Cosmological dynamics with modified induced gravity on the normal DGP branch

In this Letter we investigate cosmological dynamics on the normal branch of a DGP-inspired scenario within a phase space approach where induced gravity is modified in the spirit of f(R)$f(R)$-theories. We apply the dynamical system analysis to achieve the stable solutions of the scenario in the normal DGP branch. Firstly, we consider a general form of the modified induced gravity and we show that there is a standard de Sitter point in phase space of the model. Then we prove that this point is stable attractor only for those f(R)$f(R)$ functions that account for late-time cosmic speed-up.     

A Vaidya-type radiating solution in Einstein-Gauss-Bonnet gravity and its application to braneworld

We consider a Vaidya-type radiating spacetime in Einstein gravity with the Gauss-Bonnet combination of quadratic curvature terms. Simply generalizing the known static black hole solutions in Einstein-Gauss-Bonnet gravity, we present an exact solution in arbitrary dimensions with the energy-momentum tensor given by a null fluid form. As an application, we derive an evolution equation for the “dark radiation” in the Gauss-Bonnet braneworld.     

Orbital resonances in discs around braneworld Kerr black holes

Rotating black holes in the brany universe of the Randall–Sundrum type with infinite additional dimension are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b < 0 rotating black holes with dimensionless spin a > 1 are allowed. We investigate the role of the tidal charge in the orbital resonance model of quasiperiodic oscillations (QPOs) in black hole systems. The orbital Keplerian frequency v _K and the radial and vertical epicyclic frequencies v _r, v _θ of the equatorial, quasicircular geodetical motion are given. Their radial profiles related to Keplerian accretion discs are discussed, assuming the inner edge of the disc located at the innermost stable circular geodesic. For completeness, naked singularity spacetimes are considered too. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances of the oscillations with the radial and vertical epicyclic frequencies, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies involving the Keplerian and radial epicyclic frequencies. It is shown, how the tidal charge could influence matching of the observational data indicating the 3 : 2 frequency ratio observed in GRS 1915 + 105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The “magic” dimensionless black hole spin enabling presence of strong resonant phenomena at the radius, where v _K: v _θ : v _r = 3 : 2 : 1, is determined in dependence on the tidal charge. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of the spin and tidal charge are given also for existence of specific radius where v _K : v _θ : v _r = s : t : u with 5≥s >t >u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.     

Spherically Symmetric Vacuum Brane and Wormhole Solutions

In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  ⁽⁴⁾ R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.     

Brane-Cosmology Dynamics with Induced Gravity

The Friedmann equations for a brane with induced gravity are analyzed and compared with the standard general relativity and Randall-Sundrum cases. Randall-Sundrum gravity modifies the early universe dynamics, whereas induced gravity changes the late universe evolution. The early and late time limits are investigated. Induced gravity effects can contribute to late-universe acceleration. The conditions for this are found. Qualitative analysis is given for a range of scalar field potentials.     

Phantom-Like Effects on Warped DGP Brane

We study phantom-like effect on the DGP brane embedded in a five-dimensional AdS bulk. We show that this effect can be realized without phantom matter on this warped DGP brahe. We investigate the role played by the bulk cosmological constant on the phantom-like effect on the brane and we show that it tends to reduce this effect. Also, warped compactification of the bulk manifold increases the values of the effective and total equation of state parameters of the model relative to the case with Minkowski bulk. We extend our study to the ease that induced curvature on the brahe is modified in the spirit of the f（R）-gravity.     

5-dimensional braneworld with gravitating Nambu–Goto matching conditions

We continue the investigation of a recent proposal on alternative matching conditions for self-gravitating defects which generalize the standard matching conditions. The reasoning for this study is the need for consistency of the various codimension defects and the existence of a meaningful equation of motion at the probe limit, things that seem to lack from the standard approach. These matching conditions arise by varying the brane–bulk action with respect to the brane embedding fields (and not with respect to the bulk metric at the brane position) in a way that takes into account the gravitational back-reaction of the brane to the bulk. They always possess a Nambu–Goto probe limit and any codimension defect is seemingly consistent for any second order bulk gravity theory. Here, we consider in detail the case of a codimension-1 brane in five-dimensional Einstein gravity, derive the generic alternative junction conditions and find the Z₂$Z_2$-symmetric braneworld cosmology, as well as its bulk extension. Compared to the standard braneworld cosmology, the new one has an extra integration constant which accounts for the today matter and dark energy contents, therefore, there is more freedom for accommodating the observed cosmic features. One branch of the solution possesses the asymptotic linearized LFRW regime. We have constrained the parameters so that to have a recent passage from a long deceleration era to a small today acceleration epoch and we have computed the age of the universe, consistent with current data, and the time-varying dark energy equation of state. For a range of the parameters it is possible for the presented cosmology to provide a large acceleration in the high energy regime.     

The universe as a five-dimensional black hole

We show the geometrical equivalence of two five-dimensional metrics, one describing a cosmology which smoothly embeds the standard Friedmann-Robertson-Walker-Lemaître models, and another describing an object which topologically is a black hole. The solutions can be interpreted using either membrane or induced-matter theory. We outline the main physics, wherein the horizon of the black hole is connected to a big bounce in the cosmology, which may in turn be connected to a phase change in the vacuum.