arXiv subjects

Reza Tavakol

Publications and source records attributed to Reza Tavakol.

At least 55 records · Page 3Linked to original sources

arXiv2004

Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity

In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow--roll inflation. In general, however, loop quantum cosmology is robust to ambiguities in the quantization and extends the range of initial conditions for inflation.

gr-qc↗

arXiv2003

The influence of density stratification and multiple nonlinearities on solar torsional oscillations

Analyses of recent helioseismic data have produced ample evidence for substantial dynamical variation of the differential rotation within the solar convection zone. Given the inevitable difficulties in resolving the precise nature of variations at deeper layers, much effort has recently gone into determining theoretically the expected modes of behaviour, using nonlinear dynamo models. Two important limitations of these models are that they have so far included only one form of nonlinearity, and as yet they have not taken into account the density stratification in the solar convection zone. Here we address both of these issues by studying the effects of including density stratification, as well as including an alpha--quenching nonlinearity in addition to the previously studied effects of the Lorentz force on the differential rotation. We find that observationally important features found in the earlier uniform density models remain qualitatively unchanged, although there are quantitative differences. This is important as it provides more realistic theoretical predictions to be compared with and guide observations, especially in the deeper regions where the uncertainties in the inversions are larger. However the presence of an effective alpha-quenching nonlinearity significantly reduces the amplitudes of the oscillations.

astro-ph↗

arXiv2003

Reformulation and Interpretation of SMS Braneworld

We reformulate the Shiromizu, Maeda and Sasaki (SMS) braneworlds within the framework of the five-dimensional Einstein equations. In many applications of the braneworld Einstein field equations, the Weyl term is attributed to the bulk, thus splitting the non-Einsteinian terms into `bulk' and `brane' terms. Here by employing standard geometrical identities, we show that such a split is non-unique, since these terms get mixed up in different formulations. An important consequence of this non-uniqueness is that even though the full brane-bulk systems in all such formulations are completely equivalent, important differences can arise were one to truncate different formulations by throwing away the associated `bulk' terms. This is particularly likely to be the case in more general anisotropic/inhomogeneous settings with non-AdS bulks, in which the usual truncation of the SMS (which throws away the Weyl term) would not coincide with the full system. We emphasize that rather than providing support for any truncation, these differences show clearly the dangers of using any truncated equations and provide a strong argument in favour of studying the full brane-bulk system. The different formulations we provide also permit different ways of approaching the full brane-bulk system which may greatly facilitate its study. An example of this is the second-order nature of the formulations given here as opposed to the SMS's formulation which is third-order.

gr-qc↗

arXiv2003

PDE System Approach to Large Extra Dimensions

We explore some fundational issues regarding the splitting of D-dimensional EFE's w.r.t timelike and spacelike (D-1)-dimensional hypersurfaces, first without and then with thin matter sheets such as branes. We begin to implement methodology, that is well-established for the GR CP and IVP, in the new field of GR-based braneworlds, identifying and comparing many different choices of procedure. We abridge fragmentary parts of the literature of embeddings, putting the Campbell--Magaard theorem into context. We recollect and refine arguments why York and not elimination methods are used for the GR IVP. We compile a list of numerous mathematical and physical impasses to using timelike splits, whereas spacelike splits are known to be well-behaved. We however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits. We look at the Shiromizu-Maeda -Sasaki braneworld by means of reformulations which emphasize different aspects from the original formulation. We show that what remains of the York method in the timelike case generalizes heuristic bulk construction schemes. We formulate timelike (brane) versions of the thin sandwich conjecture. We discuss whether it is plausible to remove singularities by timelike embeddings. We point out how the braneworld geodesic postulates lead to further difficulties with the notion of singularities than in GR where these postulates are simpler. Having argued for the use of the spacelike split, we study how to progress to the construction of more general data sets for spaces partially bounded by branes. Boundary conditions are found and algorithms provided. Working with (finitely) thick branes would appear to facilitate such a study.

gr-qc↗

arXiv2003

Running of the Scalar Spectral Index and Observational Signatures of Inflation

Some of the consequences for inflationary cosmology of a scale dependence (running) in the tilt of the scalar perturbation spectrum are considered. In the limit where the running is itself approximately scale-invariant, a relationship is found between the scalar and tensor perturbation amplitudes, the scalar spectral index and its running. This relationship is independent of the functional form of the inflaton potential. More general settings, including that of braneworld cosmological models, are also considered. It is found that for the Randall-Sundrum single braneworld scenario, the corresponding relation between the observables takes precisely the same form as that arising in the standard cosmology. Some implications of the observations failing to satisfy such a relationship are discussed.

