43,420 research outputs found
Symplectic matrices with predetermined left eigenvalues
We prove that given four arbitrary quaternion numbers of norm 1 there always
exists a symplectic matrix for which those numbers are left
eigenvalues. The proof is constructive. An application to the LS category of
Lie groups is given.Comment: 7 page
An unified cosmological evolution driven by a mass dimension one fermionic field
An unified cosmological model for an Universe filled with a mass dimension
one (MDO) fermionic field plus the standard matter fields is considered. After
a primordial quantum fluctuation the field slowly rolls down to the bottom of a
symmetry breaking potential, driving the Universe to an inflationary regime
that increases the scale factor for about 71 e-folds. After the end of
inflation, the field starts to oscillate and can transfer its energy to the
standard model particles through a reheating mechanism. Such a process is
briefly discussed in terms of the admissible couplings of the MDO field with
the electromagnetic and Higgs fields. We show that even if the field loses all
its kinetic energy during reheating, it can evolve as dark matter due a
gravitational coupling (of spinorial origin) with baryonic matter. Since the
field acquires a constant value at the bottom of the potential, a non-null,
although tiny, mass term acts as a dark energy component nowadays. Therefore,
we conclude that MDO fermionic field is a good candidate to drive the whole
evolution of the Universe, in such a way that the inflationary field, dark
matter and dark energy are described by different manifestations of a single
field.Comment: 22 pages, 5 figure
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