37 research outputs found
Essential core of the Hawking--Ellis types
The Hawking-Ellis (Segre-Plebanski) classification of possible stress-energy
tensors is an essential tool in analyzing the implications of the Einstein
field equations in a more-or-less model-independent manner. In the current
article the basic idea is to simplify the Hawking-Ellis type I, II, III, and IV
classification by isolating the "essential core" of the type II, type III, and
type IV stress-energy tensors; this being done by subtracting (special cases
of) type I to simplify the (Lorentz invariant) eigenvalue structure as much as
possible without disturbing the eigenvector structure. We will denote these
"simplified cores" type II, type III, and type IV. These
"simplified cores" have very nice and simple algebraic properties. Furthermore,
types I and II have very simple classical interpretations, while type
IV is known to arise semi-classically (in renormalized expectation values
of standard stress-energy tensors). In contrast type III stands out in that
it has neither a simple classical interpretation, nor even a simple
semi-classical interpretation. We will also consider the robustness of this
classification considering the stability of the different Hawking-Ellis types
under perturbations. We argue that types II and III are definitively unstable,
whereas types I and IV are stable.Comment: V1: 18 pages; V2: reformatted, now 14 pages; some clarifications
added; no significant physics changes. This version accepted for publication
in Classical and Quantum Gravit
Semi-classical and nonlinear energy conditions
We consider the characteristics of nonlinear energy conditions and of quantum
extensions of these and the usual energy conditions. We show that they are
satisfied by some quantum vacuum states that violate the usual energy
conditions.Comment: 6 pages; contribution to the proceedings of "The Fourtheenth Marcel
Grossmann Meeting on General Relativity", University of Rome "La Sapienza",
Rome, July 12-18, 2015, based on a talk delivered at the AT3 parallel sessio
Classical and quantum flux energy conditions for quantum vacuum states
The classical energy conditions are known to not be fundamental physics --
they are typically violated by semiclassical quantum effects. Consequently,
some effort has gone into finding possible semiclassical replacements for the
classical energy conditions -- the most well developed being the Ford-Roman
quantum inequalities. In the current article we shall instead develop classical
and quantum versions of a "flux energy condition" (FEC and QFEC) based on the
notion of constraining the possible fluxes measured by timelike observers. The
naive classical FEC will be seen to be satisfied in some situations, and even
for some quantum vacuum states, while its quantum analogue (the QFEC) is
satisfied (for naturally defined quantum vacuum states) under a rather wide
range of conditions. The situation for completely general (nonvacuum) quantum
states is less clear.Comment: V1: 4 pages. V2: 5 pages. Some changes in presentation emphasizing
necessary versus sufficient conditions. No changes in physics conclusions.
V3: Change in title emphasizing the relevance of quantum vacuum states. Extra
discussion regarding quantum vacuum states. Nine additional references, some
updates. This version accepted for publication in PR
Semiclassical energy conditions for quantum vacuum states
We present and develop several nonlinear energy conditions suitable for use
in the semiclassical regime. In particular, we consider the recently formulated
"flux energy condition" (FEC), and the novel "trace-of-square" (TOSEC) and
"determinant" (DETEC) energy conditions. As we shall show, these nonlinear
energy conditions behave much better than the classical linear energy
conditions in the presence of semiclassical quantum effects. Moreover, whereas
the quantum extensions of these nonlinear energy conditions seem to be quite
widely satisfied as one enters the quantum realm, analogous quantum extensions
are generally not useful for the linear classical energy conditions.Comment: V1: 42 pages, 6 figures. V2: 43 pages, 6 figures. Title changed, some
discussion added, 3 references added, some typos fixed. V3: Minor edits.
Published versio
Tracking our Universe to de Sitter by a Horndeski scalar
Assuming both that our Universe is evolving into a de Sitter space and a
vanishing cosmological constant, leaves only the option that the observed
acceleration is provided by a "kinetic" energy of a scalar field. From an
effective field theory point of view, the absence of Ostrogradsky instabilities
restricts the choice to shift-symmetric Horndeski theories. Within these
theories, we find the conditions for the existence of a de Sitter critical
point in a universe filled by matter, radiation and a Horndeski scalar.
