24 research outputs found
Non-zero torsion and late cosmology
In this work, we study some thermodynamical aspects associated with torsion
in a flat FLRW spacetime cosmic evolution. By implementing two Ansatze for the
torsion term, we find that the model admits a phantom regime or a quintessence
behavior. This scheme differs from the CDM model at the
thermodynamical level. The resulting cosmic expansion is not adiabatic, the
fulfillment of the second law of thermodynamics requires a positive torsion
term, and the temperature of the cosmic fluid is always positive. The entropy
of the torsion phantom scenario is negative, but introducing chemical potential
solves this issue. For a Dirac-Milne type Universe, the torsion leads to a
growing behavior for the temperature of the fluid but has no incidence on the
rate of expansion.Comment: 20 pages, 1 figure. Accepted version in EPJ
Dirac Matrices for Chern-Simons Gravity
A genuine gauge theory for the Poincar\'e, de Sitter or anti-de Sitter
algebras can be constructed in (2n-1)-dimensional spacetime by means of the
Chern-Simons form, yielding a gravitational theory that differs from General
Relativity but shares many of its properties, such as second order field
equations for the metric. The particular form of the Lagrangian is determined
by a rank n, symmetric tensor invariant under the relevant algebra. In
practice, the calculation of this invariant tensor can be reduced to the
computation of the trace of the symmetrized product of n Dirac Gamma matrices
\Gamma_{ab} in 2n-dimensional spacetime. While straightforward in principle,
this calculation can become extremely cumbersome in practice. For large enough
n, existing computer algebra packages take an inordinate long time to produce
the answer or plainly fail having used up all available memory. In this talk we
show that the general formula for the trace of the symmetrized product of 2n
Gamma matrices \Gamma_{ab} can be written as a certain sum over the integer
partitions s of n, with every term being multiplied by a numerical coefficient
\alpha_{s}. We then give a general algorithm that computes the
\alpha-coefficients as the solution of a linear system of equations generated
by evaluating the general formula for different sets of tensors B^{ab} with
random numerical entries. A recurrence relation between different coefficients
is shown to hold and is used in a second, "minimal" algorithm to greatly speed
up the computations. Runtime of the minimal algorithm stays below 1 min on a
typical desktop computer for up to n=25, which easily covers all foreseeable
applications of the trace formula.Comment: v2: 6 pages, no figures. Based on talk presented at I Cosmosul, Rio
de Janeiro, Brazil, August 2011. v3: references adde
Linear and Second-order Geometry Perturbations on Spacetimes with Torsion
In order to study gravitational waves in any realistic astrophysical
scenario, one must consider geometry perturbations up to second order. Here, we
present a general technique for studying linear and quadratic perturbations on
a spacetime with torsion. Besides the standard metric mode, a "torsionon"
perturbation mode appears. This torsional mode will be able to propagate only
in a certain kind of theories.Comment: 6 pages, no figures. v2: version accepted for publication in EPJ