arXiv subjects

E. Elizalde

Publications and source records attributed to E. Elizalde.

At least 37 records · Page 2Linked to original sources

arXiv2014

Renormalization-group inflationary scalar electrodynamics and SU(5) scenarios confronted with Planck2013 and BICEP2 results

The possibility to construct inflationary models for the renormalization-group improved potentials corresponding to scalar electrodynamics and to $SU(2)$ and $SU(5)$ models is investigated. In all cases, the tree-level potential, which corresponds to the cosmological constant in the Einstein frame, is seen to be non-suitable for inflation. Rather than adding the Hilbert-Einstein term to the action, quantum corrections to the potential, coming from to the RG-equation, are included. The inflationary scenario is analyzed with unstable de Sitter solutions which correspond to positive values of the coupling function, only. We show that, for the finite $SU(2)$ model and $SU(2)$ gauge model, there are no de Sitter solutions suitable for inflation, unless exit from it occurs according to some weird, non-standard scenarios. Inflation is realized both for scalar electrodynamics and for $SU(5)$ RG-improved potentials, and the corresponding values of the coupling function are seen to be positive. It is shown that, for quite reasonable values of the parameters, the inflationary models obtained both from scalar electrodynamics and from the $SU(5)$ RG-improved potentials, are in good agreement with the most recent observational data coming from the Planck2013 and BICEP2 collaborations.

hep-th↗

arXiv2014

Inhomogeneous viscous dark fluid coupled with dark matter in the FRW universe

A cosmological model with an inhomogeneous viscous dark fluid coupled with dark matter in a flat Friedman-Robertson-Walker universe is investigated. The influence of dark matter on the behavior of an inhomogeneous viscous fluid of this kind, responsible for cosmic acceleration and for the appearance of different types of singularities, is analyzed in detail. In particular, the critical points corresponding to the solutions of the background equations in a useful approximation are obtained explicitly.

gr-qc↗

arXiv2013

On Partition Functions of Hyperbolic Three-Geometry and Associated Hilbert Schemes

Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions (elliptic genera) are conveniently transformed into product expressions, which may inherit the homology properties of appropriate (poly)graded Lie algebras. Specifically, the role of (Selberg-type) Ruelle spectral functions of hyperbolic geometry in the calculation of partition functions and associated $q$-series are discussed. Examples of these connection in quantum field theory are considered (in particular, within the AdS/CFT correspondence), as the AdS$_{3}$ case where one has Ruelle/Selberg spectral functions, whereas on the CFT side, partition functions and modular forms arise. These objects are here shown to have a common background, expressible in terms of Euler-Poincaré and Macdonald identities, which, in turn, describe homological aspects of (finite or infinite) Lie algebra representations. Finally, some other applications of modular forms and spectral functions (mainly related with the congruence subgroup of $SL(2, {\mathbb Z})$) to partition functions, Hilbert schemes of points, and symmetric products are investigated by means of homological and K-theory methods.

math-ph↗

arXiv2013

Reconstruction Procedure in Nonlocal Cosmological Models

A nonlocal gravity model is considered which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator. Using a reconstruction procedure for the local scalar-tensor formulation of this model, a function f is obtained for which the model exhibits power-law solutions with the Hubble parameter $H=n/t$, for any value of the constant n. For generic n - namely except for a few special values which are characterized and also specifically studied - the corresponding function f is a sum of exponential functions. Corresponding power-law solutions are found explicitly. Also the case is solved in all detail of a function f such that the model contains both de Sitter and power-law solutions.

