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Bianchi cosmologies are ``natural'' anisotropic extensions of the Friedmann universes and they have long been used to investigate the cosmological implications of anisotropy. The latter introduces new ingredients to the standard scenarios, although there are physical processes and effects that maintain their basic Friedmann features when extended to Bianchi universes. Here, we assume a perturbed Bianchi model and look into the implications of the observers' peculiar flow for their measurement and their interpretation of the deceleration parameter. Our motivation is twofold. To begin with, relative motions have long been known to deceive the observers by ``contaminating'' the observations, which also still suffer from sample limitations that cloud the statistical significance of the findings. Further motivation comes from claims that observers in bulk flows that expand slightly slower than their surroundings can have the illusion of cosmic acceleration in a universe that is actually decelerating. The claim was originally based on studies of a perturbed tilted Einstein-de Sitter model, but persisted when the background cosmology was replaced by any of the three Friedmann universes. This raised the possibility that the peculiar-motion effect on the deceleration parameter may be generic and largely independent of the host spacetime. Here, we investigate this possibility by extending the earlier studies to perturbed Bianchi models. We find that the Friedmann picture remains unchanged, unless the Bianchi background has unrealistically high anisotropy. The bulk-flow observers can still be misled to the illusion of accelerated expansion by their own peculiar motion., Comment: Revised version, to appear in EPJC

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulae governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalise them. Thus, we confirm earlier claims that, compared to the Newtonian studies, the relativistic analysis supports considerably stronger linear growth-rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth-rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the universe., Comment: Minor revision. To appear in PRD

Recent surveys have been reporting bulk peculiar flows considerably faster than expected. Bulk flows are moving matter and matter in motion implies nonzero energy flux. In relativity, as opposed to Newtonian physics, matter fluxes gravitate as well, since they also contribute to the energy-momentum tensor. The gravitational input of the "peculiar" flux survives at the linear level and it can drastically change our understanding of the way bulk flows have evolved in time. By default, the Newtonian analysis of peculiar motions bypasses the relativistic flux-contribution to the gravitational field. The problem is that there are also studies, with an otherwise relativistic profile, which inadvertently do the same. As result, these treatments reduce to Newtonian and they misleadingly reproduce the slow Newtonian growth-rate of linear peculiar velocities. In contrast, by accounting for the flux effects, the proper relativistic analysis arrives at a considerably stronger growth. We show that it is the flux input of the moving matter to gravity that separates the relativistic studies of peculiar motions from the rest and, in so doing, it could provide an answer to the bulk-flow question., Comment: 9 pages, no figures

Large-scale peculiar motions are commonplace in our universe. Nevertheless, their origin, evolution and implications are still largely unknown. It is generally assumed that bulk motions are a relatively recent addition to the universal kinematics, triggered by the increasing inhomogeneity and anisotropy of the post-recombination epoch. In this work, we focus on the linear evolution of peculiar velocities prior to recombination, namely in the late radiation era and also during a phase of de Sitter inflation. We begin by showing/confirming that bulk motions are triggered and sustained by the non-gravitational forces developed during structure formation. Since density and therefore peculiar-velocity perturbations cannot grow in the baryonic sector before recombination, we consider drift motions in non-baryonic species, which can start growing in the late radiation era. Using relativistic linear cosmological perturbation theory, we find that peculiar motions in the low-energy dark component exhibit power-law growth, which increases further after equipartition. Turning to the very early universe, we consider the evolution of linear peculiar velocities during a phase of de Sitter inflation. We find that typical slow-roll scenarios do not source peculiar motions. Moreover, even if the latter were to be present at the onset of the de Sitter phase, the subsequent exponential expansion should quickly wash away any traces of peculiar-velocity perturbations., Comment: Typos corrected. Published version

We study the potential effects of spacetime non-metricity in cosmology. In the spirit of Einstein-Cartan gravity, but with non-metricity replacing torsion, we consider the Einstein-Hilbert action and assume zero torsion. Adopting certain hyperfluid models, with non-vanishing hypermomentum that can source spacetime non-metricity, we add a matter component into the action and derive the field equations, along with the conservation laws. Applying our formulae to cosmology, we generalize the Friedmann and the Raychaudhuri equations in the presence of non-metricity. Our results show that, in a number of cases, non-metricity can mimic the effects of matter with unconventional equation of state. For instance, specific types of hypermomentum are found to act as an effective stiff fluid, thus opening the possibility that non-metricity could have played a significant role in the early stages of the universe's evolution. Alternative forms of hypermomentum can dominate the universal dynamics at late times. In either case, the equilibrium moment depends on the initial conditions and it is determined by a simple relation between the matter component and the hyperfluid., Comment: 19 pages, no figures

Information exchanged between observers in the universe typically travels along the null rays of the associated light signals. One may therefore decompose the luminosity distance of a given radiation source along these null geodesics, instead of the timelike worldlines of the emitting/receiving observers. In so doing, one obtains (among others) the null counterparts of the familiar Hubble and deceleration parameters. Although the timelike and the null sets of these parameters coincide in an exact Friedmann universe, they generally differ in perturbed cosmological models. The situation becomes more involved in tilted cosmologies, namely in those equipped with two families of relatively moving observers. There, the two observer groups generally disagree on the values of these parameters, simply because of their relative motion. Assuming a tilted, perturbed Friedmann universe with dust, we find that the relative-motion effects alone can locally change the sign of the null deceleration parameter from positive to negative, while at the same time the host universe is globally decelerating. An exactly analogous effect has also been reported with regard to the timelike deceleration parameter. The difference is that, in the null case, the impact of the relative motion is twice as strong, thus making it easier for the unsuspecting observers to misinterpret a local change in the sign of the deceleration parameter as recent global acceleration., Comment: Revised version. Presentation changed. Results the same

