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Objective: To study normative values of range of motion (ROM), strength, and functional performance and investigate changes over 1 year in adolescent female football players.Design: Cross-sectional.Participants: 418 adolescent female football players aged 12-17 years.Main outcome measures: The physical characteristic assessments included (1) ROM assessment of the trunk, hips, and ankles; (2) strength measures (maximal isometric and eccentric strength for the trunk, hips, and knees, and strength endurance for the neck, back, trunk and calves), and (3) functional per-formance (the one-leg long box jump test and the square hop test).Results: Older players were stronger, but not when normalized to body weight. Only small differences in ROM regarding age were found. ROM increased over 1 year in most measurements with the largest change in hip external rotation, which increased by 6-7 degrees (Cohens d = 0.83-0.87). Hip (d = 0.28-1.07) and knee (d = 0.38-0.53) muscle strength and the square hop test (d = 0.71-0.99) improved over 1 year.Conclusions: Normative values for ROM and strength assessments of neck, back, trunk, hips, knees, calves and ankles are presented for adolescent female football players. Generally, fluctuations in ROM were small with little clinical meaning, whereas strength improved over 1 year.(c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funding Agencies|Swedish Research Council for Sport Science [P2019-0045, P2020-0100, P2022-0074]; Swedish Naprapathic Association; Norwegian Naprapathic Association; Sophiahemmet foundation; Active life foundation

Football is a popular sport among adolescent females. Given the rate of injuries in female footballers, identifying factors that can predict injuries are important. These injuries are often caused by complex reasons. The aim of this study was to investigate if the combination of demographic (age, number of training and match play hours/week), psychosocial (perceived stress, adaptive coping strategies) and physiological factors (functional performance) can predict a traumatic injury in adolescent female footballers. A cohort consisting of 419 female football players aged 13–16 years was established. Baseline questionnaires covered potential risk factors for sport injuries, and measurements included football-related functional performance tests. Data were collected prospectively with a weekly online questionnaire for 52 weeks covering, e.g., injuries, training, and match play hours/week. A total of 62% of the players reported at least one traumatic injury during the 52 weeks. The coping strategy “positive reframing” had the strongest association with the risk of traumatic injuries. The combination of more frequent use of the coping strategy, positive reframing, and high levels of physical performance capacity may prevent a traumatic injury in adolescent female footballers. Coaches are encouraged to adopt both physiological and psychological factors when preventing injuries in young female footballers.

We discuss the impact of quadratic quantum fluctuations on the Wilson loop extracted from classical string theory. We show that a large class of models, which includes the near horizon limit of D_p branes with 16 supersymmetries, admits a L\"{u}scher type correction to the classical potential. We confirm that the quantum determinant associated with a BPS configuration of a single quark in the AdS_5 \times S^5 model is free from divergences. We find that for the Wilson loop in that model, unlike the situation in flat space-time, the fermionic determinant does not cancel the bosonic one. For string models that correspond to gauge theories in the confining phase, we show that the correction to the potential is of a L\"{u}scher type and is attractive., Comment: 1+33 pages, 3 figures, a minor correction, references added

We analyze the scalar field sector of the Kazakov--Migdal model of induced QCD. We present a detailed description of the simplest one dimensional {($d$$=$$1$)} model which supports the hypothesis of wide applicability of the mean--field approximation for the scalar fields and the existence of critical behaviour in the model when the scalar action is Gaussian. Despite the ocurrence of various non--trivial types of critical behaviour in the $d=1$ model as $N\rightarrow\infty$, only the conventional large-$N$ limit is relevant for its {\it continuum} limit. We also give a mean--field analysis of the $N=2$ model in {\it any} $d$ and show that a saddle point always exists in the region $m^2>m_{\rm crit}^2(=d)$. In $d=1$ it exhibits critical behaviour as $m^2\rightarrow m_{\rm crit}^2$. However when $d$$>$$1$ there is no critical behaviour unless non--Gaussian terms are added to the scalar field action. We argue that similar behaviour should occur for any finite $N$ thus providing a simple explanation of a recent result of D. Gross. We show that critical behaviour at $d$$>$$1$ and $m^2>m^2_{\rm crit}$ can be obtained by adding a $logarithmic$ term to the scalar potential. This is equivalent to a local modification of the integration measure in the original Kazakov--Migdal model. Experience from previous studies of the Generalized Kontsevich Model implies that, unlike the inclusion of higher powers in the potential, this minor modification should not substantially alter the behaviour of the Gaussian model., 31 pages

