Friedmann–Lemaître–Robertson–Walker metric

About: Friedmann–Lemaître–Robertson–Walker metric is a research topic. Over the lifetime, 4113 publications have been published within this topic receiving 87752 citations. The topic is also known as: FLRW metric.

Generalized cardassian expansion: a model in which the universe is flat, matter dominated, and accelerating

Abstract: The Cardassian universe is a proposed modification to the Friedmann Robertson Walker equation (FRW) in which the universe is flat, matter dominated, and accelerating. In this presentation, we generalize the original Cardassian proposal to include additional variants on the FRW equation, specific examples are presented. In the ordinary FRW equation, the right hand side is a linear function of the energy density, H2 ∼ ϱ. Here, instead, the right hand side of the FRW equation is a different function of the energy density, H2 ∼ g(ϱ). This function returns to ordinary FRW at early times, but modifies the expansion at a late epoch of the universe. The only ingredients in this universe are matter and radiation: in particular, there is NO vacuum contribution. Currently the modification of the FRW equation is such that the universe accelerates; we call this period of acceleration the Cardassian era. The universe can be flat and yet consist of only matter and radiation, and still be compatible with observations. The energy density required to close the universe is much smaller than in a standard cosmology, so that matter can be sufficient to provide a flat geometry. The new term required may arise, e.g., as a consequence of our observable universe living as a 3-dimensional brane in a higher dimensional universe. The Cardassian model survives several observational tests, including the cosmic background radiation, the age of the universe, the cluster baryon fraction, and structure formation. As will be shown in future work, he predictions for observational tests of the generalized Cardassian models can be very different from generic quintessence models, whether the equation of state is constant or time dependent.

Complete cosmic scenario from inflation to late time acceleration: Nonequilibrium thermodynamics in the context of particle creation

Abstract: The paper deals with the mechanism of particle creation in the framework of irreversible thermodynamics. The second order nonequilibrium thermodynamical prescription of Israel and Stewart has been presented with particle creation rate, treated as the dissipative effect. In the background of a flat Friedmann-Robertson-Walker (FRW) model, we assume the nonequilibrium thermodynamical process to be isentropic so that the entropy per particle does not change and consequently the dissipative pressure can be expressed linearly in terms of the particle creation rate. Here the dissipative pressure behaves as a dynamical variable having a nonlinear inhomogeneous evolution equation and the entropy flow vector satisfies the second law of thermodynamics. Further, using the Friedmann equations and by proper choice of the particle creation rate as a function of the Hubble parameter, it is possible to show (separately) a transition from the inflationary phase to the radiation era and also from the matter dominated era to late time acceleration. Also, in analogy to analytic continuation, it is possible to show a continuous cosmic evolution from inflation to late time acceleration by adjusting the parameters. It is found that in the de Sitter phase, the comoving entropy increases exponentially with time, keeping entropy per particle unchanged. Subsequently, the above cosmological scenarios have been described from a field theoretic point of view by introducing a scalar field having self-interacting potential. Finally, we make an attempt to show the cosmological phenomenon of particle creation as Hawking radiation, particularly during the inflationary era.

Kinematic self-similarity

Abstract: Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind (which can be obtained from dimensional considerations and is invariantly characterized by the existence of a homothetic vector in perfect-fluid spacetimes) and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of relativistic fluid mechanics is defined. It has been argued that kinematic self-similarity is an appropriate generalization of homothety and is the natural relativistic counterpart of self-similarity of the more general second (and zeroth) kind. Various mathematical and physical properties of spacetimes admitting a kinematic self-similarity are discussed. The governing equations for perfect-fluid cosmological models are introduced and a set of integrability conditions for the existence of a proper kinematic self-similarity in these models is derived. Exact solutions of the irrotational perfect-fluid Einstein field equations admitting a kinematic self-similarity are then sought in a number of special cases, and it is found that: (i) in the geodesic case the 3-spaces orthogonal to the fluid velocity vector are necessarily Ricci-flat; (ii) in the further specialization to dust (i.e. zero pressure) the differential equation governing the expansion can be completely integrated and the asymptotic properties of these solutions can be determined; (iii) the solutions in the case of zero expansion consist of a class of shear-free and static models and a class of stiff perfect-fluid (and non-static) models; and (iv) solutions in which the kinematic self-similar vector is parallel to the fluid velocity vector are necessarily Friedmann - Robertson - Walker (FRW) models. Solutions in which the kinematic self-similarity is orthogonal to the velocity vector are also considered. In addition, the existence of kinematic self-similarities in FRW spacetimes is comprehensively studied. It is known that there are a variety of circumstances in general relativity in which self-similar models act as asymptotic states of more general models. Finally, the questions of under what conditions are models which admit a proper kinematic self-similarity asymptotic to an exact homothetic solution and under what conditions are the asymptotic states of cosmological models represented by exact solutions of Einstein's field equations which admit a generalized self-similarity are addressed.

Comment about quasi-isotropic solution of Einstein equations near the cosmological singularity

Abstract: For the case of arbitrary hydrodynamical matter, we generalize the quasi-isotropic solution of Einstein equations near the cosmological singularity, found by Lifshitz and Khalatnikov in 1960 for the case of the radiation-dominated universe. It is shown that this solution always exists, but dependence of terms in the quasi-isotropic expansion acquires a more complicated form.