We study a parametrization of the deceleration parameter in a tilted universe, namely a cosmological model equipped with two families of observers. The first family follows the smooth Hubble flow, while the second are the real observers residing in a typical galaxy inside a bulk flow and moving relative to the smooth Hubble expansion with finite peculiar velocity. We use the compilation of Type Ia Supernovae (SnIa) data, as described in the Pantheon dataset, to find the quality of fit to the data and study the redshift evolution of the deceleration parameter. In so doing, we consider two alternative scenarios, assuming that the bulk-flow observers live in the $\Lambda$CDM and in the Einstein-de Sitter universe. We show that a tilted Einstein-de Sitter model can reproduce the recent acceleration history of the universe, without the need of a cosmological constant or dark energy, by simply taking into account linear effects of peculiar motions. By means of a Markov Chain Monte Carlo (MCMC) method, we also constrain the magnitude and the uncertainties of the parameters of the two models. From our statistical analysis, we find that the tilted Einstein-de Sitter model, equipped with one or two additional parameters that describe the assumed large-scale velocity flows, performs similar to the standard $\Lambda$CDM paradigm in the context of model selection criteria (Akaike Information Criterion and Bayesian Information Criterion)., Comment: 13 pages, 5 figures and 3 tables. Accepted for publication in MNRAS. References added, subsection added with details on the Pantheon dataset. The numerical analysis files for the reproduction of the figures can be downloaded from https://github.com/lkazantzi/tilted-cosmology

Large-scale bulk peculiar motions introduce a characteristic length scale, inside which the local kinematics are dominated by peculiar-velocity perturbations rather than by the background Hubble expansion. Regions smaller than the aforementioned critical length, which typically varies between few hundred and several hundred Mpc, can be heavily "contaminated" by the observers' relative motion. For example, at the critical length -- hereafter referred to as the "transition scale", the sign of the locally measured deceleration parameter can change from positive to negative, while the surrounding universe is still decelerating globally. Overall, distant observers can assign very different values to their local deceleration parameters, entirely because of their relative motion. In practice, this suggests that information selected from regions inside and close to the transition scale hold only locally and they should not be readily extrapolated to the global universe. We show that this principle applies to essentially all Friedmann backgrounds, irrespective of their equation of state and spatial curvature. Put another way, the transition scale and the related effects are generic to linear peculiar-velocity perturbations. This study generalises previous work applied, primarily for reasons of mathematical simplicity, to a perturbed Einstein-de Sitter universe., Comment: Minor revision, references added. To appear in EPJC

Within the context of general relativity we study in a fully covariant way the so-called Euler-Maxwell system of equations. In particular, on decomposing the aforementioned system into its 1 temporal and 1 + 2 spatial components at the ideal magnetohydrodynamic limit, we bring it in a simplified form that favors physical insight to the problem of a self-gravitating, magnetized fluid. Of central interest is the decomposition of Faraday's equation which leads to a new general solution governing the evolution of the magnetic field during the motion of the highly conducting fluid. According to the latter relation, the magnetic field generally grows or decays in proportion to the inverse cube law of the scale factor--associated with the continuous contraction or expansion of the fluid's volume respectively. The magnetic field's law of variation, which has remarkable implications for the motion of the whole fluid, is subsequently applied to homogeneous (anisotropic-magnetized) cosmological models--especially to the Bianchi I case--as well as to the study of homogeneous and anisotropic gravitational collapse in a magnetized environment. Concerning the cosmological application, we derive the evolution equations of Bianchi I spacetime permeated by large-scale magnetic fields (these equations reduce to their FRW counterparts at the small/large--scale limit). Also, the compatibility of the new evolution formula for the magnetic field with the standard cosmic nucleosynthesis constraint is examined. As for the application in astrophysics, our results predict that homogeneous gravitational implosion is impeded when the electric Weyl tensor (associated with tidal forces) along the magnetic forcelines overwhelms the magnetic energy density. Lastly, our model denotes that the satisfaction of the aforementioned criterion is ultimately driven into a problem of initial conditions., Comment: 34 pages, minor comments added

Electromagnetic potentials allow for an alternative description of the Maxwell field, the electric and magnetic components of which emerge as gradients of the vector and the scalar potential. We provide a general relativistic analysis of these potentials, by deriving their wave equations in an arbitrary Riemannian spacetime containing a generalised imperfect fluid. Some of the driving agents in the resulting wave formulae are explicitly due to the curvature of the host spacetime. Focusing on the implications of non-Euclidean geometry, we look into the linear evolution of the vector potential in Friedmann universes with nonzero spatial curvature. Our results reveal a qualitative difference in the evolution of the potential between the closed and the open Friedmann models, solely triggered by the different spatial geometry of these spacetimes. We then consider the interaction between gravitational and electromagnetic radiation and the effects of the former upon the latter. In so doing, we apply the wave formulae of both potentials to a Minkowski background and study the Weyl-Maxwell coupling at the second perturbative level. Our solutions, which apply to low-density interstellar environments away from massive compact stars, allow for the resonant amplification of both the electromagnetic potentials by gravitational-wave distortions., Comment: "Minor revision, to appear in CQG"

