6 research outputs found
Nonstandard approach to gravity for the dark sector of the Universe
We summarize the present state of research on the darkon fluid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein’s equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3 . We reduce the EOMs to Friedmann-like equations and derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model
Analytical solutions for two inhomogeneous cosmological models with energy flow and dynamical curvature
Recently we have introduced a nonrelativistic cosmological model (NRCM)
exhibiting a dynamical spatial curvature. For this model the present day cosmic
acceleration is not attributed to a negative pressure (dark energy) but it is
driven by a nontrivial energy flow leading to a negative spatial curvature. In
this paper we generalize the NRCM in two different ways to the relativistic
regime and present analytical solutions of the corresponding Einstein
equations. These relativistic models are characterized by two inequivalent
extensions of the FLWR metric with a time-dependent curvature function
and an expansion scalar . The fluid flow is supposed to be geodesic. The
model V1 is shear-free with isotropic pressure and therefore conformal flat. In
contrast to V1 the second model V2 shows a nontrivial shear and an anisotropic
pressure. For both models the inhomogeneous solutions of the corresponding
Einstein equations will agree in leading order at small distances with the NRCM
if a(t) and K(t) are each identical with those determined in the NCRM. Then the
metric is completely fixed by three constants. The arising energy momentum
tensor contains a nontrivial energy flow vector. Our models violate locally the
weak energy condition. Global volume averaging leads to explicit expressions
for the effective scale factor and the expansion rate . Backreaction
effects cancel each other for the model V2 but they are nonzero and
proportional to the square of the magnitude of the energy flow for the model
V1. The large scale (relativistic) corrections to the NCRM results are small
for the model V2 for a small-sized energy flow. We have reproduced a
corresponding adjustment of the three free constants from [1] to cosmic
chronometer data leading to the prediction of an almost constant, negative
value for the dimensionless curvature function for redshifts .Comment: 17 pages, enlarged version, accepted by Phys. Rev.
Space-time Schr\"odinger symmetries of a post-Galilean particle
We study the space-time symmetries of the actions obtained by expanding the
action for a massive free relativistic particle around the Galilean action. We
obtain all the point space-time symmetries of the post-Galilean actions by
working in canonical space. We also construct an infinite collection of
generalized Schr\"odinger algebras parameterized by an integer , with
corresponding to the standard Schr\"odinger algebra. We discuss the
Schr\"odinger equations associated to these algebras, their solutions and
projective phases.Comment: Version accepted for publication in JHE