astro-ph↗

arXiv2002

BritGravII - The Second British Gravity Meeting

The second of the annual BritGrav meetings on current research in Gravitational Physics in Britain took place at the School of Mathematical Sciences of Queen Mary, University of London on June 10/11, 2002. 47 plenary talks of 12min duration were given. We make available the abstracts of the talks and the references to the electronic preprints at arXiv.org where they exist.

gr-qc↗

arXiv2002

Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $Λ\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.

gr-qc↗

arXiv2002

Generalisation of the Einstein-Straus model to anisotropic settings

We study the possibility of generalising the Einstein--Straus model to anisotropic settings, by considering the matching of locally cylindrically symmetric static regions to the set of $G_4$ on $S_3$ locally rotationally symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry are only possible for a restricted subset of the LRS models in which there is no evolution in one spacelike direction. These results are applied to spatially homogeneous (Bianchi) exteriors where the static part represents a finite bounded interior region without holes. We find that it is impossible to embed finite static strings or other locally cylindrically symmetric static objects (such as bottle or coin-shaped objects) in reasonable Bianchi cosmological models, irrespective of the matter content. Furthermore, we find that if the exterior spacetime is assumed to have a perfect fluid source satisfying the dominant energy condition, then only a very particular family of LRS stiff fluid solutions are compatible with this model. Finally, given the interior/exterior duality in the matching procedure, our results have the interesting consequence that the Oppenheimer-Snyder model of collapse cannot be generalised to such anisotropic cases.

gr-qc↗

arXiv2002

Effects of boundary conditions on the dynamics of the solar convection zone

Recent analyses of the helioseismic data have produced evidence for a variety of interesting dynamical behaviour associated with torsional oscillations. What is not so far clear is whether these oscillations extend all the way to the bottom of the convection zone and, if so, whether the oscillatory behaviour at the top and the bottom of the convection zone is different. Attempts have been made to understand such modes of behaviour within the framework of nonlinear dynamo models which include the nonlinear action of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. One aspect of these models that remains uncertain is the nature of the boundary conditions on the magnetic field. Here by employing a range of physically plausible boundary conditions, we show that for near-critical and moderately supercritical dynamo regimes, the oscillations extend all the way down to the bottom of the convection zone. Thus, such penetration is an extremely robust feature of the models considered. We also find parameter ranges for which the supercritical models show spatiotemporal fragmentation for a range of choices of boundary conditions. Given their observational importance, we also make a comparative study of the amplitude of torsional oscillations as a function of the boundary conditions.

astro-ph↗

arXiv2001

Robustness of the Quintessence Scenario in Particle Cosmologies

We study the robustness of the quintessence tracking scenario in the context of more general cosmological models that derive from high-energy physics. We consider the effects of inclusion of multiple scalar fields, corrections to the Hubble expansion law (such as those that arise in brane cosmological models), and potentials that decay with expansion of the Universe. We find that in a successful tracking quintessence model the average equation of state must remain nearly constant. Overall, the conditions for successful tracking become more complex in these more general settings. Tracking can become more fragile in presence of multiple scalar fields, and more stable when temperature dependent potentials are present. Interestingly though, most of the cases where tracking is disrupted are those in which the cosmological model is itself non-viable due to other constraints. In this sense tracking remains robust in models that are cosmologically viable.

astro-ph↗

arXiv2001

Cosmic no-hair: non-linear asymptotic stability of de Sitter universe

We study the asymptotic stability of de Sitter spacetime with respect to non-linear perturbations, by considering second order perturbations of a flat Robertson-Walker universe with dust and a positive cosmological constant. Using the synchronous comoving gauge we find that, as in the case of linear perturbations, the non-linear perturbations also tend to constants, asymptotically in time. Analysing curvature and other spacetime invariants we show, however, that these quantities asymptotically tend to their de Sitter values, thus demonstrating that the geometry is indeed locally asymptotically de Sitter, despite the fact that matter inhomogeneities tend to constants in time. Our results support the inflationary picture of frozen amplitude matter perturbations that are stretched outside the horizon, and demonstrate the validity of the cosmic no-hair conjecture in the nonlinear inhomogeneous settings considered here.

gr-qc↗

arXiv2001

Aspects of the dynamics underlying solar and stellar dynamo models

Observations of the Sun and solar-type stars continue to reveal phenomena whose understanding is very likely to require a nonlinear framework. Here we shall concentrate on two such phenomena, namely the grand minima type behaviour observed in the Sun and solar-type stars and the recent dynamical variations of the differential rotation in the solar convection zone, deduced from the helioseismic observations, and discuss how their explanations have recently motivated the development/employment of novel ideas from nonlinear dynamics.