Typical observers in the universe do not follow the smooth Hubble expansion, but move relative to it. Such bulk peculiar motions introduce a characteristic scale that is closely analogous to the familiar Jeans length. This "peculiar Jeans length" marks the threshold below which relative-motion effects dominate the linear kinematics. There, cosmological measurements can vary considerably between the bulk-flow frame and that of the Hubble expansion, entirely due to the observers' relative motion. When dealing with the deceleration parameter, we find that the peculiar Jeans length varies between few and several hundred Mpc. On these scales, the deceleration parameter measured by the bulk-flow observers can be considerably larger (or smaller) than its Hubble-frame counterpart. This depends on whether the peculiar motion is locally expanding (or contracting), relative to the background expansion. Then, provided expanding and contracting bulk flows are randomly distributed, nearly half of the observers in the universe could be misled to think that their cosmos is over-decelerated. The rest of them, on the other hand, may come to believe that their universe is under-decelerated, or even accelerated in some cases. We make two phenomenological predictions that could in principle support this scenario., Comment: Revised and extended version. References added. Matches published manuscript

Electromagnetism appears to have the potential to alter the fate of relativistic gravitational implosion. Coulomb forces, for example, can in principle prevent the ultimate collapse of charged matter to a singularity. Also, half a century ago, Mael Melvin noted that magnetic forcelines do not collapse under their own gravity, no matter how strong the latter may be. Instead, magnetic fields seemed capable of stabilising themselves against gravitational self-contraction. Intrigued, Melvin wondered whether magnetism could also support against the realistic collapse of charged matter. Here, we look back into these issues by means of two complementary scenarios. The first reconsiders Melvin's highly idealised "magnetic universe" and reaches the same conclusion, namely that magnetic fields do not self-gravitate. The second is a realistic collapse scenario, like that of magnetised massive compact stars. Looking for answers to Melvin's question, we find that magnetic fields do show a generic tendency to support against relativistic gravitational implosion. The magnetic effect in question involves the curvature of the host space, it grows stronger as the collapse progresses and the triggering agent is the field's tension. In other words, the reason is the elasticity of the field lines and their inherent tendency to react against anything that distorts them from equilibrium. In this case, the distorting agent is the ever increasing curvature of the collapsing host space., Comment: Typos corrected. Matches published version

We consider the kinematical and dynamical evolution of Friedmann universes with a mixture of non-interacting matter and a ghost-like field, in a scenario analogous to that advocated by the Quintom model. Assuming that the conventional matter dominates today, we find that the ghost component can bring the future expansion and the past contraction of the model to a finite halt. Moreover, at the moment the expansion or contraction stops, we find that the tendency of the universe is to bounce back and re-collapse or re-expand. Therefore, the presence of a (never dominant) ghost-field with negative density could, in principle, drive the universe into an eternal cycle of finite expansion, collapse, and re-expansion. Our study outlines the key features of such a scenario and provides a simple condition for it to occur. We also derive an autonomous set of differential equations and then employ dynamical-system techniques to identify two families of fixed points, with and without spatial curvature respectively. The members of the first family correspond to coasting universes and are stable in the Lyapunov sense. Those of the latter family are unstable repellers when their matter satisfies the strong energy condition and Lyapunov stable in the opposite case., Comment: Minor revision. References added. To appear in CQG

We employ a perturbative analysis to study the evolution of large-scale peculiar velocity fields within the framework of Newtonian gravity and then compare our results to those of the corresponding relativistic treatment. In so doing, we use the same mathematical formalism and apply the same physical approach. This facilitates a direct and transparent comparison between the two treatments. Our study recovers and extends the familiar Newtonian results on the one hand, while on the other it shows that the Newtonian analysis leads to substantially weaker growth-rates for the peculiar velocity field, compared to the relativistic approach. This implies that, by using Newton's rather than Einstein's theory, one could seriously underestimate the overall kinematic evolution of cosmological peculiar motions. We are also in the position to identify the reason the two theories arrive at such considerably different results and conclusions., Comment: Typos corrected. Published version

We consider the linear kinematics of large-scale peculiar motions in a perturbed Friedmann universe. In so doing, we take the viewpoint of the "real" observers that move along with the peculiar flow, relative to the smooth Hubble expansion. Using relativistic cosmological perturbation theory, we study the linear evolution of the peculiar velocity field, as well as the expansion/contraction, the shear and the rotation of the bulk motion. Our solutions show growth rates considerably stronger than those of the earlier treatments, which were mostly Newtonian. On scales near and beyond the Hubble radius, namely at the long-wavelength limit, peculiar velocities are found to grow as $a^2$, in terms of the scale factor, instead of the Newtonian $a^{1/2}$-law. We attribute this to the fact that, in general relativity, the energy flux, triggered here by the peculiar motion of the matter, also contributes to the local gravitational field. In a sense, the bulk flow gravitates, an effect that has been bypassed in related relativistic studies. These stronger growth-rates imply faster peculiar velocities at horizon crossing and higher residual values for the peculiar-velocity field. Alternatively, one could say that our study favours bulk peculiar flows larger and faster than anticipated., Comment: Typos corrected. Matches published version

Torsion and nonmetricity are inherent ingredients in modifications of Eintein's gravity that are based on affine spacetime geometries. In the context of pure f(R) gravity we discuss here, in some detail, the relatively unnoticed duality between torsion and nonmetricity. In particular we show that for R2 gravity torsion and nonmetricity are related by projective transformations. Since the latter correspond simply to redefining the affine parameters of autoparallels, we conclude that torsion and nonmetricity are physically equivalent properties of spacetime. As a simple example we show that both torsion and nonmetricity can act as geometric sources of accelerated expansion in a spatially homogenous cosmological model within R2 gravity and we brie y discuss possible implications of our results., Comment: 11 pages, no figures

