arXiv subjects

Jaume Garriga

Publications and source records attributed to Jaume Garriga.

69 records · Page 4Linked to original sources

arXiv1999

Spectrum of Cosmological Perturbations in the One-Bubble Open Universe

The spectrum of cosmological perturbations in the context of the one-bubble open inflation model is discussed, taking into account fluctuations of the metric. We find that, quite generically,thin wall single field models have no supercurvature modes. However, single field models with supercurvature modes do exist. In these models the density parameter $Ω$ becomes a random variable taking a range of values inside of each bubble. We also show that the model dependence of the continuous spectrum for both scalar and tensor-type perturbations is small as long as the kinetic energy density of the background field does not dominate the total energy density. We conclude that the spectrum of the density perturbation predicted in the single-field model of the one-bubble open inflation is rather robust. We also consider the spectrum of scalar and tensor perturbations in a model of the Hawking-Turok type, without a false vacuum.

astro-ph↗

arXiv1998

Microwave background anisotropies in quasiopen inflation

Quasiopenness seems to be generic to multi-field models of single-bubble open inflation. Instead of producing infinite open universes, these models actually produce an ensemble of very large but finite inflating islands. In this paper we study the possible constraints from CMB anisotropies on existing models of open inflation. The effect of supercurvature anisotropies combined with the quasiopenness of the inflating regions make some models incompatible with observations, and severely reduces the parameter space of others. Supernatural open inflation and the uncoupled two-field model seem to be ruled out due to these constraints for values of $Ω_0\lesssim0.98$. Others, such as the open hybrid inflation model with suitable parameters for the slow roll potential can be made compatible with observations.

hep-ph↗

arXiv1998

Smooth ``creation'' of an open universe in five dimensions

We present a non-singular instanton describing the creation of an open universe with a compactified extra dimension. The four dimensional section of this solution is a singular instanton of the type introduced by Hawking and Turok. The ``singularity'' is viewed in five dimensions as a smooth bubble of ``nothing'' which eats up a portion of spacetime as it expands. Flat space with a compact extra dimension is shown to be gravitationally metastable, but sufficiently long lived if the size of the extra dimension is large compared with the Planck length.

hep-th↗

arXiv1998

Open inflation and the singular boundary

The singularity in Hawking and Turok's model (hep-th/9802030) of open inflation has some appealing properties. We suggest that this singularity should be regularized with matter. The singular instanton can then be obtained as the limit of a family of ``no-boundary'' solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking boundary term. Unrelated to this question, we also point out that gravitational backreaction improves the behaviour of scalar perturbations near the singularity. As a result, the problem of quantizing scalar perturbations and gravity waves seems to be very well posed.

hep-th↗

arXiv1997

Quasi-open inflation

We show that a large class of two-field models of single-bubble open inflation do not lead to infinite open universes, as it was previously thought, but to an ensemble of very large but finite inflating `islands'. The reason is that the quantum tunneling responsible for the nucleation of the bubble does not occur simultaneously along both field directions and equal-time hypersurfaces in the open universe are not synchronized with equal-density or fixed-field hypersurfaces. The most probable tunneling trajectory corresponds to a zero value of the inflaton field; large values, necessary for the second period of inflation inside the bubble, only arise as localized fluctuations. The interior of each nucleated bubble will contain an infinite number of such inflating regions of comoving size of order $γ^{-1}$, where $γ$ depends on the parameters of the model. Each one of these islands will be a quasi-open universe. Since the volume of the hyperboloid is infinite, inflating islands with all possible values of the field at their center will be realized inside of a single bubble. We may happen to live in one of those patches of comoving size $d\lesssim γ^{-1}$, where the universe appears to be open. In particular, we consider the ``supernatural'' model proposed by Linde and Mezhlumian. There, an approximate U(1) symmetry is broken by a tunneling field in a first order phase transition, and slow-roll inflation inside the nucleated bubble is driven by the pseudo-Goldstone field. We find that the excitations of the pseudo-Goldstone produced by the nucleation and subsequent expansion of the bubble place severe constraints on this model. We also discuss the coupled and uncoupled two-field models.

hep-ph↗

arXiv1997

Recycling universe

If the effective cosmological constant is non-zero, our observable universe may enter a stage of exponential expansion. In such case, regions of it may tunnel back to the false vacuum of an inflaton scalar field, and inflation with a high expansion rate may resume in those regions. An ``ideal'' eternal observer would then witness an infinite succession of cycles from false vacuum to true, and back. Within each cycle, the entire history of a hot universe would be replayed. If there were several minima of the inflaton potential, our ideal observer would visit each one of these minima with a frequency which depends on the shape of the potential. We generalize the formalism of stochastic inflation to analyze the global structure of the universe when this `recycling' process is taken into account.

astro-ph↗

arXiv1997

Canonical Quantization of Cosmological Perturbations in the One Bubble Open Universe

Faddeev and Jackiw's method for constrained systems is used to derive a gauge invariant formulation of cosmological perturbations in the one bubble inflationary universe. For scalar perturbations in a flat universe, reduction of the action to the one with a single physical degree of freedom has been derived in the literature. A straightforward generalization of it to the case of an open universe is possible but it is not adequate for quantizing perturbations in the one bubble universe, because of the lack of Cauchy surfaces inside the bubble. Therefore we perform the reduction of the action outside the lightcone emanating from the center of the bubble or nucleation event, where the natural time constant hypersurfaces are no longer homogeneous and isotropic and as a result the conventional classification of perturbations in terms of scalar and tensor modes is not possible. Nevertheless, after reduction of the action we find three decoupled actions for three independent degrees of freedom, one of which corresponds to the scalar mode and the other two to the tensor modes. Implications for the one bubble open inflationary models are briefly discussed. As an application of our formalism, the spectrum of long wavelength gravity waves is simply obtained in terms of the real part of the reflection amplitude for a one dimensional scattering problem, where the potential barrier is given in terms of the bubble profile.

astro-ph↗

arXiv1997

On classical anisotropies in models of Open Inflation

In the simplest model of open inflation there are two inflaton fields decoupled from each other. One of them, the tunneling field, produces a first stage of inflation which prepares the ground for the nucleation of a highly symmetric bubble. The other, a free field, drives a second period of slow roll inflation inside the bubble. However, the second field also evolves during the first stage of inflation, which to some extent breaks the needed symmetry. We show that this generates large supercurvature anisotropies which, together with the results of Tanaka and Sasaki, rule out this class of simple models (unless, of course, $Ω_0$ is sufficiently close to one.) The problem does not arise in modified models where the second field does not evolve in the first stage of inflation.

astro-ph↗

arXiv1995

STABILITY OF Z-STRINGS IN STRONG MAGNETIC FIELDS

We show that the Z-strings of the standard electroweak theory can be stabilized by strong external magnetic fields, provided that $β^{1/2} \equiv M_H/M_Z\leq 1$, where $M_H$ and $M_Z$ are the Higgs and Z masses. The magnetic fields needed are larger than $β^{1/2} B_c$ and smaller than $B_c$, where $B_c\equiv M^2_W/e$ is the critical magnetic field which causes W-condensation in the usual broken phase vacuum. If such magnetic fields were present after the electroweak transition, they would stabilize strings for a period comparable to the inverse Hubble rate at that time. Pair creation of monopoles and antimonopoles linked by segments of string is briefly considered.

hep-ph↗

arXiv1995

Bubble fluctuations in $Ω<1$ inflation

In the context of the open inflationary universe, we calculate the amplitude of quantum fluctuations which deform the bubble shape. These give rise to scalar field fluctuations in the open Friedman-Robertson-Walker universe which is contained inside the bubble. One can transform to a new gauge in which matter looks perfectly smooth, and then the perturbations behave as tensor modes (gravitational waves of very long wavelength). For $(1-Ω)<<1$, where $Ω$ is the density parameter, the microwave temperature anisotropies produced by these modes are of order $δT/T\sim H(R_0μl)^{-1/2} (1-Ω)^{l/2}$. Here, $H$ is the expansion rate during inflation, $R_0$ is the intrinsic radius of the bubble at the time of nucleation, $μ$ is the bubble wall tension and $l$ labels the different multipoles ($l>1$). The gravitational backreaction of the bubble has been ignored. In this approximation, $GμR_0<<1$, and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course, $Ω$ gets too close to one, in which case the new effect disappears).

gr-qc↗

arXiv1994

Zero Modes on Linked Strings

We study linked loops of string in the presence of bosonic condensates and fermionic zero modes on the strings. We find that the strings necessarily carry a current if the bosons have an Aharanov-Bohm interaction with the string. The fermionic case is analyzed in the context of the standard model where there are lepton and quark zero modes on $Z-$strings. Here we find that the fermionic ground state in the linked string background is lower than the ground state when the loops are unlinked but otherwise identical. As in the bosonic case, the $Z-$strings carry a non-vanishing electric current in the ground state. The baryon number of the linked configuration is found to agree with previous indirect results. We also evaluate the angular momentum, electromagnetic charge and baryonic three current on the linked $Z-$string configuration. Finally we point out a possible gravitational analogue of the linked string system.

hep-ph↗

arXiv1994

Lensing Properties of Lightlike Current Carrying Cosmic Strings

The lensing properties of superconducting cosmic strings endowed with a time dependent pulse of lightlike current are investigated. The metric outside the core of the string belongs to the $pp$--wave class, with a deficit angle. We study the field theoretic bosonic Witten model coupled to gravity, and we show that the full metric (both outside and inside the core) is a Taub-Kerr-Shild generalization of that for the static string with no current. It is shown that the double image due to the deficit angle evolves in an unambiguous way as a pulse of lightlike current passes between the source and the observer. Observational consequences of this signature of the existence of cosmic strings are briefly discussed.

gr-qc↗

arXiv1994

Instantons for Vacuum Decay at Finite Temperature in the Thin Wall Limit

In $N+1$ dimensions, false vacuum decay at zero temperature is dominated by the $O(N+1)$ symmetric instanton, a sphere of radius $R_0$, whereas at temperatures $T>>R_0^{-1}$, the decay is dominated by a `cylindrical' (static) $O(N)$ symmetric instanton. We study the transition between these two regimes in the thin wall approximation. Taking an $O(N)$ symmetric ansatz for the instantons, we show that for $N=2$ and $N=3$ new periodic solutions exist in a finite temperature range in the neighborhood of $T\sim R_0^{-1}$. However, these solutions have higher action than the spherical or the cylindrical one. This suggests that there is a sudden change (a first order transition) in the derivative of the nucleation rate at a certain temperature $T_*$, when the static instanton starts dominating. For $N=1$, on the other hand, the new solutions are dominant and they smoothly interpolate between the zero temperature instanton and the high temperature one, so the transition is of second order. The determinantal prefactors corresponding to the `cylindrical' instantons are discussed, and it is pointed out that the entropic contributions from massless excitations corresponding to deformations of the domain wall give rise to an exponential enhancement of the nucleation rate for $T>>R_0^{-1}$.

hep-th↗

arXiv1993

Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy momentum tensor, both in the O(4) invariant states introduced by Allen and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum energy density in the O(4) invariant case is larger than in the de Sitter invariant case.

gr-qc↗

arXiv1992

Black Holes from Nucleating Strings

We evaluate the probability that a loop of string that has spontaneously nucleated during inflation will form a black hole upon collapse, after the end of inflation. We then use the observational bounds on the density of primordial black holes to put constraints on the parameters of the model. Other constraints from the distortions of the microwave background and emission of gravitational radiation by the loops are considered. Also, observational constraints on domain wall nucleation and monopole pair production during inflation are briefly discussed.

hep-ph↗