Field Independent Cosmic Evolution

Abstract

It has been shown earlier that Noether symmetry does not admit a form of ( ) corresponding to an action in which ( ) is coupled to scalar-tensor theory of gravity or even for pure ( ) theory of gravity taking anisotropic model into account. Here, we prove that ( ) theory of gravity does not admit Noether symmetry even if it is coupled to tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higherorder curvature part from the field part. This condition, in principle, solves for the scale-factor independently. Thus, cosmological evolution remains independent of the form of the chosen field, whether it is a scalar or a tachyon.

Noether symmetry of Palatini F(ℜ) gravity

“…Search of a better form of F (R) taking a scalar field minimally or non-minimally into account failed to produce symmetry [22]. It is also found that Noether symmetry does not yield anything new in the presence of gauge [29,30,31]. Here, it has been shown that Noether Symmetry selects F (ℜ) ∝ ℜ 3 2 along with a conserved current Σ 0 a[ȧ a +Φ 2Φ ] in Palatini gravity.…”

“…(ii) It does not yield any symmetry when the configuration space is enlarged by including scalar field or in anisotropic model [22]. (iii) Inclusion of gauge term does not improve the situation [29,30,31]. (iv) Exact solution in R-W metric does not satisfy all cosmological data and a linear term may be necessary in addition [22].…”

“…(vi) A non-Noether conserved current exists in general for gravity when a non-minimally coupled scalar field is added to F (R). It has been shown that it is useful to obtain improved exact solution [22,31].…”

Noether symmetry in f ( T ) teleparallel gravity

“…Thus, the claim that arbitrary power of R generates Noether symmetry is not correct. The claim of Jamil et-al [26] had also been reviewed by the same authors Sk and Sanyal [28] and it was shown that f (R) ∝ R 2 do not satisfy the Tachyonic field equations. Shamir et-al [29] on the contrary, had claimed that Noether symmetry of f (R) ∝ R 3 2 admits four different generators corresponding to which four different conserved currents exist in the presence of non-zero gauge.…”

Untitled

“…, , , , , , )A A B B f V ω . It is important to mention that while general conserved current always exists for2 V f ∝ ,[49][50][51]60,61 Noether symmetry exists for3 V f ∝, in the absence of Lambda. This clearly depicts that Noether symmetry procedure is unable to explore all the available symmetries of a theory.…”