We introduce and develop the 1+3 covariant approach to relativity and cosmology to spacetimes of arbitrary dimensions that have nonzero torsion and do not satisfy the metricity condition. Focusing on timelike observers, we identify and discuss the main differences between their kinematics and those of their counterparts living in standard Riemannian spacetimes. At the centre of our analysis lies the Raychaudhuri equation, which is the fundamental formula monitoring the convergence/divergence, namely the collapse/expansion, of timelike worldline congruences. To the best of our knowledge, we provide the most general expression so far of the Raychaudhuri equation, with applications to an extensive range of non-standard astrophysical and cosmological studies. Assuming that metricity holds, but allowing for nonzero torsion, we recover the results of analogous previous treatments. Focusing on non-metricity alone, we identify a host of effects that depend on the nature of the timelike congruence and on the type of the adopted non-metricity. We also demonstrate that in spaces of high symmetry one can recover the pure-torsion results from their pure non-metricity analogues, and vice-versa, via a simple ansatz between torsion and non-metricity., Comment: Revised version. References added. To appear in PRD

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field's pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field's tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field's pressure and tension, on the linear evolution of cosmological density perturbations., Comment: Invited contribution to the CQG Focus special issue "Magnetic fields at cosmological scales". Published version

We consider the "kinematics" of spacelike congruences and apply them to a family of self-gravitating magnetic forcelines. Our aim is to investigate the convergence and the possible focusing of these lines, as well as their rotation and shear deformation. In so going, we introduce a covariant 1+2 splitting of the 3-dimensional space, parallel and orthogonal to the direction of the field lines. The convergence, or the divergence, of the latter is monitored by the associated Raychaudhuri equation, which is obtained by propagating the spatial divergence of a unitary spacelike vector along its own direction. Applied to a magnetic vector, the resulting expression shows that, although the convergence of the magnetic forcelines is affected by the gravitational pull of all the other sources, it is unaffected by the field's own gravity, irrespective of how strong the latter is. This rather counterintuitive result is entirely due to the magnetic tension, namely to the negative pressure the field exerts parallel to its lines of force. In particular, the magnetic tension always cancels out the field's energy-density input to the Raychaudhuri equation, leaving the latter free of any direct magnetic-energy contribution. Similarly, the rotation and the shear deformation of the aforementioned forcelines are also unaffected by the magnetic input to the total gravitational energy. In a sense, the magnetic lines do not seem to "feel" their own gravity no matter how strong the latter may be., Comment: Typos corrected. Published version

We analyse the kinematics of cosmological spacetimes with nonzero torsion, in the framework of the classical Einstein-Cartan gravity. After a brief introduction to the basic features of spaces with non-vanishing torsion, we consider a family of observers moving along timelike worldlines and focus on their kinematic behaviour. In so doing, we isolate the irreducible variables monitoring the observers' motion and derive their evolution formulae and associated constraint equations. Our aim is to identify the effects of spacetime torsion, and the changes they introduce into the kinematics of the standard, torsion-free, cosmological models. We employ a fully geometrical approach, imposing no restrictions on the material content, or any a priori couplings between torsion and spin. Also, we do not apply the familiar splitting of the equations, into a purely Riemannian component plus a torsion/spin part, at the start of our study, but only introduce it at the very end. With the general formulae at hand, we use the Einstein-Cartan field equations to incorporate explicitly the spin of the matter. The resulting formulae fully describe the kinematics of dynamical spacetimes within the framework of the Einstein-Cartan gravity, while in the special case of the so-called Weyssenhoff fluid, they recover results previously reported in the literature., Comment: Typos corrected, published version

The post-inflationary evolution of inflation-produced magnetic fields, conventional or not, can change dramatically when two fundamental issues are accounted for. The first is causality, which demands that local physical processes can never affect superhorizon perturbations. The second is the nature of the transition from inflation to reheating and then to the radiation era, which determine the initial conditions at the start of these epochs. Causality implies that inflationary magnetic fields dot not freeze into the matter until they have re-entered the causal horizon. The nature of the cosmological transitions and the associated initial conditions, on the other hand, determine the large-scale magnetic evolution after inflation. Put together, the two can slow down the adiabatic magnetic decay on superhorizon scales throughout the universe's post-inflationary evolution and thus lead to considerably stronger residual magnetic fields. This is "good news" for both the conventional and the non-conventional scenarios of cosmic magnetogenesis. Mechanisms operating outside standard electromagnetism, in particular, do not need to enhance their fields too much during inflation, in order to produce seeds that can feed the galactic dynamo today. In fact, even conventionally produced inflationary magnetic fields might be able to sustain the dynamo., Comment: Typos corrected. Published version

Gravitational waves are propagating undulations in the spacetime fabric, which interact very weakly with their environment. In cosmology, gravitational-wave distortions are produced by most of the inflationary scenarios and their anticipated detection should open a new window to the early universe. Motivated by the relative lack of studies on the potential implications of gravitational radiation for the large-scale structure of the universe, we consider its coupling to density perturbations during the post-recombination era. We do so by assuming an Einstein-de Sitter background cosmology and by employing a second-order perturbation study. At this perturbative level and on superhorizon scales, we find that gravitational radiation adds a distinct and faster growing mode to the standard linear solution for the density contrast. Given the expected weakness of cosmological gravitational waves, however, the effect of the new mode is currently subdominant and it could start becoming noticeable only in the far future. Nevertheless, this still raises the intriguing possibility that the late-time evolution of large-scale density perturbations may be dictated by the long-range (the Weyl), rather than the local (the Ricci) component of the gravitational field., Comment: typos corrected. published version