We examine some properties of the filled Wilson loop observables in the Kazakov-Migdal model of induced QCD. We show that they have a natural interpretation in a modification of the original model in which the $Z_N$ gauge symmetry is broken explicitly by a Wilson kinetic term for the gauge fields. We argue that there are two large N limits of this theory, one leads to ordinary Wilson lattice gauge theory coupled to a dynamical scalar field and the other leads to a version of the Kazakov-Migdal model in which the large N solution found by Migdal can still be used. We discuss the properties of the string theory which emerges., 13 pages, PUPT 1358, UBCTP92-032

We show that a lattice model for induced lattice QCD which was recently proposed by Kazakov and Migdal has a Z[sub [ital N]] gauge symmetry which, in the strong coupling phase, results in a local confinement where only color singlets are allowed to propagate along links and all Wilson loops for nonsinglets average to zero. We argue that if this model is to give QCD in its continuum limit, it must have a phase transition. We give arguments to support the presence of such a phase transition.

At high temperatures, some SU (N) gauge theories with fermions have metastable states related to the ZN symmetry of the theory. It has recently been argued that the possible existence of domains of these metastable states may lead to some interesting cosmological consequences. We show that these states, generically, have unaacceptable thermodynamic behavior. Their free energy F∝T4 with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the euclidean theory, they cannot be interpreted as physical domains in Minkowski space. This conclusion remains valid even if sufficient color singlet particles (such as leptons and weak gauge bosons) are added to the system to make the total free energy negative.

Particles in two spatial dimensions with fractional statistics known, generically, as anyons, have been of interest to particle physicists for nearly ten years. A major change in the direction of research occurred when it was discovered that anyons could play a role as quasiparticles in condensed-matter systems. This was originally discovered to be the case in systems exhibiting the Fractional Quantum Hall Effect. The application of anyons to condensed-matter systems received yet another boost when it was discovered by Laughlin that even an ideal gas of anyons was a superfluid and, as a result, a gas of charged anyons would be a superconductor. This led immediately to attempts to explain the superconductivity of high-T{sub c} materials which are layered ceramics in terms of anyons. The main challenge was to find a reasonable model for these materials which has quasiparticles obeying anyonic statistics. The goal of this article is to review the theory of anyonic superconductivity and its possible relation to high-T{sub c} materials. The emphasis in this review is on field-theoretical methods. In this paper the authors explain what an anyon is and how it can be modeled mathematically. The authors discuss the possible relationship between anyons and high-T{sub c}more » materials. The authors review several of the attempts to obtain anyonic quasiparticles from the Hubbard model which is commonly used to describe these materials. The authors describe the mathematical modeling of anyons in terms of their interaction with an Abelian gauge field with a Chern-Simons term. This description of anyons is used extensively in this article. The authors discuss the possible criteria for superconductivity in anyonic systems with particular emphasis on criteria which would be useful in the Chern-Simons description.« less

We derive several results pertaining to anyonic superconductivity as described by a Chern-Simons field theory. (1) The renormalized Chern-Simons term at finite density is shown to vanish when the renormalized coefficient at zero density takes values Ne2/2π. This is the field-theoretical requirement to have a massless pole in the current-current correlator. We can then show that in the Chern-Simons description a system of charged anyons at zero temperature is a superconductor. This result is shown to hold to all orders in perturbation theory by generalizing a nonrenormalization theorem of the zero density case. (2) At finite temperature the renormalized Chern-Simons term does not vanish at the one-loop perturbative level. We compute the mass of this apparent “pseudo-Goldstone mode”. We also exhibit an effect suggestive of critical behavior, for this same system, at a nonzero Tc. We discuss the possible implications of these perturbative results. (3) A low energy effective action for an anyonic superconductor is derived directly from Chern-Simons field theory. Several P and T violating effects occur.

