Landscape Of Vacua Research Articles

The cosmological constant and the weak gravity conjecture

We examine the descent via membrane nucleation through a landscape of vacua where the cosmological constant is given by a combination of four-form fluxes. It has been shown that this descent can be slowed exponentially for very low curvature vacua close to Minkowski space in a wide class of models satisfying certain parametric conditions, providing a possible solution to the cosmological constant problem. We explore in detail whether or not those parametric conditions are compatible with the membrane weak gravity conjecture. Whilst it is true that there is often tension, we show that this is not always the case and present an explicit model where Minkowski space is absolutely stable and the weak gravity conjecture is satisfied. This corresponds to an extension of the Bousso-Polchinski model into a generalised DBI action for four-forms. We also clarify how the landscape should be populated in a consistent model.

Numerical study of a cosmological relaxation model of the Higgs boson mass

In light of no new physics being discovered at the LHC, ideas which tackle the hierarchy problem without novelties around the TeV scale must be taken seriously. Such is a cosmological relaxation model of the Higgs boson mass, proposed in the pre-LHC era, which does not rely on new physics below the Planck scale. This scenario introduces a different notion of naturalness according to which the vacuum with a small expectation value of the Higgs field corresponds to an infinitely enhanced entropy point of the vacuum landscape that becomes an attractor of cosmological inflationary evolution. In this framework we study numerically the evolution of the Higgs vacuum expectation value (VEV). We model the inflationary vacuum-to-vacuum transitions that are triggered by nucleation of branes charged under three-form fields as a random walk. In particular, we investigate the impact of the number of coupled three-forms on the convergence rate of the Higgs VEV. We discover an enhanced rate when increasing the number of brane charges. Moreover, we show that for late times the inclusion of more charges is equivalent to additional brane nucleations.

New inflation in the landscape and typicality of the observed cosmic perturbation

We investigate if the observed small and nearly scale-invariant primordial cosmic perturbation, i.e. the perturbation amplitude $P_\zeta\sim10^{-9}$ and the spectral index $n_s \simeq 0.965$, is typical in the landscape of vacua after imposing anthropic selections on them. We consider the situation where the universe begins from a metastable vacuum driving a precedent inflation, a curvature-dominated open universe is created by tunneling, and the curvature energy is inflated away by new inflation. We argue that the initial inflaton field value is homogeneous but typically non-zero because of the quantum fluctuation of long wavelength modes created during the precedent inflation, and only the universe which accidentally has a small inflaton field value is anthropically selected. We show that this bias, together with certain distributions of inflation model parameters that are physically well-motivated, makes the observed small and nearly scale-invariant spectrum typical.

Tensor modes on the string theory landscape

Abstract We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.

The CMB and the measure of the multiverse

In the context of eternal inflation, cosmological predictions depend on the choice of measure to regulate the diverging spacetime volume. The spectrum of inflationary perturbations is no exception, as we demonstrate by comparing the predictions of the fat geodesic and causal patch measures. To highlight the effect of the measure — as opposed to any effects related to a possible landscape of vacua — we take the cosmological model, including the model of inflation, to be fixed. We also condition on the average CMB temperature accompanying the measurement. Both measures predict a 1-point expectation value for the gauge-invariant Newtonian potential, which takes the form of a (scale-dependent) monopole, in addition to a related contribution to the 3-point correlation function, with the detailed form of these quantities differing between the measures. However, for both measures both effects are well within cosmic variance. Our results make clear the theoretical relevance of the measure, and at the same time validate the standard inflationary predictions in the context of eternal inflation.

Comments on gaugino mass and landscape of vacua

In direct gauge mediation, gaugino masses often vanish at the leading order of supersymmetry breaking. Recently, this phenomenon is understood in connection with the global structure of vacua in O'Raifeartaigh-type models. In this note, we further explore a connection between gaugino masses and the landscape of vacua in more general situations, focusing on a few examples which demonstrate our idea. In particular, we present a calculable model with non-vanishing leading order gaugino masses on the lowest energy vacuum.