Inflation has long been thought as the best way of producing primordial large-scale magnetic fields. To achieve fields strong enough to seed the galactic dynamo, most of the mechanisms operate outside conventional electromagnetic theory. The latter is typically restored after the end of the de Sitter phase. Breaking away from standard electromagnetism can lead to substantially stronger magnetic fields by the end of inflation, thus compensating for the their subsequent adiabatic depletion. We argue that the drastic magnetic enhancement during the de Sitter era may no longer be necessary because, contrary to the widespread perception, superhorizon-sized magnetic fields decay at a slower pace after inflation. The principle behind this claim is causality, which confines the post-inflationary electric currents inside the horizon. Without the currents there can be no magnetic-flux freezing on super-Hubble lengths. There, the magnetic decay-rate slows down, thus making it much easier to produce primordial fields of astrophysical interest. To quantify this qualitative statement, one can start from the current galactic-dynamo requirements and `reverse engineer' the magnetic strengths needed at the end of inflation, in order to produce astrophysically relevant residual seeds today. Our results suggest that, depending on the magnetic scale, mechanisms of inflationary magnetogenesis generating fields stronger than $10^{17}$ G by the end of the de Sitter phase, could successfully seed the galactic dynamo at present., Comment: Revised version. To appear in PRD(RC)

We study inhomogeneous magnetised cosmologies through the post-recombination era in the framework of Newtonian gravity and the ideal-magnetohydrodynamic limit. The nonlinear kinematic and dynamic equations are derived and linearised around the Newtonian counterpart of the Einstein-de Sitter universe. This allows for a direct comparison with the earlier relativistic treatments of the issue. Focusing on the evolution of linear density perturbations, we provide new analytic solutions which include the effects of the magnetic pressure as well as those of the field's tension. We confirm that the pressure of field inhibits the growth of density distortions and can induce a purely magnetic Jeans length. On scales larger than the aforementioned characteristic length the inhomogeneities grow, though slower than in non-magnetised universes. Wavelengths smaller than the magnetic Jeans length typically oscillate with decreasing amplitude. We also identify a narrow range of scales, just below the Jeans length, where the perturbations exhibit a slower power-law decay. In all cases, the effect of the field is proportional to its strength and increases as we move to progressively smaller lengths., Comment: Published version

Large-scale peculiar motions are believed to reflect the local inhomogeneity and anisotropy of the universe, triggered by the ongoing process of structure formation. As a result, realistic observers do not follow the smooth Hubble flow but have a peculiar, `tilt', velocity relative to it. Our Local Group of galaxies, in particular, moves with respect to the universal expansion at a speed of roughly 600~km/sec. Relative motion effects are known to interfere with the observations and their interpretation. The strong dipolar anisotropy seen in the Cosmic Microwave Background, for example, is not treated as a sign of real universal anisotropy, but as a mere artifact of our peculiar motion relative to the Hubble flow. With these in mind, we look into the implications of large-scale bulk motions for the kinematics of their associated observers, by adopting a `tilted' Friedmann model. Our aim is to examine whether the deceleration parameter measured in the rest-frame of the bulk flow can differ from that of the actual universe due to relative-motion effects alone. We find that there is a difference, which depends on the speed as well as the scale of the bulk motion. The faster and the smaller the drifting domain, the larger the difference. In principle, this allows relatively slow peculiar velocities to have a disproportionately strong effect on the value of the deceleration parameter measured by observers within bulk flows of, say, few hundred megaparsecs. In fact, under certain circumstances, it is even possible to change the sign of the deceleration parameter. It goes without saying that all these effects vanish identically in the Hubble frame, which makes then an illusion and mere artifact of the observers' relative motion., Comment: Typos corrected, published version

We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without~abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a~priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a~power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes., Comment: 26 pages, published version

We use a general relativistic approach to investigate the effects of weak cosmological magnetic fields on linear rotational perturbations during the radiation and dust epochs of the universe. This includes ordinary kinematic vorticity, as well as vortex-like inhomogeneities in the density distribution of the cosmic medium. Our study confirms that magnetic fields can source both types of perturbations and shows that their presence also helps cosmic rotation to survive longer. In agreement with previous Newtonian studies, we find that during the dust era vorticity decays slower than in non-magnetised cosmologies. Prior to equipartition the magnetic effect is more pronounced, since it helps the aforementioned rotational distortions to maintain constant magnitude. Overall, magnetised universes seem to provide a much better environment for the survival of cosmic vorticity than their magnetic-free counterparts., Comment: Typos corrected, references added. PRD in press

