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

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

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