Escaping the crunch: Gravitational effects in classical transitions

During eternal inflation, a landscape of vacua can be populated by the nucleation of bubbles. These bubbles inevitably collide, and collisions sometimes displace the field into a new minimum in a process known as a classical transition. In this paper, we examine some new features of classical transitions that arise when gravitational effects are included. Using the junction condition formalism, we study the conditions for energy conservation in detail, and solve explicitly for the types of allowed classical transition geometries. We show that the repulsive nature of domain walls, and the de Sitter expansion associated with a positive energy minimum, can allow for classical transitions to vacua of higher energy than that of the colliding bubbles. Transitions can be made out of negative or zero energy (terminal) vacua to a de Sitter phase, re-starting eternal inflation, and populating new vacua. However, the classical transition cannot produce vacua with energy higher than the original parent vacuum, which agrees with previous results on the construction of pockets of false vacuum. We briefly comment on the possible implications of these results for various measure proposals in eternal inflation.

Explicit R-symmetry breaking and metastable vacua

We consider O'Raifeartaigh-like models with explicit R-symmetry breaking and analyze the vacuum landscape. Taking such models as candidates for the hidden sector, we analyze the gauge mediation of the supersymmetry breaking, focusing on the effects produced by R-symmetry breaking. First, we construct families of non-R-symmetric models containing only singlet chiral superfields, and determine the conditions under which SUSY vacua, runaway directions and (longlived) metastable vacua exist. We then extend the results to the case in which some of the chiral fields are in the 5 ⊕ representation of SU(5). Gauging this symmetry, we compute soft masses for gauginos and sfermions, and analyze several issues such as doublet/triplet splitting, unification of coupling constants and CP violation phases.

Evidence for the multiverse in the standard model and beyond

In any theory it is unnatural if the observed values of parameters lie very close to special values that determine the existence of complex structures necessary for observers. A naturalness probability $P$ is introduced to numerically evaluate the degree of unnaturalness. If $P$ is very small in all known theories, corresponding to a high degree of fine-tuning, then there is an observer naturalness problem. In addition to the well-known case of the cosmological constant, we argue that nuclear stability and electroweak symmetry breaking represent significant observer naturalness problems. The naturalness probability associated with nuclear stability depends on the theory of flavor, but for all known theories is conservatively estimated as ${P}_{\mathrm{nuc}}\ensuremath{\lesssim}({10}^{\ensuremath{-}3}--{10}^{\ensuremath{-}2})$, and for simple theories of electroweak symmetry breaking ${P}_{\mathrm{EWSB}}\ensuremath{\lesssim}({10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}1})$. This pattern of unnaturalness in three different arenas, cosmology, nuclear physics, and electroweak symmetry breaking, provides evidence for the multiverse, since each problem may be easily solved by environmental selection. In the nuclear case the problem is largely solved even if the multiverse distribution for the relevant parameters is relatively flat. With somewhat strongly varying distributions, it is possible to understand both the close proximity to neutron stability and the values of ${m}_{e}$ and ${m}_{d}\ensuremath{-}{m}_{u}$ in terms of the electromagnetic mass difference between the proton and neutron, ${\ensuremath{\delta}}_{\mathrm{EM}}\ensuremath{\simeq}1\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }\mathrm{MeV}$. It is reasonable that multiverse distributions are strong functions of Lagrangian parameters, since they depend not only on the landscape of vacua, but also on the population mechanism, ``integrating out'' other parameters, and on a density of observers factor. In any theory with mass scale $M$ that is the origin of electroweak symmetry breaking, strongly varying multiverse distributions typically lead either to a little hierarchy $v/M\ensuremath{\approx}({10}^{\ensuremath{-}2}--{10}^{\ensuremath{-}1})$, or to a large hierarchy $v\ensuremath{\ll}M$. In certain multiverses, where electroweak symmetry breaking occurs only if $M$ is below some critical value, we find that a little hierarchy develops with the value of ${v}^{2}/{M}^{2}$ suppressed by an extra loop factor, as well as by the strength of the distribution. Since the correct theory of electroweak symmetry breaking is unknown, our estimate for ${P}_{\mathrm{EWSB}}$ is theoretical. The LHC will lead to a much more robust determination of ${P}_{\mathrm{EWSB}}$, and, depending on which theory is indicated by the data, the observer naturalness problem of electroweak symmetry breaking may be removed or strengthened. For each of the three arenas, the discovery of a natural theory would eliminate the evidence for the multiverse; but in the absence of such a theory, the multiverse provides a provisional understanding of the data.