astro-ph.CO↗

arXiv2013

Fermionic Casimir densities in anti-de Sitter spacetime

The fermionic condensate and vacuum expectation value of the energy-momentum tensor, for a massive fermionic field on the background of anti-de Sitter spacetime, in the geometry of two parallel boundaries with bag boundary conditions, are investigated. Vacuum expectation values, expressed as series involving the eigenvalues of the radial quantum number, are neatly decomposed into boundary-free, single-boundary-induced, and second-boundary-induced parts, with the help of the generalized Abel-Plana summation formula. In this way, the renormalization procedure is very conveniently reduced to the one corresponding to boundary-free AdS spacetime. The boundary-induced contributions to the fermionic condensate and to the vacuum expectation value of the energy density are proven to be everywhere negative. The vacuum expectation values are exponentially suppressed at distances from the boundaries much larger than the curvature radius of the AdS space. Near the boundaries, effects related with the curvature of the background spacetime are shown to be subdominant and, to leading order, all known results for boundaries in the Minkowski bulk are recovered. Zeta function techniques are successfully used for the evaluation of the total vacuum energy in the region between the boundaries. It is proven that the resulting interaction forces between them are attractive and that, for large separations, they also decay exponentially. Finally, our results are extended and explicitly translated to fermionic Casimir densities in braneworld scenarios of Randall-Sundrum type.

hep-th↗

arXiv2013

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Several dark energy models on the brane are investigated. They are compared with corresponding theories in the frame of 4d Friedmann-Robertson-Walker cosmology. To constrain the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Explicit formulas of the so-called {\it state-finder} parameters in teleparallel theories are obtained that could be useful to test these models and to establish a link between Loop Quantum Cosmology and Brane Cosmology. It is concluded that a joint analysis as the one developed here allows to estimate, in a very convenient way, possible deviation of the real universe cosmology from the standard Friedmann-Robertson-Walker one.

gr-qc↗

arXiv2013

One-loop Euclidean Einstein-Weyl gravity in de Sitter universe

By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.

gr-qc↗

arXiv2012

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

It is observed that one of Einstein-Friedmann's equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, $Λ$, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for $Λ$, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to $L^2$ space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for $Λ>0$ and a continuous one for $Λ<0$. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.

astro-ph.CO↗

arXiv2012

Multiple $Λ$CDM cosmology with string landscape features and future singularities

Multiple $Λ$CDM cosmology is studied in a way that is formally a classical analog of the Casimir effect. Such cosmology corresponds to a time-dependent dark fluid model or, alternatively, to its scalar field presentation, and it motivated by the string landscape picture. The future evolution of the several dark energy models constructed within the scheme is carefully investigated. It turns out to be almost always possible to choose the parameters in the models so that they match the most recent and accurate astronomical values. To this end, several universes are presented which mimick (multiple) $Λ$CDM cosmology but exhibit Little Rip, asymptotically de Sitter, or Type I, II, III, and IV finite-time singularity behavior in the far future, with disintegration of all bound objects in the cases of Big Rip, Little Rip and Pseudo-Rip cosmologies.

gr-qc↗

arXiv2012

Sudden singularities in semiclassical gravity

It has been claimed in a recent paper \cite{bbfhd12} that sudden singularities will survive in semiclassical gravity. This issue is here carefully reviewed, pointing out that such conclusion, even if valid under some specific conditions, does not stand in other cases. An explicit example is studied in detail to support our statement, stemming from these other situations, that quantum effects may in fact drastically modify the behavior of sudden singularities.

gr-qc↗

arXiv2012

Cosmological models with Yang-Mills fields

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.

hep-th↗

arXiv2012

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, $B(T)$, at different temperatures is here developed, and the value $B(T_{ew}) \sim 10^{14} G$ at the electroweak phase transition temperature, is derived by taking into consideration the present value of the intergalactic magnetic field strength, $B_0 \sim 10^{- 15} G$, coherent on the $\sim 1$ Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model dependent properties of the phenomena under investigation are briefly discussed, too.

hep-ph↗

arXiv2012

De Sitter Universe in Nonlocal Gravity

A nonlocal gravity model, which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator, is considered. The model is proven to have de Sitter solutions only if the function f satisfies a certain second-order linear differential equation. The de Sitter solutions corresponding to the simplest case, an exponential function f, are explored, without any restrictions on the parameters. If the value of the Hubble parameter is positive, the de Sitter solution is stable at late times, both for negative and for positive values of the cosmological constant. Also, the stability of the solutions with zero cosmological constant is discussed and sufficient conditions for it are established in this case. New de Sitter solutions are obtained which correspond to the model with dark matter and stability is proven in this situation for nonzero values of the cosmological constant.