Motivated by the effect of matter on neutrino oscillations (the MSW effect) we study in more detail the propagation of neutrinos in a dense medium. The dispersion relation for massive neutrinos in a medium is known to have a minimum at nonzero momentum p \sim (G_F\rho)/\sqrt{2}. We study in detail the origin and consequences of this dispersion relation for both Dirac and Majorana neutrinos both in a toy model with only neutral currents and a single neutrino flavour and in a realistic "Standard Model" with two neutrino flavours. We find that for a range of neutrino momenta near the minimum of the dispersion relation, Dirac neutrinos are trapped by their coherent interactions with the medium. This effect does not lead to the trapping of Majorana neutrinos., Comment: 28 pages, 6 figures, Latex; minor changes, one reference added; version to appear in Phys. Rev. D

We attempt the numerical construction of an effective action in three dimensions for Ising spins which represent the Wilson lines in the four-dimensional SU(3) gauge theory at finite temperature. For each configuration of the gauge theory, each spin is determined by averaging the Wilson lines over a small neighborhood and then projecting the average to +/-1 according to whether the neighborhood is ordered or disordered. The effective Ising action, determined via the lattice Schwinger-Dyson equations, contains even (two-spin) and odd (one- and three-spin) terms with short range. We find that the truncation to Ising degrees of freedom produces an effective action which is discontinuous across the gauge theory's phase transition. This discontinuity may disappear if the effective action is made more elaborate., Comment: 12 pages, revtex, including 2 Postscript figures; conclusions have changed slightly to conform to the theorem of Van Enter, Fernandez, and Sokal on the continuity of RG maps

The nature of Mean Field Solutions to the Equations of Motion of the Chern--Simons Landau--Ginsberg (CSLG) description of the Fractional Quantum Hall Effect (FQHE) is studied. Beginning with the conventional description of this model at some chemical potential $\mu_0$ and magnetic field $B$ corresponding to a ``special'' filling fraction $\nu=2\pi\rho/eB=1/n$ ($n=1,3,5\cdot \cdot\cdot$) we show that a deviation of $\mu$ in a finite range around $\mu_0$ does not change the Mean Field solution and thus the mean density of particles in the model. This result holds not only for the lowest energy Mean Field solution but for the vortex excitations as well. The vortex configurations do not depend on $\mu$ in a finite range about $\mu_0$ in this model. However when $\mu-\mu_0 < \mu_{cr}^-$ (or $\mu-\mu_0>\mu_{cr}^+$) the lowest energy Mean Field solution describes a condensate of vortices (or antivortices). We give numerical examples of vortex and antivortex configurations and discuss the range of $\mu$ and $\nu$ over which the system of vortices is dilute., Comment: Revtex document; 12 pages and 4 postscript figures in a file

We study the effect of coherent and incoherent broadening on neutrino oscillations both in vacuum and in the presence of matter (the MSW effect). We show under very general assumptions that it is not possible to distinguish experimentally neutrinos produced in some region of space as wave packets from those produced in the same region of space as plane waves with the same energy distribution., Comment: 19 page Latex file including one postscript figure. File is in "uufiles" format

Mean Field Theory has been extensively used in the study of systems of anyons in two spatial dimensions. In this paper we study the physical grounds for the validity of this approximation by considering the Quantum Mechanical scattering of a charged particle from a two dimensional array of magnetic flux tubes. The flux tubes are arranged on a regular lattice which is infinitely long in the ``$y$'' direction but which has a (small) finite number of columns in the ``$x$'' direction. Their physical size is assumed to be infinitesimally small. We develop a method for computing the scattering angle as well as the reflection and transmission coefficients to lowest order in the Aharonov--Bohm interaction. The results of our calculation are compared to the scattering of the same particle from a region of constant magnetic field whose magnitude is equal to the mean field of all the flux tubes. For an incident plane wave, the Mean Field approximation is shown to be valid provided the flux in each tube is much less than a single flux quantum. This is precisely the regime in which Mean Field Theory for anyons is expected to be valid. When the flux per tube becomes of order 1, Mean Field Theory is no longer valid., Comment: 23 pages, University of British Columbia Preprint UBCTP93-010