Peculiar motions are commonplace in the universe. Our local group of galaxies, for example, drifts relative to the Hubble flow at about 600 km/sec. Such bulk flows are believed to fade away as we move on to progressively larger scales. Recently, however, there have been reports of peculiar motions larger and faster than typically expected. If these claims are correct, the role of peculiar flows in shaping the kinematics of our universe has been probably underestimated. Here, we use general relativistic techniques to analyse the average kinematics of large-scale bulk motions and compute the nonlinear Raychaudhuri equation of such flows. In doing so, we introduce two families of observers. One at rest with the Hubble expansion and another following the peculiar motion. We first derive the fully nonlinear expressions of the "peculiar" Raychaudhuri equation in both frames and identify a range of relative motion effects. Linearised around a Friedmann universe with pressureless dust, the full equations reduce to a simple relation with no explicit contribution from the matter component of the universe. Using cosmological perturbation theory, we obtain a scale-dependent formula, which also incorporates the effects of universe's inhomogeneity and anisotropy. When the latter are secondary, the peculiar Raychaudhuri equation can be solved analytically. Also, combining the resulting expression with data from recent peculiar-velocity surveys, we estimate the relative deceleration/acceleration rates of such bulk motions., Comment: Typos corrected, references added. Published version

We consider the interaction between gravitational and electromagnetic radiation propagating on a Minkowski background and look into the effects of the former upon the latter. Not surprisingly, the coupling between these two sources leads to gravitationally driven electromagnetic waves. At the second perturbative level, the driving force appears as the superposition of two waves, the properties of which are decided by the initial conditions. We find that the Weyl-Maxwell interaction typically leads to electromagnetic beat-like signals and, in some cases, to the resonant amplification of the driven electromagnetic wave. For physically reasonable initial conditions, we show that these resonances imply a linear (in time) growth for the amplitude of the electromagnetic signal, with the overall amplification also depending on the strength of the driving gravity wave. Finally, we provide order-of-magnitude estimates of the achieved amplification by applying our analysis to astrophysical environments where both gravitational and electromagnetic waves are expected to coexist., Comment: Typos corrected. Published version

We review current ideas on the origin of galactic and extragalactic magnetic fields. We begin by summarizing observations of magnetic fields at cosmological redshifts and on cosmological scales. These observations translate into constraints on the strength and scale magnetic fields must have during the early stages of galaxy formation in order to seed the galactic dynamo. We examine mechanisms for the generation of magnetic fields that operate prior during inflation and during subsequent phase transitions such as electroweak symmetry breaking and the quark-hadron phase transition. The implications of strong primordial magnetic fields for the reionization epoch as well as the first generation of stars is discussed in detail. The exotic, early-Universe mechanisms are contrasted with astrophysical processes that generate fields after recombination. For example, a Biermann-type battery can operate in a proto-galaxy during the early stages of structure formation. Moreover, magnetic fields in either an early generation of stars or active galactic nuclei can be dispersed into the intergalactic medium., Comment: Accepted for publication in Space Science Reviews. Pdf can be also downloaded from http://canopus.cnu.ac.kr/ryu/cosmic-mag1.pdf

Magnetic fields appear to be ubiquitous in astrophysical environments. Their existence in the intracluster medium is established through observations of synchrotron emission and Faraday rotation. On the other hand, the nature of magnetic fields outside of clusters, where observations are scarce and controversial, remains largely unknown. In this chapter, we review recent developments in our understanding of the nature and origin of intergalactic magnetic fields, and in particular, intercluster fields. A plausible scenario for the origin of galactic and intergalactic magnetic fields is for seed fields, created in the early universe, to be amplified by turbulent flows induced during the formation of the large scale structure. We present several mechanisms for the generation of seed fields both before and after recombination. We then discuss the evolution and role of magnetic fields during the formation of the first starts. We describe the turbulent amplification of seed fields during the formation of large scale structure and the nature of the magnetic fields that arise. Finally, we discuss implications of intergalactic magnetic fields., Comment: Accepted for publication in Space Science Reviews. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/cosmic-mag2.pdf

Peculiar velocities change the expansion rate of any observer moving relative to the smooth Hubble flow. As a result, observers in a galaxy like our Milky Way can experience accelerated expansion within a globally decelerating universe, even when the drift velocities are small. The effect is local, but the affected scales can be large enough to give the false impression that the whole cosmos has recently entered an accelerating phase. Generally, peculiar velocities are also associated with dipole-like anisotropies, triggered by the fact that they introduce a preferred spatial direction. This implies that observers experiencing locally accelerated expansion, as a result of their own drift motion, may also find that the acceleration is maximised in one direction and minimised in the opposite. We argue that, typically, such a dipole anisotropy should be relatively small and the axis should probably lie fairly close to the one seen in the spectrum of the Cosmic Microwave Background., Comment: Typos corrected. Published version

The interaction between gravitational and electromagnetic radiation has a rather long research history. It is well known, in particular, that gravity-wave distortions can drive propagating electromagnetic signals. Since forced oscillations provide the natural stage for resonances to occur, gravito-electromagnetic resonances have been investigated as a means of more efficient gravity-wave detection methods. In this report, we consider the coupling between the Weyl and the Maxwell fields on a Minkowski background, which also applies to astrophysical environments where gravity is weak, at the second perturbative level. We use covariant methods that describe gravitational waves via the transverse component of the shear, instead of pure-tensor metric perturbations. The aim is to calculate the properties of the electromagnetic signal, which emerges from the interaction of its linear counterpart with an incoming gravitational wave. Our analysis shows how the wavelength and the amplitude of the gravitationally driven electromagnetic wave vary with the initial conditions. More specifically, for certain initial data, the amplitude of the induced electromagnetic signal is found to diverge. Analogous, diverging, gravito-electromagnetic resonances were also reported in cosmology. Given that, we extend our Minkowski-space study to cosmology and discuss analogies and differences in the physics and in the phenomenology of the Weyl-Maxwell coupling between the aforementioned two physical environments., Comment: Minor changes, to appear in PRD

