Comment on the general vacuum solutions in Brans-Dicke cosmology

Lorenz-Petzold, D.

doi:10.1007/bf00651688

Cited by 26 publications

(14 citation statements)

References 5 publications

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“…When convergence to GR (3 + 2ω → ±∞) is imposed at late-times (τ → ∞), Eqs. (12), (14) and (17) imply y ′ → 0 and x(τ ) ≃ γ 2 1 τ 2 /4. The integration method described in Sect.…”

Section: Late Time Solutionsmentioning

confidence: 93%

“…(16); iii) x(τ ) is then obtained from Eqs. (14) and (17); iv) Φ(τ ) from Eq. (22); v) ω(Φ) by inverting Φ(τ ) and using 3 + 2ω(τ ); vi) a(τ ) from Eq.…”

Section: Case γ < 4/3 (General Perfect Fluids)mentioning

confidence: 99%

“…As a matter of fact, the requirement x(τ ) > 0 together with Eq. (14) imply that f (τ ) > y(τ )/2 for any τ > 0. Consequently, h(τ ) is always positive.…”

Section: General Features At Arbitrary Timesmentioning

confidence: 99%

“…A great improvement in the search of solutions of the scalar-tensor field equations has recently arisen in the form of methods which allow analytical integration through suitable changes of variables. This approach was first presented by Barrow [13], who generalized the method by Lorentz-Petzold [14] to solve the vacuum and radiation-dominated cosmological equations of any scalar-tensor theory. By using and extending this method, Serna & Alimi [15] have performed an exhaustive study of the early-time behavior during the radiationdominated epoch of scalar-tensor theories where ω(φ) is a monotonic, but arbitrary, function of φ.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic and exact solutions of perfect-fluid scalar-tensor cosmologies

1999

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We present a method which enables exact solutions to be found for flat homogeneous and isotropic scalar-tensor cosmologies with an arbitrary ω(Φ) function and satisfying the general perfect fluid state equationThis method has been used to analyze a wide range of asymptotic analytical solutions at early and late times for different epochs in the cosmic history:false vacuum inflationary models, vacuum and radiation-dominated models, and matter-dominated models. We also describe the qualitative behavior of models at intermediary times and give exact solutions at any time for some particular scalar-tensor theories PACS number(s): 04.50.+h, 04.80.+z, 98.80.Cq, 98.80.Hw

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Section: Late Time Solutionsmentioning

confidence: 93%

“…(16); iii) x(τ ) is then obtained from Eqs. (14) and (17); iv) Φ(τ ) from Eq. (22); v) ω(Φ) by inverting Φ(τ ) and using 3 + 2ω(τ ); vi) a(τ ) from Eq.…”

Section: Case γ < 4/3 (General Perfect Fluids)mentioning

confidence: 99%

“…As a matter of fact, the requirement x(τ ) > 0 together with Eq. (14) imply that f (τ ) > y(τ )/2 for any τ > 0. Consequently, h(τ ) is always positive.…”

Section: General Features At Arbitrary Timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic and exact solutions of perfect-fluid scalar-tensor cosmologies

1999

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“…we introduce a conformal time r] through then, denoting d / d g by a prime,(12) becomesThis integrates to giveIf we introduce the variable employed by Lorenz-Petzold[7] in the more specialized context of the Brans-Dicke…”

