Cosmological screening and the phantom braneworld model

Abstract

The scalar and vector cosmological perturbations at all length scales of our Universe are studied in the framework of the phantom braneworld model. The model is characterized by the parameter ΩM ≡ M 3 /2m 2 H0, with M and m the 5-and 4-dimensional Planck scales, respectively, and H0 the Hubble parameter today, while ΩM → 0 recovers the ΛCDM model. Ignoring the backreaction due to the peculiar velocities and also the bulk cosmological constant, allows the explicit computation of the gravitational potentials, Φ and Ψ. They exhibit exponentially decreasing screening behaviour characterized by a screening length which is a function of the quasidensity parameter ΩM .the study of gravitational lensing in this model. While the extra dimension is usually taken to be spacelike, we refer our reader to [13] for a timelike extra dimension.Discussions on static solutions such as a black hole in the BW model can be seen in [14,15,16,17] and references therein. For the so called two branch RS-I model, from the modification of Newton's law, the upper bound on the bulk anti-de Sitter radius turns out to be l 14 µm; whereas for the one branch RS-II model, the binary gravity wave data puts a bound : l 3.9 µm [18]. Probing the extra dimensional effects by studying the strong gravitational lensing can be seen in [19]. We refer our reader to [20] for a modification of the RS model with cosmological constants associated with both the bulk and the brane, fine tuned to make the bulk flat. This scenario is in particular helpful to estimate the energy lost by the brane via the Kaluza-Klein gravitons. In [21,22], the effect of brane -bulk energy exchange on cosmology was investigated and a model where our current universe is obtained as a late time attractor was proposed. We further refer our reader to [23] for a vast review and an exhaustive list of references pertaining to gravity and cosmology in the context of the braneworld model.In this paper, we shall be interested in an extension of the Dvali-Gabadadze-Porrati braneworld (DGP) model [24]-[27] containing in the action, the 4-dimensional Ricci scalar on the brane, induced by the one loop correction due to the graviton-matter interaction, and the extrinsic curvature of the brane. This model, unlike the Randall-Sundrum case, modifies gravity only beyond a characteristic length scale, depending on the five-and four-dimensional Newton constants. The relevant equation of motion gives rise to two branches of cosmological solutions, both with flat spatial sections, one being self accelerated without requiring any dark energy/cosmological constant, whereas the other branch (the normal branch) requires at least one cosmological constant to accommodate for the current accelerated expansion [28,29,30]. However, the former was shown to have ghost instability in subsequent works [31,32], leaving only the "normal" branch to be a possible alternative to the ΛCDM model. Furthermore, the equation of state parameter for the effective dark energy source is time dependent, w(t), and turns out to be less...

New black-string solutions for an anti–de Sitter brane in scalar-tensor gravity

“…Brane-world models based on a five-dimensional bulk scalar field leading to a cosmologically evolving brane were also studied in[86,87].…”

Incorporating physical constraints in braneworld black-string solutions for a Minkowski brane in scalar-tensor gravity

“…In [31,38], a brane-world model, that contained a bulk scalar field with an arbitrary potential and a nonminimal coupling to gravity, was studied. Scalar-tensor theories of this type are very popular and have been extensively studied in the context of four-dimensional gravity, while brane-world generalizations have been studied in the literature before, both in static and non-static backgrounds [75][76][77][78][79][80]. The objective of the analyses in [31,38] was to derive an analytical solution describing a regular, localised black hole; although no such solution was found, these studies hinted that black-string solutions were in fact much easier to emerge in the context of a non-minimally coupled scalar-tensor brane-world model.…”

Duel of cosmological screening lengths

“…Hereinafter this Yukawa-type screening is sometimes called "cosmological" or "cosmic", since it originates from the presence of the cosmological background.Both cosmic screening approaches have been formulated in the framework of the standard ΛCDM (Λ cold dark matter) model, which is consistent with the observational data [8], though it is noteworthy that currently there is tension between the direct local measurement of the Hubble constant and the value of this very constant following from the Planck data on cosmic microwave background temperature and polarization (see, e.g., [9,10,11]). Furthermore, both original papers [6,7] focus on the matter-and Λ-dominated stages of the Universe evolution, so radiation and relativistic neutrinos are disregarded (though the results of [6] have been subsequently generalized to the case of additional perfect fluids with linear and nonlinear equations of state [12,13,14], as well as to the cases of nonzero spatial curvature [15], f (R) gravity [16] and the phantom braneworld model [17]). From the mathematical point of view, the cosmological Yukawa screening inevitably comes into play when the Einstein equation for the gravitational potential (scalar perturbation) is reduced to the Helmholtz equation, which replaces its popular rival of Poisson type.…”