We consider a cosmological scenario where the dark sector is described by two perfect fluids that interact through a velocity-dependent coupling. This coupling gives rise to an interaction in the dark sector driven by the relative velocity of the components, thus making the background evolution oblivious to the interaction and only the perturbed Euler equations are affected at first order. We obtain the equations governing this system with the Schutz-Sorkin Lagrangian formulation for perfect fluids and derive the corresponding stability conditions to avoid ghosts and Laplacian instabilities. As a particular example, we study a model where dark energy behaves as a radiation fluid at high redshift while it effectively becomes a cosmological constant in the late Universe. Within this scenario, we show that the interaction of both dark components leads to a suppression of the dark matter clustering at late times. We also argue the possibility that this suppression of clustering together with the additional dark radiation at early times can simultaneously alleviate the $σ_8$ and $H_0$ tensions.
A Lagrangian formulation of perfect fluid due to a noncanonical three-form field is investigated. The thermodynamic quantities such as energy density, pressure and the four velocity are obtained and then analyzed by comparing with the k-essence scalar field. The nonrelativistic matter due to the generalized three-form field with the equation of state parameter being zero is realized while it might not be possible for the k-essence scalar field. We also found that nonadiabatic pressure perturbations can be possibly generated. The fluid dynamics of the perfect fluid due to the three-form field c…
In this paper we show that the on-shell Lagrangian of a perfect fluid depends on microscopic properties of the fluid, giving specific examples of perfect fluids with different on-shell Lagrangians but with the same energy-momentum tensor. We demonstrate that if the fluid is constituted by localized concentrations of energy with fixed rest mass and structure (solitons) then the average on-shell Lagrangian of a perfect fluid is given by ${\mathcal L}_m=T$, where $T$ is the trace of the energy-momentum tensor. We show that our results have profound implications for theories of gravity where the m…
In this paper we give a simple proof that when the particle number is conserved, the Lagrangian of a barotropic perfect fluid is $\mathcal{L}_m=-ρ[c^2 +\int P(ρ)/ρ^2 dρ]$, where $ρ$ is the \textit{rest mass} density and $P(ρ)$ 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 ($\na…
We study in some detail an interacting cosmological model based on two canonical scalar fields starting from a Lagrangian description. Contrary to other more phenomenological approaches where non-relativistic matter and dark energy are cosmological perfect fluids, and where a source term is added by hand at the level of the continuity equations, here within Einstein's theory we model the dark sector, which dominates the evolution of the universe, as two minimally coupled scalar fields, out of which the first play the role of dark matter and the second plays the role of dark energy. We compute …
In the standard model of cosmology, the background evolution of the Universe can in general be adequately described by general relativity and a uniform and isotropic metric minimally coupled with a collection of perfect fluids. These fluids are usually described by their energy-momentum tensor, which can be derived from the fluid's Lagrangian density. Under general relativity, the Lagrangian density is only relevant to the extent that it results in the correct energy-momentum tensor for a specific perfect fluid. This is not the case in theories that feature a nonminimal coupling (NMC) between …
Existing cosmological simulation methods lack a high degree of parallelism due to the long-range nature of the gravitational force, which limits the size of simulations that can be run at high resolution. To solve this problem, we propose a new, perfectly parallel approach to simulate cosmic structure formation, which is based on the spatial COmoving Lagrangian Acceleration (sCOLA) framework. Building upon a hybrid analytical and numerical description of particles' trajectories, our algorithm allows for an efficient tiling of a cosmological volume, where the dynamics within each tile is comput…
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
In this paper, we investigated the theoretical and cosmological effects of the matter Lagrangian degeneracy in an extension of the Symmetric Teleparallel Equivalent of General Relativity, denoted as $f (Q, T )$ gravity. This degeneracy comes from the fact that both $\mathcal{L}_m = p$ and $\mathcal{L}_m = -ρ$ can give rise to the stress-energy tensor of a perfect fluid. The $f(Q,T)$ equations depend on the form of the matter Lagrangian and hence they also have a degeneracy that has influence on the density evolution of dust matter and radiation, on the form of the generalized Friedmann equatio…
Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.