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confidence: 99%

Nonsingular scalar-tensor cosmologies

Barrow

1993

Phys. Rev. D

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We present a class of scalar-tensor gravity theories which admit simple Friedmann cosmological models in the vacuum and radiation-dominated cases. A subclass of these theories yields a one-parameter family of cosmological models displaying either expansion from an initial singularity or a bounce following contraction from an infinitely extended initial state. PACS number(s1: 98.80.Hw, 04.50. +h, 04.60. +n, 12.10.Gq I. SCALAR-TENSOR GRAVITATION THEORIES Scalar-tensor gravity theories have been formulated in two different ways. Steinhardt and Accetta [I] express the Lagrangian of the theory in the form where @ is a scalar field f with coupling to the fourcurvature and L , is the Lagrangian of the remaining matter fields. If we define a new scalar field 4= f ( @ ) with a coupling then ( 1 becomes The theory proposed by Brans and Dicke [2] arises in the special case that w = const and f ( @ ) a @' . The relative merits of adopting (I), as do La and Steinhardt [3], or (3) as do Barrow and Maeda [4], have been discussed by Liddle and Wands [5].By varying the action associated with (3) with respect to the space-time metric and the scalar field we obtain the generalized Einstein equations and the wave equation for $ as follows:for the prescribed matter content. We shall study a class of exact cosmological solutions in which 4 is not constant, using the methods introduced in Ref.[6]. FRIEDMANN UNIVERSESWe shall confine our attention to zero-curvature Friedmann models with metric ( c --1 ), ds2=dt2-a2(t)(d~2+r2de2+r2sin28d$2) ,where a ( t ) is the expansion scale factor. We shall assume that the material content of the universe is blackbody radiation with the equation of the state relating the pressure p to the density p as Equations (6) and (7) then reduce to Hence, with (8) we have where l-1 0 is a constant. The case r = 0 will define the vacuum model in which p =p=O.The metric (7) reduces (4)-(6) to the two equations where T a b is the energy-momentum tensor of the matter content of the theory.Clearly, if T, the trace of the energy momentum tensor, vanishes, and $ is a constant, then ( 4 ) -( 6 ) reduce to the standard Einstein equations with a gravitational constant G = $ -I . Hence, any exact solution of Einstein's equations with a trace-free matter source will also be a particular exact solution of the scalar-tensor theory with $, and hence w(4), constant. However, these particular solutions will not necessarily constitute the general solution where an overdot denotes d /dt.If we introduce a conformal time r] through then, denoting d / d g by a prime, (12) becomes This integrates to giveIf we introduce the variable employed by in the more specialized context of the Brans-Dicke

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The conformal status of ο = -3/2 Brans-Dicke cosmology

Dąbrowski¹,

Denkiewicz

Blaschke

2007

Ann. Phys.

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Following recent fit of supernovae data to Brans-Dicke theory which favours the model with ω = −3/2 [1] we discuss the status of this special case of Brans-Dicke cosmology in both isotropic and anisotropic framework. It emerges that the limit ω = −3/2 is consistent only with the vacuum field equations and it makes such a Brans-Dicke theory conformally invariant. Then it is an example of the conformal relativity theory which allows the invariance with respect to conformal transformations of the metric. Besides, Brans-Dicke theory with ω = −3/2 gives a border between a standard scalar field model and a ghost/phantom model.In this paper we show that in ω = −3/2 Brans-Dicke theory, i.e., in the conformal relativity there are no isotropic Friedmann solutions of non-zero spatial curvature except for k = −1 case. Further we show that this k = −1 case, after the conformal transformation into the Einstein frame, is just the Milne universe and, as such, it is equivalent to Minkowski spacetime. It generally means that only flat models are fully consistent with the field equations. On the other hand, it is shown explicitly that the anisotropic non-zero spatial curvature models of Kantowski-Sachs type are admissible in ω = −3/2 Brans-Dicke theory. It then seems that an additional scale factor which appears in anisotropic models gives an extra deegre of freedom and makes it less restrictive than in an isotropic Friedmann case.

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Comment on the general vacuum solutions in Brans-Dicke cosmology

Cited by 26 publications

References 5 publications

Asymptotic and exact solutions of perfect-fluid scalar-tensor cosmologies

Asymptotic and exact solutions of perfect-fluid scalar-tensor cosmologies

Nonsingular scalar-tensor cosmologies

The conformal status of ο = -3/2 Brans-Dicke cosmology

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