The possibility of an accelerating cosmology in Rastall's theory

Abstract

In an attempt to look for a viable mechanism leading to a present-day accelerated expansion, we investigate the possibility that the observed cosmic speed up may be recovered in the framework of the Rastall's theory, relying on the non-conservativity of the stress-energy tensor, i.e. T µ ν;µ = 0. We derive the modified Friedmann equations and show that they correspond to Cardassian-like equations. We also show that, under suitable assumptions on the equation of state of the matter term sourcing the gravitational field, it is indeed possible to get an accelerated expansion, in agreement with the Hubble diagram of both Type Ia Supernovae (SNeIa) and Gamma Ray Bursts (GRBs). Unfortunately, to achieve such a result one has to postulate a matter density parameter much larger than the typical ΩM ≃ 0.3 value inferred from cluster gas mass fraction data.

A generalization to the Rastall theory and cosmic eras

“…Therefore, because λ is constant and the R(4κ λ − 1) = κ T condition applies to all spacetimes and energy-momentum sources, the κ λ = 1 4 case is not allowed [23]. More studies on the various aspects of this theory can be found in [74,[77][78][79][80][81][82][83][84][85][86][87][88][89][90].…”

Traversable asymptotically flat wormholes in Rastall gravity

“…Besides, since the time-time component of the Ricci tensor (R 00 ) should meet the Newtonian limit [47,50,66], we get…”

“…(51) gives a lower bound for α, and therefore, we should have 1−γ γ < α < 1 to meet the the asymptotically flat condition (α < 1). Inserting (50) and (49) into (48), one can obtain…”

“…In fact, the curvature-matter theory is a kind of f (R) gravity, in which matter and geometry are coupled to each other in a non-minimal way [39][40][41], and its lagrangian differs from that of the Rastall theory [49,50]. As we have mentioned, the wormholes structures are addressed in the curvature-matter coupling framework [23][24][25].…”

Scalar QNMs for higher dimensional black holes surrounded by quintessence in Rastall gravity

“…This framework has been attracted some attentions over the last few years, and some results have been already obtained, both related to astrophysical [2][3][4][5][6][7][8][9] and cosmological solutions [10][11][12][13][14][15][16]. In particular, black holes solutions surrounded by exotic matter fields have been obtained based on the idea developed by Kiselev [17], who states that one should consider astrophysical solutions surrounded by a dark energy field, in accordance with the recent cosmological observations about the acceleration of the universe.…”