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Register a new userMulti-fluid cosmology in Einstein gravity: analytical solutions
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We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant equations of state. Effective fluids include spatial curvature, the cosmological constant, and scalar fields. We provide a description with unified notation, explicit and parametric forms of the solutions, and relations between different expressions present in the literature. Interesting solutions from a modern point of view include interacting fluids and scalar fields. Old solutions, integrability conditions, and solution methods keep being rediscovered, which motivates a review with modern eyes.
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Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recently, it has been shown that energy diffusion that may arise in quantum gravity and in theories with spontaneous collapse is compatible with this framework by virtue of its restricted diffeomorphism invariance. New studies suggest that this phenomenon could lead to higher-order equations in the context of homogeneous and isotropic Universe, affecting the well-posedness of their Cauchy initial-value problem. In this work, we show that this issue can be circumvented by assuming an equation of state that relates the energy density to the function that characterizes the diffusion. As an application, we solve the field equations analytically for an isotropic and homogeneous Universes in a barotropic model and in the mass-proportional continuous spontaneous localization (CSL) scenario, assuming that only dark matter develops energy diffusion. Different solutions possessing phase transition from decelerated to accelerated expansion are found. We use cosmological data of type Ia Supernovae and observational Hubble data to constrain the free parameters of both models. It is found that very small but nontrivial energy nonconservation is compatible with the barotropic model. However, for the CSL model, we find that the best-fit values are not compatible with previous laboratory experiments. We comment on this fact and propose future directions to explore energy diffusion in cosmology.
In a very recent paper [1], we have proposed a novel $4$-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of $Dto4$ Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant $tilde{alpha}$. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent $4$-dimensional theory and those from the previously considered, naive (and inconsistent) $Drightarrow 4$ limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for $tilde{alpha}>0$ and $dot{H}<0$, perturbations are free of any pathologies so that we can implement the setup to construct early and/or late time cosmological models. Interestingly, a $k^4$ term appears in the dispersion relation of tensor modes which plays significant roles at small scales and makes the theory different than not only general relativity but also many other modified gravity theories as well as the naive (and inconsistent) $Dto 4$ limit. Taking into account the $k^4$ term, the observational constraint on the propagation of gravitational waves yields the bound $tilde{alpha} lesssim (10,{rm meV})^{-2}$. This is the first bound on the only parameter (besides the Newtons constant and the choice of a constraint that stems from a temporal gauge fixing) in the consistent theory of $Dto 4$ Einstein-Gauss-Bonnet gravity.
Applying the seminal work of Bose in 1924 on what was later known as Bose-Einstein statistics, Einstein predicted in 1925 that at sufficiently low temperatures, a macroscopic fraction of constituents of a gas of bosons will drop down to the lowest available energy state, forming a `giant molecule or a Bose-Einstein condensate (BEC), described by a `macroscopic wavefunction. In this article we show that when the BEC of ultralight bosons extends over cosmological length scales, it can potentially explain the origins of both dark matter and dark energy. We speculate on the nature of these bosons.
Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background cosmology and the static, spherically symmetric solutions (for example approximating the gravitational potential of the solar system), there are four directions in the parameter space in which general relativity is approached. Requiring that there is a working screening mechanism and a nonsingular evolution of the Universe, we place analytical constraints on the parameter space which rule out many of the models studied in the literature. Cosmological solutions where the accelerated expansion of the Universe is explained by the dynamical interaction of the massive spin-2 field rather than by a cosmological constant, are still viable.
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in ($beta-$) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
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