We examine the properties of observables in the Kazakov-Migdal model. We present explicit formulae for the leading asymptotics of adjoint Wilson loops as well as some other observables for the model with a Gaussian potential. We discuss the phase transiton in the large $N$ limit of the $d=1$ model. One of appendices is devoted to discussion of the $N =\infty$ Itzykson-Zuber integrals for arbitrary eigenvalue densities., Comment: plain LATEX, 22pp, preprint UBC-27/93, ITEP-M5/93

We present a Monte Carlo study in which we used weighted quantum numbers of hadron jets in an attempt to identify the parent parton of these jets. Two-jet events produced by {ital e}{sup +}{ital e{minus}} annihilation were studied using the Lund Monte Carlo program. It was found that the sign of the charge of the leading parton could be determined in a majority of events and that the quark jet could be distinguished from the antiquark jet in a majority of events containing baryons. A careful selection of a subset of the events by making cuts on the value of these weighted quantum numbers increased significantly the accuracy with which both the charge and the baryon number of the leading parton could be determined. Some success was also made in differentiating light-quark from heavy-quark events and in determining the leading quark flavor in the light-quark events. Unfortunately quantum number retention does not differentiate gluon jets from quark jets. The consequences of this for three-jet events and for jet identification in other reactions is discussed.

We study the Quantum Field Theory of nonrelativistic bosons coupled to a Chern--Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as {\bf bosons} with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern--Simons coefficient $N=2\pi\theta/g^2$ is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed., Comment: 10 Pages

Using the path-integral formulation of quantum field theory, we generalize the result that an accelerated observer sees a thermal spectrum to a large class of interacting field theories.

The existence and uniqueness of a Yang-Mills potential for a given field strength is discussed. Previous results are reviewed. In two space-time dimensions every nonzero field strength can be derived from any element of a very large class of potentials which are not related by a gauge transformation. We exhibit these potentials explicitly. In four dimensions we show that both a constant electric field and a Coulomb field can be described by a variety of nongauge-related potentials which describe very different physical situations.

A 15-month-old black male infant of drug-abusing parents presented with failure to thrive, lymphadenopathy, hepatosplenomegaly, and interstitial pneumonia. At 4 years, oral candidiasis, purulent ot...

SU(n) gauge theories at finite temperature are examined in terms of the spontaneous breaking of a Z(n) symmetry. It is suggested that the phase transition at finite temperature results from the formation of "bubbles" of an alternate Z(n) vacuum. These Z(n) bubbles are analyzed for lattice gauge theories in the dilute gas approximation and the results are compared with the Monte-Carlo calculations of McLerran and Svetitsky.

Quantum-number retention in the fragmentation region of a jet is investigated as a means to identify and classify quark and multiquark systems in lepton- and hadron-induced reactions. We show that a simple "inside-outside" cascade model with a causal space-time structure predicts that the mean charge of hadrons in the jet fragmentation region equals the charge of the parent quark system modulo a universal constant ${\ensuremath{\eta}}_{Q}$ (the mean quark charge of the sea) confirming previous analyses. Specific tests are discussed, including deep-inelastic neutrino scattering, ${e}^{+}{e}^{\ensuremath{-}}$ annihilation with a strongly leading hadron, and massive-lepton-pair production. We emphasize that the Drell-Yan process could play a crucial role in testing these ideas for multiquark jets and identifying a possible "hole" fragmentation region. We also discuss the utility of using a charge-momentum vector as a discriminant of jet structure. Finally we emphasize the utility of charge-retention tests in large-${p}_{T}$ hadronic reactions in order to discriminate between various contributing subprocesses.

It is shown that if our universe is described by the cosmological, classical, Einstein equations based on a manifold M 4 × G where G is the product of any number of Ricci flat manifolds (as is expected to occur in superstring theories) then our universe must, today, be radiation dominated. A matter-dominated universe (or an inflationary universe) would lead to large variations in the size of the extra dimensions. This would lead to changes in coupling constants of sufficiently large magnitude to be rules out by observation. If a model based on M 4 x G with G Ricci flat is to viable, there are only two possibilities. Either the universe is radiation dominated today (for which no satisfactory model exists) or the compactification is controlled dominantly by some (thus far) unquantifiable “quantum gravity” effects.

