Ellipsoidal universe in the brane world

We study a scenario of the ellipsoidal universe in the brane world cosmology with a cosmological constant in the bulk . From the five-dimensional Einstein equations we derive the evolution equations for the eccentricity and the scale factor of the universe, which are coupled to each other. It is found that if the anisotropy of our universe is originated from a uniform magnetic field inside the brane, the eccentricity decays faster in the bulk in comparison with a four-dimensional ellipsoidal universe. We also investigate the ellipsoidal universe in the brane-induced gravity and find the evolution equation for the eccentricity which has a contribution determined by the four- and five-dimensional Newton's constants. The role of the eccentricity is discussed in explaining the quadrupole problem of the cosmic microwave background.Comment: 15 pages, 1 figure, Version 3, references added, contents expande

Modified-Source Gravity and Cosmological Structure Formation

One way to account for the acceleration of the universe is to modify general relativity, rather than introducing dark energy. Typically, such modifications introduce new degrees of freedom. It is interesting to consider models with no new degrees of freedom, but with a modified dependence on the conventional energy-momentum tensor; the Palatini formulation of $f(R)$ theories is one example. Such theories offer an interesting testing ground for investigations of cosmological modified gravity. In this paper we study the evolution of structure in these ``modified-source gravity'' theories. In the linear regime, density perturbations exhibit scale dependent runaway growth at late times and, in particular, a mode of a given wavenumber goes nonlinear at a higher redshift than in the standard $\Lambda$CDM model. We discuss the implications of this behavior and why there are reasons to expect that the growth will be cut off in the nonlinear regime. Assuming that this holds in a full nonlinear analysis, we briefly describe how upcoming measurements may probe the differences between the modified theory and the standard $\Lambda$CDM model.Comment: 22 pages, 6 figures, uses iopart styl

Perturbations of Self-Accelerated Universe

We discuss small perturbations on the self-accelerated solution of the DGP model, and argue that claims of instability of the solution that are based on linearized calculations are unwarranted because of the following: (1) Small perturbations of an empty self-accelerated background can be quantized consistently without yielding ghosts. (2) Conformal sources, such as radiation, do not give rise to instabilities either. (3) A typical non-conformal source could introduce ghosts in the linearized approximation and become unstable, however, it also invalidates the approximation itself. Such a source creates a halo of variable curvature that locally dominates over the self-accelerated background and extends over a domain in which the linearization breaks down. Perturbations that are valid outside the halo may not continue inside, as it is suggested by some non-perturbative solutions. (4) In the Euclidean continuation of the theory, with arbitrary sources, we derive certain constraints imposed by the second order equations on first order perturbations, thus restricting the linearized solutions that could be continued into the full nonlinear theory. Naive linearized solutions fail to satisfy the above constraints. (5) Finally, we clarify in detail subtleties associated with the boundary conditions and analytic properties of the Green's functions.Comment: 39 LaTex page

Accelerating Universe and Cosmological Perturbation in the Ghost Condensate

In the simplest Higgs phase of gravity called ghost condensation, an accelerating universe with a phantom era (w<-1) can be realized without ghost or any other instabilities. In this paper we show how to reconstruct the potential in the Higgs sector Lagrangian from a given cosmological history (H(t), \rho(t)). This in principle allows us to constrain the potential by geometrical information of the universe such as supernova distance-redshift relation. We also derive the evolution equation for cosmological perturbations in the Higgs phase of gravity by employing a systematic low energy expansion. This formalism is expected to be useful to test the theory by dynamical information of large scale structure in the universe such as cosmic microwave background anisotropy, weak gravitational lensing and galaxy clustering.Comment: 30 pages; typos corrected; version accepted for publication in JCA

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom