We point out that the lower bound on the primordial magnetic field required to seed the galactic dynamo is significantly relaxed in an open universe or in a universe with a positive cosmological constant. It is shown that, for reasonable cosmological parameters, primordial seed fields of strength 10 −30 Gauss or less at the time of galaxy formation could explain observed galactic magnetic fields. As a consequence, mechanisms of primordial magnetic seed-field generation that have previously been ruled out could well be viable. We also comment on the implications of the observation of micro-Gauss magnetic fields in galaxies at high redshift.PACS numbers: 98.35.Eq, 98.62.En, 98.80.Es Magnetic fields pervade most astrophysical systems [1], but their origin is unknown. Spiral galaxies are observed to possess large-scale magnetic fields with strength of the order of 10 −6 G and direction aligned with the rotational motion. A plausible explanation is that galactic magnetic fields result from the exponential amplification of an initially weak seed field by a mean-field dynamo [2,3]. Many proposals have been put forward regarding the origin of such a seed field. One suggestion is that it might arise spontaneously from non-parallel gradients of pressure and charge-density during galaxy formation [4]. A wider range of possibilities is offered if the seed field is of primordial origin. This category includes cosmological magnetic fields [5] as well as magnetic fields created by any of a number of early-universe particle-physics mechanisms [6] such as collisions of bubbles in a first-order phase transition [7] or false-vacuum inflation [8,9].The seed-field strength required at the time of completed galaxy formation (t gf ) for a galactic dynamo to produce the present magnetic field strength B 0 ∼ 10 −6 G is usually quoted in the range ∼ 10 −23 -10 −19 G. Such lower bounds are obtained by considering the dynamo amplification in a flat universe with zero cosmological constant for "typical" values of the parameters of the αω-dynamo. The seed field must also be coherent on a scale at least as large as the size of the largest turbulent eddy, ∼ 100 pc [2]. Most proposed models of primordial seed-field generation fail to meet these requirements as formulated above.In this paper we address the issue in the light of recent developments in cosmology. Observations of distant type-IA supernovae [10] and of anisotropies in the cosmic microwave background (CMB) [11] in combination have made it increasingly likely that the universe is less dense than the critical density and has a positive cosmological constant Λ. Most previous studies of magnetic fields have assumed a Λ = 0 universe with critical matter density. We shall recalculate the constraints on primordial seed fields for general Friedmann universes with matter density parameter Ω 0 and vacuum energy density parameter λ 0 ≡ Λ/(3H 2 0 ) such that Ω 0 + λ 0 ≤ 1 (the subscript 0 here indicates quantities at present time and H 0 is the Hubble parameter). In addition to finding revis...

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A B S T R A C TThe locations of the peaks of the cosmic microwave background (CMB) spectrum are sensitive indicators of cosmological parameters, yet there is no known analytic formula which accurately describes their dependence on them. We parametrize the location of the peaks as l m ¼ l A ðm 2 w m Þ, where l A is the analytically calculable acoustic scale and m labels the peak number. Fitting formulae for the phase shifts w m for the first three peaks and the first trough are given. It is shown that in a wide range of parameter space, the acoustic scale l A can be retrieved from actual CMB measurements of the first three peaks within 1 per cent accuracy. This can be used to speed up likelihood analysis. We describe how the peak shifts can be used to distinguish between different models of dark energy. 1 The peaks are labelled by integer values of m and the troughs by halfinteger values.Mon. Not. R. Astron. Soc. 330, 965-970 (2002) q 2002 RAS

In cosmological first-order phase transitions, the progress of true-vacuum bubbles is expected to be significantly retarded by the interaction between the bubble wall and the hot plasma. We examine the evolution and collision of slow-moving true-vacuum bubbles. Our lattice simulations indicate that phase oscillations, predicted and observed in systems with a local symmetry and with a global symmetry where the bubbles move at speeds less than the speed of light, do not occur inside collisions of slow-moving local-symmetry bubbles. We observe almost instantaneous phase equilibration which would lead to a decrease in the expected initial defect density, or possibly prevent defects from forming at all. We illustrate our findings with an example of defect formation suppressed in slow-moving bubbles. Slow-moving bubble walls also prevent the formation of ''extra defects,'' and in the presence of plasma conductivity may lead to an increase in the magnitude of any primordial magnetic field formed.

The CMB data recently released by BOOMERANG and MAXIMA suggest that the anisotropy spectrum has a third peak in the range 800 < l3 < 900. A combination of this result with constraints from large-scale structure permit us to differentiate between different quintessence models. In particular, we find that inverse power law models with power α > 1 are disfavoured. Models with more than 5% quintessence before last scattering require a spectral index greater than 1. These constraints are compared with supernovae observations. We also show that the CMB alone now provides strong evidence for an accelerating universe.PACS numbers: 98.80.Es, 98.80.Cq, 95.35.+d