The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry

We show that in modified $f(R)$ type gravity models with non-minimal coupling between matter and geometry, both the matter Lagrangian, and the energy-momentum tensor, are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with non-minimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra-force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is non-zero in the case of a fluid of dust particles.Comment: 6 pages, accepted for publication in PRD; references adde

Cosmic strings in f(R,Lm)f\left(R,L_m\right) gravity

We consider Kasner-type static, cylindrically symmetric interior string solutions in the $f\left(R,L_m\right)$ theory of modified gravity. The physical properties of the string are described by an anisotropic energy-momentum tensor satisfying the condition $T_t^t=T_z^z$; that is, the energy density of the string along the $z$-axis is equal to minus the string tension. As a first step in our study we obtain the gravitational field equations in the $f\left(R,L_m\right)$ theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor components have a power law dependence on the radial coordinate $r$. String solutions in two particular modified gravity models are investigated in detail. The first is the so-called "exponential" modified gravity, in which the gravitational action is proportional to the exponential of the sum of the Ricci scalar and matter Lagrangian, and the second is the "self-consistent model", obtained by explicitly determining the gravitational action from the field equations under the assumption of a power law dependent matter Lagrangian. In each case, the thermodynamic parameters of the string, as well as the precise form of the matter Lagrangian, are explicitly obtained.Comment: 20 pages, no figures. Published versio

New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state

In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is $\mathcal{L}_m=-\rho [c^2 +\int P(\rho)/\rho^2 d\rho]$, where $\rho$ is the \textit{rest mass} density and $P(\rho)$ is the pressure. To prove this result nor additional fields neither Lagrange multipliers are needed. Besides, the result is applicable to a wide range of theories of gravitation. The only assumptions used in the derivation are: 1) the matter part of the Lagrangian does not depend on the derivatives of the metric, and 2) the particle number of the fluid is conserved ($\nabla_\sigma (\rho u^\sigma)=0$)

Cosmological evolution of finite temperature Bose-Einstein Condensate dark matter

Once the temperature of a bosonic gas is smaller than the critical, density dependent, transition temperature, a Bose - Einstein Condensation process can take place during the cosmological evolution of the Universe. Bose - Einstein Condensates are very strong candidates for dark matter, since they can solve some major issues in observational astrophysics, like, for example, the galactic core/cusp problem. The presence of the dark matter condensates also drastically affects the cosmic history of the Universe. In the present paper we analyze the effects of the finite dark matter temperature on the cosmological evolution of the Bose-Einstein Condensate dark matter systems. We formulate the basic equations describing the finite temperature condensate, representing a generalized Gross-Pitaevskii equation that takes into account the presence of the thermal cloud in thermodynamic equilibrium with the condensate. The temperature dependent equations of state of the thermal cloud and of the condensate are explicitly obtained in an analytical form. By assuming a flat Friedmann-Robertson-Walker (FRW) geometry, the cosmological evolution of the finite temperature dark matter filled Universe is considered in detail in the framework of a two interacting fluid dark matter model, describing the transition from the initial thermal cloud to the low temperature condensate state. The dynamics of the cosmological parameters during the finite temperature dominated phase of the dark matter evolution are investigated in detail, and it is shown that the presence of the thermal excitations leads to an overall increase in the expansion rate of the Universe.Comment: 14 pages, 11 figures, accepted for publication in PR

Dynamical behavior and Jacobi stability analysis of wound strings

We numerically solve the equations of motion (EOM) for two models of circular cosmic string loops with windings in a simply connected internal space. Since the windings cannot be topologically stabilized, stability must be achieved (if at all) dynamically. As toy models for realistic compactifications, we consider windings on a small section of $\mathbb{R}^2$, which is valid as an approximation to any simply connected internal manifold if the winding radius is sufficiently small, and windings on an $S^2$ of constant radius $\mathcal{R}$. We then use Kosambi-Cartan-Chern (KCC) theory to analyze the Jacobi stability of the string equations and determine bounds on the physical parameters that ensure dynamical stability of the windings. We find that, for the same initial conditions, the curvature and topology of the internal space have nontrivial effects on the microscopic behavior of the string in the higher dimensions, but that the macroscopic behavior is remarkably insensitive to the details of the motion in the compact space. This suggests that higher-dimensional signatures may be extremely difficult to detect in the effective $(3+1)$-dimensional dynamics of strings compactified on an internal space, even if configurations with nontrivial windings persist over long time periods.Comment: 46 pages, 26 figures, accepted for publication in EPJC; matches the published version. Updated references (v3

On Einstein clusters as galactic dark matter halos

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of WIMPs as galactic dark matter halos. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters, as compared to the singular isothermal density sphere model for dark matter. Therefore lensing observations may discriminate, at least in principle, between Einstein cluster and other dark matter models.Comment: MNRAS LaTeX, 7 pages, accepted by MNRAS; reference adde

Constraints on extra-dimensions and variable constants from cosmological gamma ray bursts

The observation of the time delay between the soft emission and the high-energy radiation from cosmological gamma ray bursts can be used as an important observational test of multi-dimensional physical theories. The main source of the time delay is the variation of the electromagnetic coupling, due to dimensional reduction, which induces an energy dependence of the speed of light. For photons with energies around 1 TeV, the time delay could range from a few seconds in the case of Kaluza-Klein models to a few days for models with large extra-dimensions. Based on these results we suggest that the detection of the 18-GeV photon $\sim$4500 s after the keV/MeV burst in GRB 940217 provides a strong evidence for the existence of extra-dimensions. The time delay of photons, if observed by the next generation of high energy detectors, like, for example, the SWIFT and GLAST satellite based detectors, or the VERITAS ground-based TeV gamma-ray instrument, could differentiate between the different models with extra-dimensions.Comment: 8 pages, 4 figures, contribution to the proceedings of the II Workshop on Unidentified Gamma-Ray Sources, Hong Kong, June 1-4, 200