The phase structure of gauge theories with fermions as a function of imaginary chemical potential is related to the confining properties of the theory. It is controlled by a remnant of the ZN which is present in the absence of fermions. At high temperature the theory has a first-order phase transition as a function of imaginary chemical potential . This transition is expected to be absent in the low-temperature phase. Monte Carlo simulations are proposed which would check these ideas. It is shown that properties of the theory at nonzero fermion density can be deduced from its behavior at finite imaginary chemical potential.

Both a constant (non-Abelian) electric field and a constant magnetic field are solutions to the sourceless Yang-Mills field equations in Minkowski space. We discuss the stability of these solutions under small fluctuations in the potentials. We conclude that a magnetic field B, which is constant over a region of size L, has instabilities which grow exponentially in time provided gBL/sup 2/ > or approx. = 1. A constant electric field is unstable. A fluctuation in such a field will accelerate continuously in the direction of the field.

$\mathrm{SU}(n)$ gauge theories at finite temperature $T={\ensuremath{\beta}}^{\ensuremath{-}1}$ are analyzed in terms of the spontaneous breakdown of a $Z(n)$ symmetry corresponding to the order parameter $L(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}})=(\frac{1}{n})\mathrm{Tr}P\mathrm{exp}[ig\ensuremath{\int}{0}^{\ensuremath{\beta}}{A}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},t)dt]$. An "effective potential" for $L$ is evaluated in the one-loop approximation for both the continuum and the lattice gauge theories. It is shown that the $Z(n)$ symmetry is broken, so that the continuum theory does not confine for high temperatures. Similarly the lattice theory does not confine for sufficiently weak coupling if the number of time sites ${N}_{t}$ is finite. It is argued that as ${N}_{t}\ensuremath{\rightarrow}\ensuremath{\infty}$ the $Z(n)$ symmetry is restored and the theory will confine for all values of the coupling.

A relativistic quantum field theory at finite temperature T = β−1 is equivalent to the same field theory at zero temperature but with one spatial dimension of finite length β. This equivalence is discussed for scalars, for fermions, and for gauge theories. The relationship is checked for free field theory. The translation of correlation functions between the two formulations is described with special emphasis on the nonlocal order parameters of gauge theories. Possible applications are mentioned.

The effective potential $V(\ensuremath{\varphi})$ of a scalar field theory coupled to fermions is undefined near $\ensuremath{\varphi}=0$ if the scalar field has a spontaneously broken symmetry. This shows up in a loop expansion as an imaginary part in $V(\ensuremath{\varphi})$ which persists to all temperatures and densities, even when the symmetry is restored. This paper presents a modification of the loop expansion which yields a real $V(\ensuremath{\varphi})$ whenever the one-loop fermion corrections restore the symmetry.

Using a new perturbative technique for evaluating real-time finite-temperature Green's functions in an expanding universe, we derive the evolution equation for the Higgs field during an inflationary phase. We also indicate how to evaluate the fluctuations of the field in this approach.

The phases of $\mathrm{SU}(N)$ gauge theories at finite temperature can be analyzed in terms of the Wilson line $L(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}})=\mathrm{Tr}P\mathrm{exp}[ig \ensuremath{\int}{0}^{\ensuremath{\beta}}{A}_{0}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{x}},\ensuremath{\tau})d\ensuremath{\tau}]$. The question of confinement is related to the spontaneous breakdown of a $Z(N)$ symmetry: $〈L〉\ensuremath{\ne}0$ corresponds to symmetry breaking and deconfinement, $〈L〉=0$ implies symmetry restoration and confinement. A previous calculation of the one-loop effective potential for $L$ is discussed in $\mathrm{SU}(N)$ theories, both with and without fermions. A possible mechanism for the confining-deconfining transition in terms of the formation of "$Z(N)$ bubbles" is discussed. For SU(2) theories, the $Z(2)$ bubbles are simply finite-temperature instantons. However, $Z(N)$ bubbles are not finite-temperature instantons for $\mathrm{SU}(N)$. It is shown that a bag picture of hadronic structure similar to that of Callan, Dashen, and Gross may emerge from this picture.

