Conformal Relativity versus Brans–Dicke and Superstring Theories

Blaschke, D.; Dąbrowski, Mariusz P.

doi:10.3390/e14101978

Cited by 11 publications

(10 citation statements)

References 60 publications

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“…Such modification has recently been considered by Kofinas (2015) in the context of energy exchange between a scalar field and the standard matter. This allows an avoidance of having the problem with singular conformal cosmology (and also cyclic conformal cosmology -CCC (Penrose 2009(Penrose , 2010Majid et al 2008)) limit ω = −3/2 (or Kofinas' λ = 2/(3+2ω) → ∞) and allows the entropy growth needed to drive our cyclic multiverse models (Blaschke & Da ¸browski 2012).…”

Section: Cyclic Brans-dicke Multiversementioning

confidence: 99%

Cyclic multiverses

Marosek

Dąbrowski

Balcerzak

2016

Mon. Not. R. Astron. Soc.

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Using the idea of regularisation of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure ("non-singular" bounce) regularised by varying gravitational constant G despite the scale factor evolution is oscillating and having sharp turning points ("singular" bounce). Both violating (big-bang) and non-violating (phantom) null energy condition models appear. Then, we extend this idea onto the multiverse containing cyclic individual universes with either growing or decreasing entropy though leaving the net entropy constant. In order to get an insight into the key idea, we consider the doubleverse with the same geometrical evolution of the two "parallel" universes with their physical evolution (physical coupling constants c(t) and G(t)) being different. An interesting point is that there is a possibility to exchange the universes at the point of maximum expansion -the fact which was already noticed in quantum cosmology. Similar scenario is also possible within the framework of Brans-Dicke theory where varying G(t) is replaced by the dynamical Brans-Dicke field φ(t) though these theories are slightly different.

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Section: Cyclic Brans-dicke Multiversementioning

confidence: 99%

Cyclic multiverses

Marosek

Dąbrowski

Balcerzak

2016

Mon. Not. R. Astron. Soc.

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“…(12) and (15) indicate that T (EMT) αβ and the induced scalar potential are null contrary to the results obtained in the literature [15]. The exception case is ω = −1 which is precisely the value predicted when the BD theory is derived as the low energy limit of some string theories [40,41].…”

Section: Generalized Bianchi Type I Metric In 5d Bd Theorymentioning

confidence: 67%

“…on i) are the energy density and the directional pressure of the induced EMT, respectively. Now, from relations (30),(41),(45),(48),(49) and(52)one obtains…”

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confidence: 99%

An anisotropic cosmological model in a modified Brans–Dicke theory

Rasouli¹,

Farhoudi²,

Sepangi³

2011

Class. Quantum Grav.

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Recently, it has been shown that a four-dimensional (4D) Brans-Dicke (BD) theory with an effective matter field and a self interacting potential can be achieved from the vacuum 5D BD field equations, where we refer to as a modified Brans-Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing the obtained formalism, we derive the induced-matter on any 4D hypersurface in the context of the MBDT. We illustrate that if the usual spatial scale factors are functions of the time while the scale factor of extra dimension is constant, and the scalar field depends on the time and the fifth coordinate, then in general, one will encounter inconsistencies in the field equations. Then, we assume the scale factors and the scalar field depend on the time and the extra coordinate as separated variables in the power-law forms. Hence, we find a few classes of solutions in 5D space-time through which, we probe the one which leads to a generalized Kasner relations among the Kasner parameters. The induced scalar potential is found to be in the power-law or in the logarithmic form, however, for a constant scaler field and even when the scalar field only depends on the fifth coordinate, it vanishes. The conservation law is indeed valid in this MBDT approach for the derived induced energy-momentum tensor (EMT). We proceed our investigations for a few cosmological quantities, where for simplicity we assume the metric and the scalar field are functions of the time. Hence, the EMT satisfies the barotropic equation of state, and the model indicates that constant mean Hubble parameter is not allowed. Thus, by appealing to the variation of Hubble parameter, we assume a fixed deceleration parameter, and set the evolution of the quantities with respect to the fixed deceleration, the BD coupling and the state parameters. The WEC allows a shrinking extra dimension for a decelerating expanding universe that, in the constant scalar field, evolves the same as the flat FRW space-time in GR. The quantities for the stiff fluid and the radiation dominated universe indicate an expanding universe commenced with a big bang. There is a horizon for each of the fluids, and the rate of expansion slows down by the time. The allowed ranges of the deceleration and the BD coupling parameters have been obtained, and the model gives an empty universe when the time goes to infinity.

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“…where, without loss of generality, we have set the integration constant equal to zero. We should note that, in some particular cases, V (η) vanishes: (i) α = −2β, in which ψ(η) takes constant values and therefore all the solutions for ζ = ±1 in the previous section as well as this section reduce to their counterparts obtained in the context of the standard BD theory in 4D space-time; (ii) ω = −1: for this particular case, there are similarities between the scalar-tensor theories and supergravity [47] (it has been believed that, for this particular value of the BD coupling parameter, the standard BD theory can be considered as a low energy limit of the bosonic string theory [47,48]); and (iii) β = 0: in this case, the BD scalar field takes constant values, therefore, our solutions in the previous section reduce to the corresponding Kantowski-Sachs and LRS Bianchi type III cosmological models in a 5D space-time obtained in general relativity, and consequently, the solutions of the present section describe the behavior of the quantities for the Kantowski-Sachs and LRS Bianchi type III cosmological models in the context of the induced-matter theory. We will further investigate the case (iii) in this paper.…”

Section: Effective Brans-dicke Cosmologies On a Four Dimensional mentioning

confidence: 72%

Extended anisotropic models in noncompact Kaluza–Klein theory

Rasouli¹,

Moniz²

2019

Class. Quantum Grav.

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In this paper, new exact solutions for locally rotational symmetric (LRS) space-times are obtained within the modified Brans-Dicke theory (MBDT) [1]. Specifically, extended five-dimensional (5D) versions of Kantowski-Sachs, LRS Bianchi type I and Bianchi type III are investigated in the context of the standard Brans-Dicke theory. We subsequently extract their corresponding dynamics on a 4D hypersurface. Our results are discussed regarding others obtained in the standard Brans-Dicke theory, induced-matter theory and general relativity. Moreover, we comment on the evolution of the scale factor of the extra spatial dimension, which is of interest in Kaluza-Klein frameworks.

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Conformal Relativity versus Brans–Dicke and Superstring Theories

Cited by 11 publications

References 60 publications

Cyclic multiverses

Cyclic multiverses

An anisotropic cosmological model in a modified Brans–Dicke theory

Extended anisotropic models in noncompact Kaluza–Klein theory

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