraint equation of Einstein [102].…”

Section: Introductionmentioning

confidence: 99%

“…Noether symmetry analysis has been extensively performed in this respect [96][97][98][99][100][101]. However, through a private communication it is learnt that none of the forms of F(T ) associated with their conserved currents so obtained, satisfy the energy constraint equation of Einstein [102]. On the contrary, the outcome of reconstruction program is (F(T ) ∝ √ T in CDM model, F(T ) ∝ T in the pressure-less dust model, and F(T ) ∝ (T 2 + 6βT − 3β 2 )) for stiff fluid [44], out of which the last form appears to be quite reasonable.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Inflation with F(T) teleparallel gravity

Chakrabortty

¹

,

Sk²,

Sanyal

³

et al. 2021

Self Cite

View full text Add to dashboard Cite

We study early universe with a particular form of F(T) teleparallel gravity theory, in which inflation is driven by a scalar field. To ensure slow rollover, two different potentials are chosen in a manner, such that they remain almost flat for large initial value of the scalar field. Inflationary parameters show wonderful fit with the presently available Planck's data set. The energy scale of inflation is sub-Planckian, and graceful exit from inflation is also administered. The chosen form of F(T) administers late-time cosmic acceleration too. In the process, unification of the early inflation with late-time acceleration is ensured. Unfortunately, a decelerated radiation-dominated era is only possible with a different form of (quartic) potential, which being devoid of a flat section does not admit slow rollover.

show abstract

“…The same authors [54] studied the existence of traversable wormhole solutions in the presence of dust and non-dust matter distributions using f (R, T ) theory and discussed their physical features. In teleparallel theory and its different extensions, numerous researchers have found the exact solutions by utilizing the technique of Noether and Noether gauge symmetries using FRW and anisotropic spacetimes [55][56][57][58][59]. In another study [60], Sadjadi explored the explicit form of the generic function in f (T ) framework by utilizing generalized Noether theorem as well as generalized vector fields as variational symmetries where cold dark matter contents have been taken into account.…”

Section: Introductionmentioning

confidence: 99%

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

Waheed

¹

,

Nawazish

²

,

Zubair

³

2021

View full text Add to dashboard Cite

The present article investigates the existence of Noether and Noether gauge symmetries of flat Friedman–Robertson–Walker universe model with perfect fluid matter ingredients in a generalized scalar field formulation namely $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) gravity, where R is the Ricci scalar and Y denotes the curvature invariant term defined by $$Y=R_{\alpha \beta }R^{\alpha \beta }$$ Y = R α β R α β , while $$\phi $$ ϕ represents scalar field. For this purpose, we assume different general cases of generic $$f(R,Y,\phi )$$ f ( R , Y , ϕ ) function and explore its possible forms along with field potential $$V(\phi )$$ V ( ϕ ) by taking constant and variable coupling function of scalar field $$\omega (\phi )$$ ω ( ϕ ) . In each case, we find non-trivial symmetry generator and its related first integrals of motion (conserved quantities). It is seen that due to complexity of the resulting system of Lagrange dynamical equations, it is difficult to find exact cosmological solutions except for few simple cases. It is found that in each case, the existence of Noether symmetries leads to power law form of scalar field potential and different new types of generic function. For the acquired exact solutions, we discuss the cosmology generated by these solutions graphically and discuss their physical significance which favors the accelerated expanding eras of cosmic evolution.

show abstract

Noether symmetry in f ( T ) teleparallel gravity

Cited by 22 publications

References 70 publications

Cosmological bouncing solutions in f(T, B) gravity

Cosmological bouncing solutions in f(T, B) gravity

Inflation with F(T) teleparallel gravity

Isotropic exact solutions in $$F(R,Y,\phi )$$ gravity via Noether symmetries

Contact Info

Product

Resources

About