Lagrangian theory of structure formation in relativistic cosmology. V. Irrotational fluids

Abstract

We extend the general relativistic Lagrangian perturbation theory, recently developed for the formation of cosmic structures in a dust continuum, to the case of model universes containing a single fluid with a single-valued analytic equation of state. Using a coframe-based perturbation approach, we investigate evolution equations for structure formation in pressure-supported irrotational fluids that generate their rest-frame spacetime foliation. We provide master equations to first order for the evolution of the trace and traceless parts of barotropic perturbations that evolve in the perturbed space, where the latter describes the propagation of gravitational waves in the fluid. We illustrate the trace evolution for a linear equation of state and for a model equation of state describing isotropic velocity dispersion, and we discuss differences to the dust matter model, to the Newtonian case, and to standard perturbation approaches. 98.80.Es,04.20.Cv,04.25.Nx,.) 2 In the convention we use here, greek letters µ, ν, · · · are spacetime indices running from 0 to 3, while lowercase latin letters i, j, · · · are spatial indices running from 1 to 3. We use units in which c = 1, if not otherwise stated.

The lift force on a charged sphere that translates and rotates in an electrolyte

“…Conversely, particles were attracted to the wall under oppositely directed flows: above a critical field strength the particles assembled into bands in the streamwise direction, with periodic spacing in the flow-gradient direction. This observation is consistent with other works that have observed cross-streamline migration of a particle undergoing electrophoresis in pressure driven flow of a Newtonian fluid [15][16][17]. The common feature of these experiments is that the particle migrates to the center(walls) of the channel when its electro-phoretic velocity is in the opposite(same) direction to(as) the ambient flow.…”

“…where Pe t = Ua/D and Pe r = ⍀a 2 /D are Péclet numbers for distortion of the cloud by the particle translation and rotation, respectively. In (17), u t and u r are the obvious dimensionless versions of (15) and (16), respectively. From (7), and attenuate at large distances.…”

“…The common feature of these experiments is that the particle migrates to the center(walls) of the channel when its electro-phoretic velocity is in the opposite(same) direction to(as) the ambient flow. Interestingly, Li and Xuan [17] demonstrate that the migration direction is switched in a viscoelastic fluid. Clearly, the band formation in [7] is a collective effect due to interactions between particles.…”

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

“…One could in the same way parametrize the Friedmann model by a different time coordinate while staying within the homogeneous foliation, and similarly get rescaled terms and an arbitrarily altered acceleration term (see, e.g., the system of equations(20) in Paper II[19] or the system of equations(40) in[66]). The usual form of the Friedmann equations removes this freedom by choosing the proper time as the most natural time parameter in this situation.…”

Relativistic cosmological large scale structures at one-loop

“…Possible refinements of our approach would be to use IR-resummation techniques, such as [86], renormalization group techniques [87] or consider viscosity [88] or velocity dispersion terms [89]. Another fruitful approach to predict LSS observable is Lagrangian perturbation theory [90], and relativistic version of it have been worked out, see for instance [91,92] and references therein. The weak field approach may also simplify the calculations involved in this framework.…”