Covariant conservation of energy momentum in modified gravities

An explicit proof of the vanishing of the covariant divergence of the energy-momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy-momentum is built-in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, we demonstrate that in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories. In the light of our interpretation of the independent connection as an auxiliary variable we can also reconsider some criticisms of the Palatini formulation originally raised by Buchdahl.Comment: 8 pages. v2: more discussio

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

Constraints on Gauss-Bonnet Gravity in Dark Energy Cosmologies

Models with a scalar field coupled to the Gauss-Bonnet Lagrangian appear naturally from Kaluza-Klein compactifications of pure higher-dimensional gravity. We study linear, cosmological perturbations in the limits of weak coupling and slow-roll, and derive simple expressions for the main observable sub-horizon quantities: the anisotropic stress factor, the time-dependent gravitational constant, and the matter perturbation growth factor. Using present observational data, and assuming slow-roll for the dark energy field, we find that the fraction of energy density associated with the coupled Gauss-Bonnet term cannot exceed 15%. The bound should be treated with caution, as there are significant uncertainies in the data used to obtain it. Even so, it indicates that the future prospects for constraining the coupled Gauss-Bonnet term with cosmological observations are encouraging.Comment: 15 pages. v3: extended analysis, conclusions change

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

The present universe in the Einstein frame, metric-affine R+1/R gravity

We study the present, flat isotropic universe in 1/R-modified gravity. We use the Palatini (metric-affine) variational principle and the Einstein (metric-compatible connected) conformal frame. We show that the energy density scaling deviates from the usual scaling for nonrelativistic matter, and the largest deviation occurs in the present epoch. We find that the current deceleration parameter derived from the apparent matter density parameter is consistent with observations. There is also a small overlap between the predicted and observed values for the redshift derivative of the deceleration parameter. The predicted redshift of the deceleration-to-acceleration transition agrees with that in the \Lambda-CDM model but it is larger than the value estimated from SNIa observations.Comment: 11 pages; published versio

On compatibility of string effective action with an accelerating universe

In this paper, we fully investigate the cosmological effects of the moduli dependent one-loop corrections to the gravitational couplings of the string effective action to explain the cosmic acceleration problem in early (and/or late) universe. These corrections comprise a Gauss-Bonnet (GB) invariant multiplied by universal non-trivial functions of the common modulus $\sigma$ and the dilaton $\phi$. The model exhibits several features of cosmological interest, including the transition between deceleration and acceleration phases. By considering some phenomenologically motivated ansatzs for one of the scalars and/or the scale factor (of the universe), we also construct a number of interesting inflationary potentials. In all examples under consideration, we find that the model leads only to a standard inflation ($w \geq -1$) when the numerical coefficient $\delta$ associated with modulus-GB coupling is positive, while the model can lead also to a non-standard inflation ($w<-1$), if $\delta$ is negative. In the absence of (or trivial) coupling between the GB term and the scalars, there is no crossing between the $w -1$ phases, while this is possible with non-trivial GB couplings, even for constant dilaton phase of the standard picture. Within our model, after a sufficient amount of e-folds of expansion, the rolling of both fields $\phi$ and $\sigma$ can be small. In turn, any possible violation of equivalence principle or deviations from the standard general relativity may be small enough to easily satisfy all astrophysical and cosmological constraints.Comment: 30 pages, 8 figures; v2 significant changes in notations, appendix and refs added; v3 significant revisions, refs added; v4 appendix extended, new refs, published versio

On cosmic inflation in vector field theories

We investigate the longitudinal ghost issue in Abelian vector inflation. It turns out that, within the class of Lorentz-invariant vector field theories with three degrees of freedom and without any extra (scalar) fields, the possibilities are essentially exhausted by the classical solution due to Larry Ford with an extremely flat potential which doesn't feel the fast roll of its argument. And, moreover, one needs to fulfil an extra condition on that potential in order to avoid severe gradient instability. At the same time, some Lorentz-violating modifications are worth to be explored.Comment: 10 pages; a few minor typos corrected; published versio