Bianchi Type II VIII and IX String Cosmological Models in F(R) Gravity

Abstract

In this present paper, we investigate Bianchi type II VIII and IX string cosmological models in the context of f (R) gravity. Exact solutions of the field equations are obtained. It is found that the scale factors (A, B) admit oscillatory nature in case of Bianchi type II and IX models. The strings do not exist in all three cosmological models for the f (R) theory of gravitation.

(Compactified) black branes in four dimensional f(R)-gravity

“…It is important to mention that solutions (33) and (34) reduce to (7) with constant nonzero Ricci scalar in the specific case when k = 2. In the generic case of course, when k = 2, we can see from ( 35) that (33) in its full generality is not a constant Ricci scalar solution.…”

“…where g rr corresponds to the radial variable of the metric and thus, express the latter in an ingoing Eddington -Finkelstein type of coordinate system. The minus in transformation (37) corresponds to line element (33), while the plus is for (34). As a result, we obtain…”

“…Line element (33) is appropriate for describing a (compactified) black brane or string in vacuum f (R) = R k gravity for those theories for which 1 < k < 5 4 . On the other hand, the spacetime characterized by ( 34) can be used for the same purpose when k < 1 2 and 5 4 < k ≤ 2.…”

“…We continue by calculating basic thermodynamic quantities like the temperature and the entropy for line elements (33) and (34) for those values of k for which they describe a black object. That is 1 < k < 5/4 for the first case and k ∈ (−∞, 1 2 ) ∪ ( 5 4 , 2] for the second.…”

“…As far as cosmology is concerned, the theory is used both to model the inflationary phase of the universe [16][17][18][19][20][21][22] and also as a dark energy candidate to describe the late-time acceleration phase [23][24][25][26][27][28][29][30][31]. In [32] it was found that new Kasner-like solutions exist, while some cosmological solutions in locally rotational spacetimes were derived in [33,34]. Some effects on the Mixmaster universe can be found in [35,36].…”