Power of black hole physics: seeing through the vacuum landscape

In this paper we generalize the black hole bound of arXiv:0706.2050 to de Sitter spaces, and apply it to various vacua in the landscape, with a special emphasis on slow-roll inflationary vacua. Non-trivial constraints on the lifetime and the Hubble expansion rate emerge. For example, the general tendency is, that for the fixed number and the increasing mass of the species, vacua must become more curved and more unstable, either classically or quantum mechanically. We also discuss the constraints on the lifetime of vacua in the landscape, due to decay into the neighboring states.

Landscape predictions for the Higgs boson and top quark masses

If the Standard Model is valid up to scales near the Planck mass, and if the cosmological constant and Higgs mass parameters scan on a landscape of vacua, it is well known that the observed orders of magnitude of these quantities can be understood from environmental selection for large-scale structure and atoms. If in addition the Higgs quartic coupling scans, with a probability distribution peaked at low values, environmental selection for a phase having a scale of electroweak symmetry breaking much less than the Planck scale leads to a most probable Higgs mass of 106 GeV. While fluctuations below this are negligible, the upward fluctuation is 25/p GeV, where p measures the strength of the peaking of the a priori distribution of the quartic coupling. If the top Yukawa coupling also scans, the most probable top quark mass is predicted to lie in the range (174--178) GeV, providing the standard model is valid to at least 10^{17} GeV. The downward fluctuation is 35 GeV/ \sqrt{p}, suggesting that p is sufficiently large to give a very precise Higgs mass prediction. While a high reheat temperature after inflation could raise the most probable value of the Higgs mass to 118 GeV, maintaining the successful top prediction suggests that reheating is limited to about 10^8 GeV, and that the most probable value of the Higgs mass remains at 106 GeV. If all Yukawa couplings scan, then the e,u,d and t masses are understood to be outliers having extreme values induced by the pressures of strong environmental selection, while the s, \mu, c, b, \tau Yukawa couplings span only two orders of magnitude, reflecting an a priori distribution peaked around 10^{-3}. Extensions of these ideas allow order of magnitude predictions for neutrino masses, the baryon asymmetry and important parameters of cosmological inflation.

Asymptotic states of the bounce geometry

We consider the question of asymptotic observables in cosmology. We assume that string theory contains a landscape of vacua, and that metastable de Sitter regions can decay to zero cosmological constant by bubble nucleation. The asymptotic properties of the corresponding bounce solution should be incorporated in a nonperturbative quantum theory of cosmology. A recent proposal for such a framework defines an S-matrix between the past and future boundaries of the bounce. We analyze in detail the properties of asymptotic states in this proposal, finding that generic small perturbations of the initial state cause a global crunch. We conclude that late-time amplitudes should be computed directly. This would require a string theory analogue of the no-boundary proposal.

Type IIA moduli stabilization

We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli stabilized at arbitrarily large volume, weak coupling, and small negative cosmological constant. We obtain these solutions from both ten-dimensional and four-dimensional perspectives. For more general backgrounds, we study the equations for supersymmetric vacua coming from the effective superpotential and show that all geometric moduli can be stabilized by fluxes. We comment on the resulting picture of statistics on the landscape of vacua.

Framework for the string theory landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine, and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background, and that it contains metastable de Sitter space as an intermediate state.

Minimal grand unification model in an anthropic landscape

It has been recently pointed out by Arkani-Hamed and Dimopoulos that if the universe is a landscape of vacua, and if therefore fine-tuning is not a valid guidance principle for searching for physics beyond the standard model, supersymmetric unification only requires the fermionic superpartners. We argue that in that landscape scenario, the fermionic superpartners are not needed for unification, which can be achieved in SO(10) either via a direct breaking to the standard model at the grand unification scale or through an intermediate gauge symmetry. In most minimal SO(10) models, the proton lifetime is long enough to avoid the experimental bounds. These models are the truly minimal fine-tuned extensions of the standard model in the sense proposed by Davoudiasl et al..