Holographic multiverse and the measure problem

We discuss the duality, conjectured in earlier work, between the wave function of the multiverse and a 3D Euclidean theory on the future boundary of spacetime. In particular, we discuss the choice of the boundary metric and the relation between the UV cutoff scale xi on the boundary and the hypersurfaces Sigma on which the wave function is defined in the bulk. We propose that in the limit of xi going to 0 these hypersurfaces should be used as cutoff surfaces in the multiverse measure. Furthermore, we argue that in the inflating regions of spacetime with a slowly varying Hubble rate H the hypersurfaces Sigma are surfaces of constant comoving apparent horizon (CAH). Finally, we introduce a measure prescription (called CAH+) which appears to have no pathological features and coincides with the constant CAH cutoff in regions of slowly varying H.Comment: A minor change: the discussion of unitarity on p.9 is clarifie

Coincident brane nucleation and the neutralization of \Lambda

Nucleation of branes by a four-form field has recently been considered in string motivated scenarios for the neutralization of the cosmological constant. An interesting question in this context is whether the nucleation of stacks of coincident branes is possible, and if so, at what rate does it proceed. Feng et al. have suggested that, at high ambient de Sitter temperature, the rate may be strongly enhanced, due to large degeneracy factors associated with the number of light species living on the worldsheet. This might facilitate the quick relaxation from a large effective cosmological constant down to the observed value. Here, we analyse this possibility in some detail. In four dimensions, and after the moduli are stabilized, branes interact via repulsive long range forces. Because of that, the Coleman-de Luccia (CdL) instanton for coincident brane nucleation may not exist, unless there is some short range interaction which keeps the branes together. If the CdL instanton exists, we find that the degeneracy factor depends only mildly on the ambient de Sitter temperature, and does not switch off even in the case of tunneling from flat space. This would result in catastrophic decay of the present vacuum. If, on the contrary, the CdL instanton does not exist, coindident brane nucleation may still proceed through a "static" instanton, representing pair creation of critical bubbles -- a process somewhat analogous to thermal activation in flat space. In that case, the branes may stick together due to thermal symmetry restoration, and the pair creation rate depends exponentially on the ambient de Sitter temperature, switching off sharply as the temperature approaches zero. Such static instanton may be well suited for the "saltatory" relaxation scenario proposed by Feng et al.Comment: 38 pages, 6 figures. Replaced with typos correcte

Second Order Perturbations of a Macroscopic String; Covariant Approach

Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the energy. We also quantize the perturbations and derive the mass-formula up to second order in perturbations for an observer using world-sheet time $\tau$. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be non-diagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass-spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.Comment: New discussion about the quantum mass-spectrum in chapter

Dynamical renormalization group methods in theory of eternal inflation

Dynamics of eternal inflation on the landscape admits description in terms of the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one correspondence with vacuum dynamics equations. On those sectors of the landscape, where transport properties of the probability measure for eternal inflation are important, renormalization group fixed points of the MSR effective action determine late time behavior of the probability measure. I argue that these RG fixed points may be relevant for the solution of the gauge invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos

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.Comment: 27 pages, tutp-92-

Solutions to the cosmological constant problems

We critically review several recent approaches to solving the two cosmological constant problems. The "old" problem is the discrepancy between the observed value of $\Lambda$ and the large values suggested by particle physics models. The second problem is the "time coincidence" between the epoch of galaxy formation $t_G$ and the epoch of $\Lambda$-domination t_\L. It is conceivable that the "old" problem can be resolved by fundamental physics alone, but we argue that in order to explain the "time coincidence" we must account for anthropic selection effects. Our main focus here is on the discrete-$\Lambda$ models in which $\Lambda$ can change through nucleation of branes. We consider the cosmology of this type of models in the context of inflation and discuss the observational constraints on the model parameters. The issue of multiple brane nucleation raised by Feng {\it et. al.} is discussed in some detail. We also review continuous-\L models in which the role of the cosmological constant is played by a slowly varying potential of a scalar field. We find that both continuous and discrete models can in principle solve both cosmological constant problems, although the required values of the parameters do not appear very natural. M-theory-motivated brane models, in which the brane tension is determined by the brane coupling to the four-form field, do not seem to be viable, except perhaps in a very tight corner of the parameter space. Finally, we point out that the time coincidence can also be explained in models where $\Lambda$ is fixed, but the primordial density contrast $Q=\delta\rho/\rho$ is treated as a random variable.Comment: 30 pages, 3 figures, two notes adde

Bubble fluctuations in Ω<1\Omega<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 $(1-\Omega)<<1$, where $\Omega$ is the density parameter, the microwave temperature anisotropies produced by these modes are of order $\delta T/T\sim H(R_0\mu l)^{-1/2} (1-\Omega)^{l/2}$. Here, $H$ is the expansion rate during inflation, $R_0$ is the intrinsic radius of the bubble at the time of nucleation, $\mu$ 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, $G\mu R_0<<1$, and the new effect can be much larger than the one due to ordinary gravitational waves generated during inflation (unless, of course, $\Omega$ gets too close to one, in which case the new effect disappears).Comment: 17 pages, 3 figs, LaTeX, epsfig.sty, available at ftp://ftp.ifae.es/preprint/ft/uabft387.p

Testing the Cosmological Constant as a Candidate for Dark Energy

It may be difficult to single out the best model of dark energy on the basis of the existing and planned cosmological observations, because many different models can lead to similar observational consequences. However, each particular model can be studied and either found consistent with observations or ruled out. In this paper, we concentrate on the possibility to test and rule out the simplest and by far the most popular of the models of dark energy, the theory described by general relativity with positive vacuum energy (the cosmological constant). We evaluate the conditions under which this model could be ruled out by the future observations made by the Supernova/Acceleration Probe SNAP (both for supernovae and weak lensing) and by the Planck Surveyor cosmic microwave background satellite.Comment: 6 pages, 2 figures, revtex

On the initial value problem for second order scalar fluctuations in Einstein static

We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe must be present if the second order constraint equations are to be integrable. I.e., the 'linearization stability' constraint forces the presence of these homogeneous modes. Since these linear homogeneous scalar modes are well known to be exponentially unstable, the tactic of neglecting these modes to create a long-lived, almost Einstein universe does not work, even if all higher order (L $>$ 1) modes are dynamically stable.Comment: 8 pages, no figures, changes made to the presentation throughout to emphasize the linear nature of the analysis and the treatment of the irrotational perfect fluid. Conclusions unchanged. Submitted to PR