156 research outputs found
On the superstrings-induced four-dimensional gravity, and its applications to cosmology
We review the status of the fourth-order (quartic in the spacetime curvature)
terms induced by superstrings/M-theory (compactified on a warped torus) in the
leading order with respect to the Regge slope parameter, and study their
(non-perturbative) impact on the evolution of the Hubble scale in the context
of the four-dimensional FRW cosmology. After taking into account the quantum
ambiguities in the definition of the off-shell superstring effective action, we
propose the generalized Friedmann equations, find the existence of their (de
Sitter) exact inflationary solutions without a spacetime singularity, and
constrain the ambiguities by demanding stability and the scale factor duality
invariance of our solutions. The most naive (Bel-Robinson tensor squared)
quartic terms are ruled out, thus giving the evidence for the necessity of
extra quartic (Ricci tensor-dependent) terms in the off-shell gravitational
effective action for superstrings. Our methods are generalizable to the higher
orders in the spacetime curvature.Comment: 33 pages, LaTeX, no figures; extensive revision, Sec.6 and references
added, stability analysis include
Algebraic Rainich conditions for the tensor V
Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler
unified field theory are known as the Rainich conditions. Penrose and more
recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the
Bel-Robinson tensor , a certain fourth rank tensor
quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like
conditions. However, we found that not only does the tensor
fulfill these conditions, but so also does our recently
proposed tensor , which has many of the desirable
properties of . For the quasilocal small sphere limit
restriction, we found that there are only two fourth rank tensors
and which form a basis for good
energy expressions. Both of them have the completely trace free and causal
properties, these two form necessary and sufficient conditions. Surprisingly
either completely traceless or causal is enough to fulfill the algebraic
Rainich conditions. Furthermore, relaxing the quasilocal restriction and
considering the general fourth rank tensor, we found two remarkable results:
(i) without any symmetry requirement, the algebraic Rainich conditions only
require totally trace free; (ii) with a symmetry requirement, we recovered the
same result as in the quasilocal small sphere limit.Comment: 17 page
FRW Universe Models in Conformally Flat Spacetime Coordinates. II: Universe models with negative and vanishing spatial curvature
We deduce general expressions for the line element of universe models with
negative and vanishing spatial curvature described by conformally flat
spacetime coordinates. The empty Milne universe model and models with dust,
radiation and vacuum energy are exhibited. Discussing the existence of particle
horizons we show that there is continual creation of space, matter and energy
when conformal time is used in Friedmann-Robertson-Walker models with negative
spatial curvature.Comment: 25 pages, 12 figure
Fourth-order gravity as the inflationary model revisited
We revisit the old (fourth-order or quadratically generated) gravity model of
Starobinsky in four space-time dimensions, and derive the (inflaton) scalar
potential in the equivalent scalar-tensor gravity model via a Legendre-Weyl
transform. The inflaton scalar potential is used to compute the (CMB)
observables of inflation associated with curvature perturbations (namely, the
scalar and tensor spectral indices, and the tensor-to-scalar ratio), including
the new next-to-leading-order terms with respect to the inverse number of
e-foldings. The results are compared to the recent (WMAP5) experimental bounds.
We confirm both mathematical and physical equivalence between f(R) gravity
theories and the corresponding scalar-tensor gravity theories.Comment: 10 pages, 1 figure, 1 table, LaTeX; few comments added, style
improved, references added and update
Palatini versus metric formulation in higher curvature gravity
We compare the metric and the Palatini formalism to obtain the Einstein
equations in the presence of higher-order curvature corrections that consist of
contractions of the Riemann tensor, but not of its derivatives. We find that
there is a class of theories for which the two formalisms are equivalent. This
class contains the Palatini version of Lovelock theory, but also more
Lagrangians that are not Lovelock, but respect certain symmetries. For the
general case, we find that imposing the Levi-Civita connection as an Ansatz,
the Palatini formalism is contained within the metric formalism, in the sense
that any solution of the former also appears as a solution of the latter, but
not necessarily the other way around. Finally we give the conditions the
solutions of the metric equations should satisfy in order to solve the Palatini
equations.Comment: 13 pages, latex. V2: reference added, major changes in section 3,
conclusions partially correcte
FRW Universe Models in Conformally Flat Spacetime Coordinates. I: General Formalism
The 3-space of a universe model is defined at a certain simultaneity. Hence
space depends on which time is used. We find a general formula generating all
known and also some new transformations to conformally flat spacetime
coordinates. A general formula for the recession velocity is deduced.Comment: 12 page
Mutated hybrid inflation in -gravity
A new hybrid inflationary scenario in the context of -gravity
is proposed. Demanding the waterfall field to 'support the potential from
below' [unlike the original proposal by Stewart in Phys. Lett. B345, 414
(1995)], we demonstrate that the scalar potential is similar to that of the
large-field chaotic inflation model proposed by Linde in Phys. Lett. B129, 177
(1983). Inflationary observables are used to constrain the parameter space of
our model; in the process, an interesting limit on the number of e-folds N is
found.Comment: 9 pages, 2 figures, LaTeX2e, v2: Sec.3 expanded and improved, 1 Fig.
added, a new result included, some Eqs. corrected, 2 References adde
Slow-roll inflation in (R+R*4) gravity
We reconsider the toy-model of topological inflation, based on the
R*4-modified gravity. By using its equivalence to the certain scalar-tensor
gravity model in four space-time dimensions, we compute the inflaton scalar
potential and investigate a possibility of inflation. We confirm the existence
of the slow-roll inflation with an exit. However, the model suffers from the
eta-problem that gives rise to the unacceptable value of the spectral index n_s
of scalar perturbations.Comment: 12 pages, 3 figures, LaTeX, misprints corrected and references
update
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