Nonlinear multidimensional cosmological models with form fields: Stabilization of extra dimensions and the cosmological constant problem

We investigate nonlinear f (R) theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A point-like matter source has the dust-like equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as General Relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.

Section: Approximate Solutionsmentioning

confidence: 99%

Asymptotic latent solitons, black strings, and black branes inf(R)gravity

Eingorn

Zhuk

2012

“…There has been considerable recent interest in the possibility that braneworld constructions give new possibilities for solving the cosmological constant problem [1,2,3,4,5,6,7,8,9,10,11,12]. One rationale is that intrinsically extra-dimensional effects might provide a loophole to Weinberg's no-go theorem against self-tuning mechanisms, which is formulated in 4D [13].…”

Section: Introductionmentioning

confidence: 99%

Codimension-two branes in six-dimensional supergravity and the cosmological constant problem

Vinet¹,

Cline²

2005

We investigate in detail recent suggestions that codimension-two braneworlds in six dimensional supergravity might circumvent Weinberg's no-go theorem for selftuning of the cosmological constant. The branes are given finite thickness in order to regularize mild singularities in their vicinity, and we allow them to have an arbitrary equation of state. We study perturbatively the time evolution of the solutions by solving the equations of motion linearized around a static background. Even allowing for the most general possibility of warping and nonconical singularities, the geometry does not relax to a static solution when the brane stress-energies are perturbed.Rather, both the internal and external geometries become time-dependent, and the system does not exhibit any self-tuning behavior.

“…Some bulk matter can mimic such behavior, e.g., vacuum fluctuations of quantum fields (Casimir effect) [24,26], monopole form fields [24,27] and gas of branes [28].…”

mentioning

confidence: 99%

Kaluza-Klein models: Can we construct a viable example?

Eingorn

Zhuk

2011

In Kaluza-Klein models with toroidal compactification of the extra dimensions, we investigate soliton solutions of Einstein equation. The nonrelativistic gravitational potential of these solitons exactly coincides with the Newtonian one. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and post-Newtonian (PPN) parameters. Using the constraint on PPN parameter , we find that the solitonic parameter k should be very big: jkj ! 2:3 Â 10 4 . We define a soliton solution which corresponds to a pointlike mass source. In this case the soliton parameter k ¼ 2, which is clearly contrary to this restriction. A similar problem with the observations takes place for static spherically symmetric perfect fluid with the dustlike equation of state in all dimensions. The common for both of these models is the same (dustlike) equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. This is the crucial point. To be in agreement with observations, it is necessary to break the symmetry (in terms of equations of state) between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k ! 1. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dustlike equation of state p 0 ¼ 0 in the external/our space and very specific equation of state p 1 ¼ Àð1=2Þ" in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.