It is widely believed that primordial magnetic fields are dramatically diluted by the expansion of the universe. As a result, cosmological magnetic fields with residual strengths of astrophysical relevance are generally sought by going outside standard cosmology, or by extending conventional electromagnetic theory. Nevertheless, the survival of strong B-fields of primordial origin is possible in spatially open Friedmann universes without changing conventional electromagnetism. The reason is the hyperbolic geometry of these spacetimes, which slows down the adiabatic magnetic decay-rate and leads to their superadiabatic amplification on large scales. So far, the effect has been found to operate on Friedmannian backgrounds containing either radiation or a slow-rolling scalar field. We show here that the superadiabatic amplification of large-scale magnetic fields, generated by quantum fluctuations during inflation, is essentially independent of the type of matter that fills the universe and appears to be a generic feature of open Friedmann spacetimes. We estimate the late-time strength of any residual field in a marginally open universe and show that it can easily meet the requirements for the dynamo generation of the magnetic fields observed in galaxies today., Comment: Equations streamlined, references updated. MNRAS in press

We use the Raychaudhuri equation to probe certain aspects related to the gravitational collapse of a charged medium. The aim is to identify the stresses the Maxwell field exerts on the fluid and discuss their potential implications. Particular attention is given to those stresses that resist contraction. After looking at the general case, we consider the two opposite limits of poor and high electrical conductivity. In the former there are electric fields but no currents, while in the latter the situation is reversed. When the conductivity is low, we find that the main agents acting against the collapse are the Coulomb forces triggered by the presence of an excess charge. At the ideal Magnetohydrodynamic (MHD) limit, on the other hand, the strongest resistance seems to come from the tension of the magnetic forcelines. In either case, we discuss whether and how the aforementioned resisting stresses may halt the contraction and provide a set of conditions making this likely to happen., Comment: Revised version, to appear in PRD

Magnetic fields appear everywhere in the universe. From stars and galaxies, all the way to galaxy clusters and remote protogalactic clouds magnetic fields of considerable strength and size have been repeatedly observed. Despite their widespread presence, however, the origin of cosmic magnetic fields is still a mystery. The galactic dynamo is believed capable of amplifying weak magnetic seeds to strengths like those measured in ours and other galaxies, but the question is where do these seed fields come from? Are they a product of late, post-recombination, physics or are they truly cosmological in origin? The idea of primordial magnetism is attractive because it makes the large-scale magnetic fields, especially those found in early protogalactic systems, easier to explain. As a result, a host of different scenarios have appeared in the literature. Nevertheless, early magnetogenesis is not problem free, with a number of issues remaining open and a matter of debate. We review the question of primordial magnetic fields and consider the limits set on their strength by the current observational data. The various mechanisms of pre-recombination magnetogenesis are presented and their advantages and shortcomings are debated. We consider both classical and quantum scenarios, that operate within as well as outside the standard model, and also discuss how future observations could be used to decide whether the large-scale magnetic fields we see in the universe today are truly primordial or not., Comment: 107 pages, 3 figures. Revised and expanded version, to be published in Physics Reports

Magnetic fields interact with gravitational waves in various ways. We consider the coupling between the Weyl and the Maxwell fields in cosmology and study the effects of the former on the latter. The approach is fully analytical and the results are gauge-invariant. We show that the nature and the outcome of the gravito-magnetic interaction depends on the electric properties of the cosmic medium. When the conductivity is high, gravitational waves reduce the standard (adiabatic) decay rate of the B-field, leading to its superadiabatic amplification. In poorly conductive environments, on the other hand, Weyl-curvature distortions can result into the resonant amplification of large-scale cosmological magnetic fields. Driven by the gravitational waves, these B-fields oscillate with an amplitude that is found to diverge when the wavelengths of the two sources coincide. We present technical and physical aspects of the gravito-magnetic interaction and discuss its potential implications., Comment: Typos corrected, clarifications added, published in PRD

Despite the widespread presence of magnetic fields, their origin, evolution and role are still not well understood. Primordial magnetism sounds appealing but is not problem free. The magnetic implications for the large-scale structure of the universe still remain an open issue. This paper outlines the advantages and shortcomings of early-time magnetogenesis and the typical role of B-fields in linear structure-formation scenarios., Comment: Invited Talk (36th EPS Conference on Plasma Physics, 2009)

We consider the classical linear stability of a static universe filled with a non-interacting mixture of isotropic radiation and a ghost scalar field. Unlike the conventional Einstein static model, this cosmology is stable against homogeneous and isotropic perturbations. This is shown by means of exact oscillatory solutions about the original static state. We also examine the linear response of the static ghost universe to all types of inhomogeneous fluctuations, namely density, vorticity and gravitational-wave perturbations. The results show that the static background constrains the linear evolution of these distortions, to the extent that density perturbations remain time invariant, vortical distortions vanish and gravitational waves oscillate with constant amplitude. We discuss the potential implications of these results for past-eternal initial states in classical general relativistic cosmology., Comment: Matches published version

Recent surveys seem to support bulk peculiar velocities well in excess of those anticipated by the standard cosmological model. In view of these results, we consider here some of the theoretical implications of large-scale drift motions. We find that observers with small, but finite, peculiar velocities have generally different expansion rates than the smooth Hubble flow. In particular, it is possible for observers with larger than the average volume expansion at their location, to experience apparently accelerated expansion when the universe is actually decelerating. Analogous results have been reported in studies of inhomogeneous (nonlinear) cosmologies and within the context of the Lemaitre-Tolman-Bondi models. Here, they are obtained within the linear regime of a perturbed, dust-dominated Friedmann-Robertson-Walker cosmology., Comment: Revised approach, discussion and references. To appear in MNRAS