Moreover, we show that this point is a universal attractor and we provide the
tracking trajectory. Therefore, if a de Sitter fixed point exists within these
models, our Universe will eventually evolve into a de Sitter space. As an
example, we have discussed the case of the combined Galileon-Slotheon system,
in which the Galileon is kinetically non-minimal coupled to the Einstein
tensor. Interestingly, we have also found that the tracker trajectory of this
system does not follow previous literature assumptions.Comment: 14 pages, v2: comment on frames added. Conclusions unchanged, version
accepted for publication in Physics of the Dark Univers
Hawking-Ellis type III spacetime geometry
The type III (and the "essential core" type III) stress-energy tensors in
the Hawking-Ellis (Segre-Plebanski) classification stand out in that there is
to date no known source (either classical or semi-classical) leading to type
III stress-energy. (In contrast the Hawking-Ells types I and II occur
classically, and type IV is known to occur semi-classically). We instead start
by asking the obverse question: What sort of spacetime (assuming the Einstein
equations) needs a type III stress-energy to support it? One key observation is
that type III is incompatible with either planar or spherical symmetry, so one
should be looking at spacetimes of low symmetry (or no symmetry). Finding such
a type III spacetime is a matter of somehow finding an appropriate ansatz for
the metric, calculating the Einstein tensor, and analyzing the pattern of
(Lorentz invariant) eigenvalues and eigenvectors. Herein we report some
(partial) success along these lines - we explicitly exhibit several (somewhat
unnatural) spacetime geometries with a type III Einstein tensor. We then build
an explicit but somewhat odd Lagrangian model leading (in Minkowski space) to
type III stress-energy. While we still have no fully acceptable general
physical model for type III stress-energy, we can at least say something about
what such a stress-energy tensor would entail.Comment: 22 pages, 1 figur
Is there vacuum when there is mass? Vacuum and non-vacuum solutions for massive gravity
Massive gravity is a theory which has a tremendous amount of freedom to
describe different cosmologies; but at the same time the various solutions one
encounters must fulfill some rather nontrivial constraints. Most of the freedom
comes not from the Lagrangian, which contains only a small number of free
parameters (typically 3 depending on counting conventions), but from the fact
that one is in principle free to choose the background reference metric almost
arbitrarily --- which effectively introduces a non-denumerable infinity of free
parameters. In the current paper we stress that although changing the reference
metric would lead to a different cosmological model, this does not mean that
the dynamics of the universe can be entirely divorced from its matter content.
That is, while the choice of reference metric certainly influences the
evolution of the physically observable foreground metric, the effect of matter
cannot be neglected. Nevertheless, the relation between matter and geometry can
be significantly changed in some specific models; effectively since the
graviton would be able to curve the spacetime by itself, without the need of
matter. Thus, even the set of vacuum solutions for massive gravity can have
significant structure. On the other hand, in some cases the effect of the
reference metric could be so strong that no conceivable material content would
be able to drastically affect the cosmological evolution.Comment: V1: 9 pages. V2: 10 pages, 5 references added. V3: 11 pages, some
discussion added. This version accepted for publication in Classical and
Quantum Gravit
Monologue of a graviton in identity crisis. Or on Alternative Theories of Gravity. (In Spanish)
The era of high precision Cosmology has shown our ignorance about the
composition of the Universe. In this context, there has been a renewed interest
on Alternative Theories of Gravity. Through the experience of a graviton
measured by the LIGO collaboration, we shall understand the conceptual
framework of those theories. They provide us with a theoretical construction
where we can contrast the predictions of General Relativity and a possible
scenario to describe the accelerated expansion of our Universe without assuming
the existence of dark components. During the dawn of gravitational wave
astronomy, gravitation is already promising to be one of the most fascinating
fields of research of the XXI century.Comment: 4 pages. In Spanish. This is an invited contribution to be published
in the Spanish Journal of Physics (Royal Spanish Physics Society
Attracted to de Sitter II: cosmology of the shift-symmetric Horndeski models
Horndeski models with a de Sitter critical point for any kind of material
content may provide a mechanism to alleviate the cosmological constant problem.
Moreover, they could allow us to understand the current accelerated expansion
of the universe as the result of the dynamical approach to the critical point
when it is an attractor. We show that this critical point is indeed an
attractor for the shift- symmetric subfamily of models with these
characteristics. We study the cosmological scenario that results when
considering radiation and matter content, and conclude that their background
dynamics is compatible with the latest observational data.Comment: V1: 20 pages, 11 figures. V2: 1 reference added. V3: 21 pages.
Clarifications in the discussion; no physics changes. This version accepted
for publication in JCA
Accelerating universe as a result of an adjustment mechanism
In this essay we propose that the theory of gravity's vacuum is described by
a de Sitter geometry. Under this assumption we consider an adjustment mechanism
able to screen any value of the vacuum energy of the matter fields. We discuss
the most general scalar-tensor cosmological models with second order equations
of motion that have a fixed de Sitter critical point for any kind of material
content. These models give rise to interesting cosmological evolutions that we
shall discuss.Comment: 7 pages, 2 figures. Essay awarded honorable mention in the Gravity
Research Foundation essay competition 201