Non-Gaussianity in three fluid curvaton model

The generation of non-gaussianity is studied in a three fluid curvaton model. By utilizing second order perturbation theory we derive general formulae for the large scale temperature fluctuation and non-gaussianity parameter, $f_{NL}$, that includes the possibility of a non-adiabatic final state. In the adiabatic limit we recover previously known results. The results are applied to a three fluid curvaton model where the curvaton decays into radiation and matter. We find that the amount of non-gaussianity decreases as the final state of the system becomes more adiabatic and that the generated non-gaussianity in the scenario is small, $|f_{NL}| \sim \mathcal{O}(1)$.Comment: 10 pages, 2 figure

Static spherically symmetric perfect fluid solutions in f(R)f(R) theories of gravity

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot determine the functional form of $f(R)$. However, we also show that matching the outside Schwarzschild-de Sitter-metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.Comment: 5 page

Cosmological expansion and the uniqueness of gravitational action

Modified theories of gravity have recently been studied by several authors as possibly viable alternatives to the cosmological concordance model. Such theories attempt to explain the accelerating expansion of the universe by changing the theory of gravity, instead of introducing dark energy. In particular, a class of models based on higher order curvature invariants, so-called $f(R)$ gravity models, has drawn attention. In this letter we show that within this framework, the expansion history of the universe does not uniquely determine the form of the gravitational action and it can be radically different from the standard Einstein-Hilbert action. We demonstrate that for any barotropic fluid, there always exists a class of $f(R)$ models that will have exactly the same expansion history as that arising from the Einstein-Hilbert action. We explicitly show how one can extend the Einstein-Hilbert action by constructing a $f(R)$ theory that is equivalent on the classical level. Due to the classical equivalence between $f(R)$ theories and Einstein-Hilbert gravity with an extra scalar field, one can also hence construct equivalent scalar-tensor theories with standard expansion.Comment: 4 page

Stellar configurations in f(R) theories of gravity

We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-\mu^4/R$ model. We show how the stellar configuration in the $f(R)$ theory can, by appropriate initial conditions, be selected to be equal to that described by the Lane-Emden -equation and how a simple scaling relation exists between the solutions. We also derive the correct solution analytically near the center of the star in $f(R)$ theory. Previous analytical and numerical results are confirmed, indicating that the space-time around the Sun is incompatible with Solar System constraints on the properties of gravity. Numerical work shows that stellar configurations, with a regular metric at the center, lead to $\gamma_{PPN}\simeq1/2$ outside the star ie. the Schwarzschild-de Sitter -space-time is not the correct vacuum solution for such configurations. Conversely, by selecting the Schwarzschild-de Sitter -metric as the outside solution, we find that the stellar configuration is unchanged but the metric is irregular at the center. The possibility of constructing a $f(R)$ theory compatible with the Solar System experiments and possible new constraints arising from the radius-mass -relation of stellar objects is discussed.Comment: 8 pages, 7 figures; typos corrected, reference adde

Constraints on the three-fluid model of curvaton decay

A three fluid system describing the decay of the curvaton is studied by numerical and analytical means. We place constraints on the allowed interaction strengths between the fluids and initial curvaton density by requiring that the curvaton decays before nucleosynthesis while nucleosynthesis, radiation-matter equality and decoupling occur at correct temperatures. We find that with a continuous, time-independent interaction, a small initial curvaton density is naturally preferred along with a low reheating temperature. Allowing for a time-dependent interaction, this constraint can be relaxed. In both cases, a purely adiabatic final state can be generated, but not without fine-tuning. Unlike in the two fluid system, the time-dependent interactions are found to have a small effect on the curvature perturbation itself due to the different nature of the system. The presence of non-gaussianity in the model is discussed.Comment: 9 pages, 10 figure

Numerical simulations of fragmentation of the Affleck-Dine condensate

We present numerical simulations of fragmentation of the Affleck-Dine condensate in two spatial dimensions. We argue analytically that the final state should consist of both Q-balls and anti-Q-balls in a state of maximum entropy, with most of the balls small and relativistic. Such a behaviour is found in simulations on a 100x100 lattice with cosmologically realistic parameter values. During fragmentation process, we observe filament-like texture in the spatial distribution of charge. The total charge in Q-balls is found to be almost equal to the charge in anti-Q-balls and typically orders of magnitude larger than charge asymmetry. Analytical considerations indicate that, apart from geometrical factors, the results of the simulated two dimensional case should apply also to the fully realistic three dimensional case.Comment: 28 pages, 39 figure

Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is required. Examples of exact solutions are given.Comment: 17 pages, to appear in Class. Quant. Gra

Constraining Newtonian stellar configurations in f(R) theories of gravity

We consider general metric $f(R)$ theories of gravity by solving the field equations in the presence of a spherical static mass distribution by analytical perturbative means. Expanding the field equations systematically in \cO(G), we solve the resulting set of equations and show that $f(R)$ theories which attempt to solve the dark energy problem very generally lead to $\gamma_{PPN}=1/2$ in the solar system. This excludes a large class of theories as possible explanations of dark energy. We also present the first order correction to $\gamma_{PPN}$ and show that it cannot have a significant effect.Comment: 4 pages; v2: added references, modified abstract and introduction, conclusions unchange

Energy-momentum complexes in f(R) theories of gravity

Despite the fact that modified theories of gravity, in particular the f(R) gravity models have attracted much attention in the last years, the problem of the energy localization in the framework of these models has not been addressed. In the present work the concept of energy-momentum complexes is presented in this context. We generalize the Landau-Lifshitz prescription of calculating the energy-momentum complex to the framework of f(R) gravity. As an important special case, we explicitly calculate the energy-momentum complex for the Schwarzschild-de Sitter metric for a general f(R) theory as well as for a number of specific, popular choices of f(R).Comment: 11 pages, no figures, LaTeX; v2: 9 pages now, rearranged Sections, references added, no changes in physics and results, version to appear in CQ