Initial Conditions for Vector Inflation

Recently, a model of inflation using non-minimally coupled massive vector fields has been proposed. For a particular choice of non-minimal coupling parameter and for a flat FRW model, the model is reduced to the model of chaotic inflation with massive scalar field. We study the effect of non-zero curvature of the universe on the onset of vector inflation. We find that in a curved universe the dynamics of vector inflation can be different from chaotic inflation, and the fraction of the initial conditions leading to inflationary solutions is reduced compared with the chaotic inflation case.Comment: 12 pages, 5 figures, version to be published in JCA

Speed of light in the extended gravity theories

We shall investigate the possibility of formulation of varying speed of light (VSL) in the framework of Palatini non-linear Ricci scalar and Ricci squared theories. Different speeds of light including the causal structure constant, electromagnetic, and gravitational wave speeds are discussed. We shall see that two local frames are distinguishable and discuss about the velocity of light in these two frames. We shall investigate which one of these local frames is inertial.Comment: 19 pages. to appear in Classical Quantum Gravit

On the Weyl - Eddington - Einstein affine gravity in the context of modern cosmology

We propose new models of an `affine' theory of gravity in $D$-dimensional space-times with symmetric connections. They are based on ideas of Weyl, Eddington and Einstein and, in particular, on Einstein's proposal to specify the space - time geometry by use of the Hamilton principle. More specifically, the connection coefficients are derived by varying a `geometric' Lagrangian that is supposed to be an arbitrary function of the generalized (non-symmetric) Ricci curvature tensor (and, possibly, of other fundamental tensors) expressed in terms of the connection coefficients regarded as independent variables. In addition to the standard Einstein gravity, such a theory predicts dark energy (the cosmological constant, in the first approximation), a neutral massive (or, tachyonic) vector field, and massive (or, tachyonic) scalar fields. These fields couple only to gravity and may generate dark matter and/or inflation. The masses (real or imaginary) have geometric origin and one cannot avoid their appearance in any concrete model. Further details of the theory - such as the nature of the vector and scalar fields that can describe massive particles, tachyons, or even `phantoms' - depend on the concrete choice of the geometric Lagrangian. In `natural' geometric theories, which are discussed here, dark energy is also unavoidable. Main parameters - mass, cosmological constant, possible dimensionless constants - cannot be predicted, but, in the framework of modern `multiverse' ideology, this is rather a virtue than a drawback of the theory. To better understand possible applications of the theory we discuss some further extensions of the affine models and analyze in more detail approximate (`physical') Lagrangians that can be applied to cosmology of the early Universe.Comment: 15 pages; a few misprints corrected, one footnote removed and two added, the formulae and results unchanged but the text somewhat edited, esp. in Sections 4,5; the reference to the RFBR grant corrected

Primordial statistical anisotropy generated at the end of inflation

We present a new mechanism for generating primordial statistical anisotropy of curvature perturbations. We introduce a vector field which has a non-minimal kinetic term and couples with a waterfall field in hybrid inflation model. In such a system, the vector field gives fluctuations of the end of inflation and hence induces a subcomponent of curvature perturbations. Since the vector has a preferred direction, the statistical anisotropy could appear in the fluctuations. We present the explicit formula for the statistical anisotropy in the primordial power spectrum and the bispectrum of curvature perturbations. Interestingly, there is the possibility that the statistical anisotropy does not appear in the power spectrum but does appear in the bispectrum. We also find that the statistical anisotropy provides the shape dependence to the bispectrum.Comment: 9 pages, This version supersedes the JCAP version. Minor revision

Cosmological perturbations in the Palatini formulation of modified gravity

Cosmology in extended theories of gravity is considered assuming the Palatini variational principle, for which the metric and connection are independent variables. The field equations are derived to linear order in perturbations about the homogeneous and isotropic but possibly spatially curved background. The results are presented in a unified form applicable to a broad class of gravity theories allowing arbitrary scalar-tensor couplings and nonlinear dependence on the Ricci scalar in the gravitational action. The gauge-ready formalism exploited here makes it possible to obtain the equations immediately in any of the commonly used gauges. Of the three type of perturbations, the main attention is on the scalar modes responsible for the cosmic large-scale structure. Evolution equations are derived for perturbations in a late universe filled with cold dark matter and accelerated by curvature corrections. Such corrections are found to induce effective pressure gradients which are problematical in the formation of large-scale structure. This is demonstrated by analytic solutions in a particular case. A physical equivalence between scalar-tensor theories in metric and in Palatini formalisms is pointed out.Comment: 14 pages; the published version (+ an appendix). Corrected typos in eqs. 30,33 and B

Anisotropic Dark Energy and the Generalized Second Law of Thermodynamics

We consider a Bianchi type $I$ model in which anisotropic dark energy is interacting with dark matter and anisotropic radiation. With this scenario, we investigate the validity of the generalized second law of thermodynamics. It is concluded that the validity of this law depends on different parameters like shear, skewness and equation of state.Comment: 12 pages, accepted for publication in Phys. Scr. arXiv admin note: text overlap with arXiv:1008.0692 and arXiv:1106.241

Modified gravity and its reconstruction from the universe expansion history

We develop the reconstruction program for the number of modified gravities: scalar-tensor theory, $f(R)$, $F(G)$ and string-inspired, scalar-Gauss-Bonnet gravity. The known (classical) universe expansion history is used for the explicit and successful reconstruction of some versions (of special form or with specific potentials) from all above modified gravities. It is demonstrated that cosmological sequence of matter dominance, decceleration-acceleration transition and acceleration era may always emerge as cosmological solutions of such theory. Moreover, the late-time dark energy FRW universe may have the approximate or exact $\Lambda$CDM form consistent with three years WMAP data. The principal possibility to extend this reconstruction scheme to include the radiation dominated era and inflation is briefly mentioned. Finally, it is indicated how even modified gravity which does not describe the matter-dominated epoch may have such a solution before acceleration era at the price of the introduction of compensating dark energy.Comment: LaTeX file, 24 pages, no figure, prepared for the proceedings of ERE 2006, minor correction