We investigate the appropriateness of the use of different Lagrangians to describe various components of the cosmic energy budget, discussing the degeneracies between them in the absence of nonminimal couplings to gravity or other fields, and clarifying some misconceptions in the literature. We further demonstrate that these degeneracies are generally broken for nonminimal coupled fluids, in which case the identification of the appropriate on-shell Lagrangian may become essential in order characterize the overall dynamics. We then show that models with the same on-shell Lagrangian may have dif…
Both k-essence and the pressureless perfect fluid develop caustic singularities at finite time. We further explore the connection between the two and show that they belong to the same class of models, which admits the caustic free completion by means of the canonical complex scalar field. Specifically, the free massive/self-interacting complex scalar reproduces dynamics of pressureless perfect fluid/shift-symmetric k-essence under certain initial conditions in the limit of large mass/sharp self-interacting potential. We elucidate a mechanism of resolving caustic singularities in the complete p…
On the Bondi accretion of a self-interacting complex scalar field
CEICO, FZU — Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Institute of Theoretical Physics and Astrophysics, University of Gdańsk（格但斯克大学理论物理与天体物理研究所）
In this short note, we obtain the necessary and sufficient condition for a class of non-canonical single scalar field models to be exactly equivalent to barotropic perfect fluids, under the assumption of an irrotational fluid flow. An immediate consequence of this result is that the non-adiabatic pressure perturbation in this class of scalar field systems vanishes exactly at all orders in perturbation theory and on all scales. The Lagrangian for this general class of scalar field models depends on both the kinetic term and the value of the field. However, after a field redefinition, it can be …
Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $V(ϕ)=\frac{(λϕ)^{2n}}{2n}$, $λ>0$, $n\in\mathbb{N}$, interacting with a perfect fluid with linear equation of state $p_\mathrm{pf}=(γ_\mathrm{pf}-1)ρ_\mathrm{pf}$, $γ_\mathrm{pf}\in(0,2)$, in flat Robertson-Walker spacetimes. The interaction is a friction-like term of the form $Γ(ϕ)=μϕ^{2p}$, $μ>0$, $p\in\mathbb{N}\cup\{0\}$. The analysis relies on the introduction of a new regular 3-dimensional dynamical systems' formulation o…
We investigate possible cosmological effects of interacting scalar radiation and dark matter. After its decoupling, scalar radiation can stream freely as neutrinos or self-interact strongly as perfect fluid, highly depending on the magnitude of its self-couplings. We obtain the general and novel structure for self-scattering rate and compare it with the expansion rate of our Universe. If its trilinear/cubic coupling is non-zero, scalar radiation can be eventually treated as perfect fluid. Possible effects on CMB are also discussed. When this scalar also mediates interaction among dark matter p…
We investigate a dark energy scenario in which a canonical scalar field $ϕ$ is coupled to the four velocity $u_{c}^μ$ of cold dark matter (CDM) through a derivative interaction $u_{c}^μ \partial_μ ϕ$. The coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends on $X=-\partial^μ ϕ\partial_μ ϕ/2$ and $Z=u_{c}^μ \partial_μ ϕ$. We derive stability conditions of linear scalar perturbations for the wavelength deep inside the Hubble radius and show that the effective CDM sound speed is close to 0 as in the standard uncoupled case, while the scalar-field propagation speed is af…
We consider two models of interacting dark energy, both of which interact only through momentum exchange. One is a phenomenological one-parameter extension to $w$CDM, and the other is a coupled quintessence model described by a Lagrangian formalism. Using a variety of high and low redshift data sets, we perform a global fitting of cosmological parameters and compare to $Λ$CDM, uncoupled quintessence, and $w$CDM. We find that the models are competitive with $Λ$CDM, even obtaining a better fit when certain data sets are included.
We present a new approach to studies of bubble dynamics in fluids. Relying on particle-based simulations, this method is general and suitable for cases where the commonly used perfect fluid description fails. We study expanding true vacuum bubbles surrounded by free or self-interacting particles and quantify how self-interactions affect the terminal bubble wall velocity. We find that, for sufficiently strongly self-interacting fluids, local thermal equilibrium is maintained around the bubble wall and the fluid profile is similar to that obtained with the perfect fluid description.