astro-ph.CO↗

arXiv2012

Stability of de Sitter Solutions in Non-local Cosmological Models

A non-local gravity model, which includes a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. For the model with an exponential $f(\Box^{-1} R)$ de Sitter solutions are explored, without any restrictions on the parameters. Using Hubble-normalized variables, the stability of the de Sitter solutions is investigated, with respect to perturbations in the Bianchi I metric, in the case of zero cosmological constant, and sufficient conditions for stability are obtained.

gr-qc↗

arXiv2011

Oscillations of the F(R) dark energy in the accelerating universe

Oscillations of the $F(R)$ dark energy around the phantom divide line, $ω_{DE}=-1$, both during the matter era and also in the de Sitter epoch are investigated. The analysis during the de Sitter epoch is revisited by expanding the modified equations of motion around the de Sitter solution. Then, during the matter epoch, the time dependence of the dark energy perturbations is discussed by using two different local expansions. For high values of the red shift, the matter epoch is a stable point of the theory, giving the possibility to expand the $F(R)$-functions in terms of the dark energy perturbations. In the late-time matter era, the realistic case is considered where dark energy tends to a constant. The results obtained are confirmed by precise numerical computation on a specific model of exponential gravity. A novel and very detailed discussion is provided on the critical points in the matter era and on the relation of the oscillations with possible singularities.

gr-qc↗

arXiv2011

Viscous Little Rip Cosmology

Dark energy of phantom or quintessence nature with an equation of state parameter $w$ almost equal to -1 often leads the universe evolution to a finite-time future singularity. An elegant solution to this problem has been recently proposed \cite{frampton11} under the form of the so-called Little Rip cosmology which appears to be a realistic alternative to the $Λ$CDM model. A viscous Little Rip cosmology is here proposed. Whereas generically bulk viscosity tends to promote the Big Rip, we find that there are a number of situations where this is not the case and where the formalism nicely adjusts itself to the Little Rip scenario. We prove, in particular, that a viscous fluid (or, equivalently, one with an inhomogeneous (imperfect) equation of state) is perfectly able to produce a Little Rip cosmology as a purely viscosity effect. The possibility of its induction as a combined result of viscosity and a general (power-like) equation of state is also investigated in detail. To finish, a physical, inertial force interpretation of the dissolution of bound structures in the Little Rip cosmology is presented.

hep-th↗

arXiv2011

Lower bound on the magnetic field strength in the hot universe

It is assumed that long range coherent magnetic fields in the universe were spontaneously generated at high temperature due to vacuum polarization of non-Abelian gauge fields, and resulted in the present intergalaxy magnetic field. The zero value of the screening mass for fields of this type was discovered recently. Here, a procedure to estimate the field strengths at different temperatures is developed and the lower bound on the magnetic field strength $B \sim 10^{14} G$, at the electroweak phase transition temperature, is derived. As a particular case, the standard model is considered. Some model dependent peculiarities of the phenomena under investigation are briefly discussed.

hep-ph↗

arXiv2011

AdS Solutions in Gauge Supergravities and the Global Anomaly for the Product of Complex Two-Cycles

Cohomological methods are applied for the special set of solutions corresponding to rotating branes in arbitrary dimensions, AdS black holes (which can be embedded in ten or eleven dimensions), and gauge supergravities. A new class of solutions is proposed, the Hilbert modular varieties, which consist of the $2n$-fold product of the two-spaces ${\bf H}^n/Γ$ (where ${\bf H}^n$ denotes the product of $n$ upper half-planes, $H^2$, equipped with the co-compact action of $Γ\subset SL(2, {\mathbb R})^n$) and $({\bf H}^n)^*/Γ$ (where $(H^2)^* = H^2\cup \{{\rm cusp\,\, of}\,\,Γ\}$ and $Γ$ is a congruence subgroup of $SL(2, {\mathbb R})^n$). The cohomology groups of the Hilbert variety, which inherit a Hodge structure (in the sense of Deligne), are analyzed, as well as bifiltered sequences, weight and Hodge filtrations, and it is argued that the torsion part of the cuspidal cohomology is involved in the global anomaly condition. Indeed, in presence of the cuspidal part, all cohomology classes can be mapped to the boundary of the space and the cuspidal contribution can be involved in the global anomaly condition.

math-ph↗