85 research outputs found
The Generalized Moyal Nahm and Continuous Moyal Toda Equations
We present in detail a class of solutions to the Moyal Anti
Self Dual Yang Mills equations that are related to of the
generalized Moyal Nahm quations using the Ivanova-Popov ansatz. The former
yields solutions to the ASDYM/SDYM equations for arbitary gauge groups. A
further dimensional reduction yields solutions to the Moyal Anti Self Dual
Gravitational equations. The Self Dual Yang Mills /Self Dual Gravity case
requires a separate study. SU(2) and (continuous) Moyal Toda
equations are derived and solutions to the latter equations in form
are proposed via the Lax-Brockett double commutator formalism . An explicit map
taking the Moyal heavenly form (after a rotational Killing symmetry reduction)
into the SU(2) Moyal Toda field is found. Finally, the generalized Moyal Nahm
equations are conjectured that contain the continuous Moyal Toda
equation after a suitable reduction. Three different embeddings of the three
different types of Moyal Toda equations into the Moyal Nahm equations are
discussed.Comment: Revised TEX file. 31 pages. The Legendre transform between the Moyal
heavenly form and the Moyal Toda field is solve
Scalar field inflation driven by a modification of the Heisenberg algebra
We study the modifications induced on scalar field inflation produced by
considering a general modification of the Heisenberg algebra. We proceed by
modifying the Poisson brackets on the classical theory whenever the
corresponding quantum commutator is modified. We do not restrict ourselves to a
specific form for such modification, instead we constrain the functions
involved by the cosmological behaviour of interest. We present whenever
possible the way in which inflation can be realized approximately via three
slow roll Hubble parameters that depend on the standard slow roll parameters in
a very different form than in the usual case and that can be less restrictive.
Furthermore we find a general analytical solution describing an expanding
universe with constant Hubble parameter that generalizes the standard
cosmological constant case by restricting the form of the modification of the
Heisenberg algebra. It is found that even if such modification can be neglected
in some limit and the cosmological constant is set to zero in that limit, the
exponential expansion is present when the modification is important. Thus an
appropriate modification of the Heisenberg algebra is sufficient to produce an
exponentially expanding universe without the need of any other source.Comment: 34 pages, 1 figur
Lorentzian Vacuum Transitions in Ho\v{r}ava-Lifshitz Gravity
The vacuum transition probabilities for a
Friedmann-Lema\^itre-Robertson-Walker universe with positive curvature in
Ho\v{r}ava-Lifshitz gravity in the presence of a scalar field potential in the
Wentzel-Kramers-Brillouin approximation are studied. We use a general procedure
to compute such transition probabilities using a Hamiltonian approach to the
Wheeler-DeWitt equation presented in a previous work. We consider two
situations of scalar fields, one in which the scalar field depends on all the
spacetime variables and other in which the scalar field depends only on the
time variable. In both cases analytic expressions for the vacuum transition
probabilities are obtained and the infrared and ultraviolet limits are
discussed for comparison with the result obtained by using general relativity.
For the case in which the scalar field depends on all spacetime variables we
obtain that in the infrared limit it is possible to obtain a similar behavior
as in general relativity, however in the ultraviolet limit the behavior found
is completely opposite. Some few comments about possible phenomenological
implications of our results are given. One of them is a plausible resolution of
the initial singularity. On the other hand for the case in which the scalar
field depends only on the time variable, the behavior coincides with that of
general relativity in both limits, although in the intermediate region the
probability is slightly altered.Comment: 26 pages, 2 figures. Some references adde
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