We show that the two possible formulations for a divergence- and curl-free vector field, namely, in terms of a scalar or a two-form potential, are equivalent, both as free quantum field theories even in the presence of a background gravitational field and in their coupling to the gravitational field. An apparent disparity in the extrema of the actions in the Euclidean formulations of these theories is resolved by showing that if boundary conditions that are common to the two formulations (which are the only boundary conditions for which the two theories can be compared) are imposed the only extrema of either action has a zero value for the vector field and thus for the stress-energy tensor.

The experimental observation of events in neutrino scattering with three outgoing muons presents a potential challenge to SU/sub 2/ x U/sub 1/ gauge models, depending on the source of such events. In this paper a comprehensive study is reported of four possible modes of trimuon production (hadronic, mixed, leptonic, and trident modes). Background sources are expected to be significant and will have to be separated from other sources. Attention is also given to two trimuon events with extraordinarily energetic muons.

We study in detail the classical Yang-Mills field equations in the presence of static external sources. Their formulation as an initial-value problem in the ${A}_{0}=0$ gauge provides us with a powerful tool for determining the existence of new solutions. In the case of point sources, the only static solutions known so far are the various Coulomb solutions which we classify according to their total energy and isospin. In the case of a localized but extended source, there are, besides the well-known Coulomb solution, two new types of solutions: the "magnetic dipole" solution which has the long-range behavior of a magnetic dipole field and which has lower energy than the Coulomb solution when the total external charge is large enough, and the "total screening" solution which has no long-range field strengths at all and which can have an arbitrarily low energy. We present a detailed study of these new solutions.

When a photon is incident on a 1 + 1 dimensional system described by the Sine–Gordon theory, transitions can occur from the ground state to soliton–antisoliton bound states called breather modes. We derive the lowest order Wentzel–Kramers–Brillouin (WKB) wave funetionals for these states and use them to estimate the transition rates. The transition to the lowest energy breather mode always dominates. The transition rates to the higher energy modes are suppressed by at least 10−2. A Monte Carlo simulation of the theory confirms this suppression. This effect is thus too small to account for the conductivity observed in the quasi-one-dimensional organic conductor tetrathiafulvene-tetraeyanoquinodimethane TTF-TCNQ.

The idea that the cosmological constant Λ may have a small, nonzero value (Λ ∼ (10 −33 eV) 2 ) has been recently revived in attempts to understand several cosmological issues. Despite the fact that such a small, nonzero Λ is aesthetically unappealing the issue of its existence will eventually be decided by experiments. In this paper the implications to particle physics of the existence of such a small, nonzero value of Λ are examined. Models are described in which the ground state of the system is assumed to have a cosmological constant equal to zero but in which we are not, presently in this ground state. The possibility that this deviation from the ground state leads to such a small, effective cosmological constant is studied.

We present two new solutions to the classical Yang-Mills field equations in the presence of a localized external source. These solutions totally screen the charge of the source. They have lower energy than the corresponding Coulomb solution.

We derive Feynman rules for evaluating the real-time Green's functions of a scalar field theory in a Robertson-Walker universe under the circumstance that at some initial time ${t}_{0}$ the system was in thermal equilibrium with density matrix exp[-\ensuremath{\beta}H(${t}_{0}$)], where H(${t}_{0}$) is the Hamiltonian at time ${t}_{0}$.

A theory with a vanishing cosmological constant can have a nonzero effective cosmological constant of cosmological significance if the theory has a scalar field with a mass m of the order of the inverse age of the Universe (\ensuremath{\tau}\ensuremath{\sim}${10}^{33}$ ${\mathrm{eV}}^{\mathrm{\ensuremath{-}}1}$) provided the field has a nonzero but evolving expectation value. We discuss the cosmological consequences of scalar fields with masses m\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}28}$ eV. The effect on the age of the Universe and on the growth of density perturbations is discussed in detail. For small masses (m\ensuremath{\lesssim}${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}33}$ eV) the Universe behaves precisely as if a cosmological constant were present. For masses several orders of magnitude greater than ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$ for which \ensuremath{\varphi} has made several oscillations only density perturbations on scales greater than ${m}^{\mathrm{\ensuremath{-}}1}$ grow significantly.