astro-ph↗

arXiv2001

Spatiotemporal fragmentation and the uncertainties in the solar rotation law

Analyses of recent helioseismic data indicate that the dynamical regimes at the base of the convection zone can be different from those observed at the top, having either significantly shorter periods or non--periodic behaviour. Recently spatiotemporal fragmentation/bifurcation has been proposed as a dynamical mechanism to account for the multi-mode behaviour that is possibly observed in the solar convection zone, without requiring separate physical mechanisms with different time scales at different depths. Here we study the robustness of this mechanism with respect to changes to the zero order rotation profile, motivated by the uncertainties of and differences between the various reductions of the helioseimic data. We find that spatiotemporal fragmentation is a common feature of the reductions investigated

astro-ph↗

arXiv2001

In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.

nlin.CD↗

arXiv2001

The influence of noise on scalings for in-out intermittency

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics of maps, ODE and PDE simulations that have symmetries. It shows itself in the form of trajectories that spend a long time near a symmetric state interspersed with short bursts away from symmetry. In contrast to on-off intermittency, there are clearly distinct mechanisms of approach towards and away from the symmetric state, and this needs to be taken into account in order to properly model the long time statistics. We do this by using a diffusion-type equation with delay integral boundary condition. This model is validated by considering the statistics of a two-dimensional map with and without the addition of noise.

nlin.CD↗

arXiv2000

Dynamical variations of the differential rotation in the solar convection zone

Recent analyses of helioseismological observations seem to suggest the presence of two new phenomena connected with the dynamics of the solar convective zone. Firstly, there are present torsional oscillations with periods of about 11 years, which penetrate significantly into the solar convection zone and secondly, oscillatory regimes exist near the base of the convection which are markedly different from those observed near the top, having either significantly reduced periods or being non-periodic. Recently spatiotemporal fragmentation/bifurcation has been proposed as a possible dynamical mechanism to account for such observed multi-mode behaviours in different parts of the solar convection zone. Evidence for this scenario was produced in the context of an axisymmetric mean field dynamo model operating in a spherical shell, with a semi-open outer boundary condition and a zero order angular velocity obtained by the inversion of the MDI data, in which the only nonlinearity was the action of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. Here we make a detailed study of the robustness of this model with respect to plausible changes to its main ingredients, including changes to the alpha and eta profiles as well as the inclusion of a nonlinear alpha quenching. We find that spatiotemporal fragmentation is present in this model for different choices of the rotation data and as the details of the model are varied. Taken together, these results give strong support to the idea that spatiotemporal fragmentation is likely to occur in general dynamo settings.

astro-ph↗

arXiv2000

Spatiotemporal fragmentation as a mechanism for different dynamical modes of behaviour in the solar convection zone

Recent analyses of the helioseismic observations indicate that the previously observed surface torsional oscillations with periods of about 11 years extend significantly downwards into the solar convective zone. Furthermore, there are indications that the dynamical regimes at the base of the convection zone are different from those observed at the top, having either significantly shorter periods or non-periodic behaviour. We propose that this behaviour can be explained by the occurrence of {\it spatiotemporal fragmentation}, a crucial feature of which is that such behaviour can be explained solely through nonlinear spatiotemporal dynamics, without requiring separate mechanisms with different time scales at different depths. We find evidence for this mechanism in the context of a two dimensional axisymmetric mean field dynamo model operating in a spherical shell, with a semi-open outer boundary condition, in which the only nonlinearity is the action of the azimuthal component of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity.

astro-ph↗

arXiv2000

Torsional oscillations in the solar convection zone

Recent analysis of the helioseismic observations indicate that the previously observed surface torsional oscillations extend significantly downwards into the solar convection zone. In an attempt to understand these oscillations, we study the nonlinear coupling between the magnetic field and the solar differential rotation in the context of a mean field dynamo model, in which the nonlinearity is due to the action of the azimuthal component of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. The underlying zero order angular velocity is chosen to be consistent with the most recent helioseismic data. The model produces butterfly diagrams which are in qualitative agreement with the observations. It displays torsional oscillations that penetrate into the convection zone, and which with time migrate towards the equator. The period of these oscillations is found to be half that of the period of the global magnetic fields. This is compatible with the observed period of the surface torsional oscillations. Inside the convection zone, this is a testable prediction that is not ruled out by the observations so far available.

astro-ph↗