We describe how magnetic fields in Friedmann universes can experience superadiabatic growth without departing from conventional electromagnetism. The reason is the relativistic coupling between vector fields and spacetime geometry, which slows down the decay of large-scale magnetic fields in open universes, compared to that seen in perfectly flat models. The result is a large relative gain in magnetic strength during the pre-galactic era that can lead to astrophysically interesting B-fields, even if our universe is only marginally open today., Comment: Typos corrected. To appear in PRD (Brief Reports)

We generalise the relativistic expression of Ohm's law by studying a multi-fluid system of charged species using the 1+3 covariant formulation of general relativistic electrodynamics. This is done by providing a fully relativistic, fully nonlinear propagation equation for the spatial component of the electric 4-current. Our analysis proceeds along the lines of the non-relativistic studies and extends previous relativistic work on cold plasmas. Exploiting the compactness and transparency of the covariant formalism, we provide a direct comparison with the standard Newtonian versions of Ohm's law and identify the relativistic corrections in an unambiguous way. The generalised expression of Ohm's law is initially given relative to an arbitrary observer and for a multi-component relativistic charged medium. Then, the law is written with respect to the Eckart frame and for a hot two-fluid plasma with zero total charge. Finally, we apply our analysis to a cold proton-electron plasma and recover the well known magnetohydrodynamic expressions. In every step, we discuss the approximations made and identify familiar effects, like the Biermann-battery and the Hall effect., Comment: 12 pages, revtex style, no figures, minor changes, accepted for publication in MNRAS

General relativity marked the beginning of modern cosmology and it has since been at the centre of many of the key developments in this field. In the present review, we discuss the general-relativistic dynamics and perturbations of the standard cosmological model, the Friedmann-Lemaitre universe, and how these can explain and predict the properties of the observable universe. Our aim is to provide an overview of the progress made in several major research areas, such as linear and non-linear cosmological perturbations, large-scale structure formation and the physics of the cosmic microwave background radiation, in view of current and upcoming observations. We do this by using a single formalism throughout the review, the 1+3 covariant approach to cosmology, which allows for a uniform and balanced presentation of technical information and physical insight., Comment: Several minor changes, typos corrected, references added and updated (Physics Reports in press)

We look at the covariant techniques and the ideas on constraints and gauge-invariance, which were recently employed in [gr-qc/0702104] to support earlier work by the same authors. That work was criticised in [gr-qc/0503042]. Using very simple and well known examples we show that, when adopted, the methods and views of [gr-qc/0702104] lead to basic-level mathematical problems, with analogous consequences for the physics. We provide a few simple rules that should help to avoid similar problems in the future., Comment: 4 pages

We examine the effects of spatial inhomogeneities on irrotational anisotropic cosmologies by looking at the average properties of anisotropic pressure-free models. Adopting the Buchert scheme, we recast the averaged scalar equations in Bianchi-type form and close the standard system by introducing a propagation formula for the average shear magnitude. We then investigate the evolution of anisotropic average vacuum models and those filled with pressureless matter. In the latter case we show that the backreaction effects can modify the familiar Kasner-like singularity and potentially remove Mixmaster-type oscillations. The presence of nonzero average shear in our equations also allows us to examine the constraints that a phase of backreaction-driven accelerated expansion might put on the anisotropy of the averaged domain. We close by assessing the status of these and other attempts to define and calculate `average' spacetime behaviour in general relativity., Comment: revised version, to appear in CQG

We use covariant and first-order formalism techniques to study the properties of general relativistic cosmology in three dimensions. The covariant approach provides an irreducible decomposition of the relativistic equations, which allows for a mathematically compact and physically transparent description of the 3-dimensional spacetimes. Using this information we review the features of homogeneous and isotropic 3-d cosmologies, provide a number of new solutions and study gauge invariant perturbations around them. The first-order formalism is then used to provide a detailed study of the most general 3-d spacetimes containing perfect-fluid matter. Assuming the material content to be dust with comoving spatial 2-velocities, we find the general solution of the Einstein equations with non-zero (and zero) cosmological constant and generalise known solutions of Kriele and the 3-d counterparts of the Szekeres solutions. In the case of a non-comoving dust fluid we find the general solution in the case of one non-zero fluid velocity component. We consider the asymptotic behaviour of the families of 3-d cosmologies with rotation and shear and analyse their singular structure. We also provide the general solution for cosmologies with one spacelike Killing vector, find solutions for cosmologies containing scalar fields and identify all the PP-wave 2+1 spacetimes., Comment: 35 pages, 2 figures

We investigate the gravitational implosion of magnetized matter by studying the inhomogeneous collapse of a weakly magnetized Tolman-Bondi spacetime. The role of the field is analyzed by looking at the convergence of neighboring particle worldlines. In particular, we identify the magnetically related stresses in the Raychaudhuri equation and use the Tolman-Bondi metric to evaluate their impact on the collapsing dust. We find that, despite the low energy level of the field, the Lorentz force dominates the advanced stages of the collapse, leading to a strongly anisotropic contraction. In addition, of all the magnetic stresses, those that resist the collapse are found to grow faster., Comment: 6 pages, RevTex; v2: physical interpretation of the results slightly changed, references added, version accepted in Phys. Rev. D (2006)