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We present a prototype model that resolves the cosmological constant problem using matter alone, i.e., without modifying gravity. Its generic cosmological solutions adjust an arbitrarily large, negative dark energy to a positive value parametrically suppressed by an initial field velocity. Inflationary initial conditions lead to a positive dark energy exponentially smaller in magnitude than any model parameter, or any scale in the initial conditions., Comment: 5 pages, 2 figures

Finding numerical solutions describing bubble nucleation is notoriously difficult in more than one field space dimension. Traditional shooting methods fail because of the extreme non-linearity of field evolution over a macroscopic distance as a function of initial conditions. Minimization methods tend to become either slow or imprecise for larger numbers of fields due to their dependence on the high dimensionality of discretized function spaces. We present a new method for finding solutions which is both very efficient and able to cope with the non-linearities. Our method directly integrates the equations of motion except at a small number of junction points, so we do not need to introduce a discrete domain for our functions. The method, based on multiple shooting, typically finds solutions involving three fields in under a minute, and can find solutions for eight fields in about an hour. We include a numerical package for Mathematica which implements the method described here., Comment: 19 pages, 7 figures, few typos fixed, improved method for calculation of action included. More detailed comparison with other techniques is included

We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such "topologically unobstructed" cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to $M_3 \times S_1$ presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification., Comment: 33 pages, 9 figures

We analyze the shapes of cosmic string loops found in large-scale simulations of an expanding-universe string network. The simulation does not include gravitational back reaction, but we model that process by smoothing the loop using Lorentzian convolution. We find that loops at formation consist of generally straight segments separated by kinks. We do not see cusps or any cusp-like structure at the scale of the entire loop, although we do see very small regions of string that move with large Lorentz boosts. However, smoothing of the string almost always introduces two cusps on each loop. The smoothing process does not lead to any significant fragmentation of loops that were in non-self-intersecting trajectories before smoothing., Comment: 19 pages, 13 figures

Despite the ultraviolet problems with canonical quantum gravity, as an effective field theory its infrared phenomena should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is known as the problem of time. Here, we provide a solution by promoting the cosmological constant $\Lambda$ to a Lagrange multiplier constraining the metric volume element to be manifestly a total derivative. Because $\Lambda$ appears linearly in the Hamiltonian constraint, it unitarily generates time evolution, yielding a functional Schroedinger equation for gravity. Two pleasant side effects of this construction are that vacuum energy is dissociated from the cosmological constant problem, much like in unimodular gravity, and the natural foliation provided by the time variable defines a sensible solution to the measure problem of eternal inflation., Comment: 5 pages, no figures. Minor changes, fixed typos, added references

Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings does not play any role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding $G\mu \leq 2.8\times 10^{-9}$. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms., Comment: 34 pages, 15 figures

We illustrate a framework for constructing models of chaotic inflation where the inflaton is the position of a D3 brane along the universal cover of a string compactification. In our scenario, a brane rolls many times around a non-trivial one-cycle, thereby unwinding a Ramond-Ramond flux. These "flux monodromies" are similar in spirit to the monodromies of Silverstein, Westphal, and McAllister, and their four-dimensional description is that of Kaloper and Sorbo. Assuming moduli stabilization is rigid enough, the large-field inflationary potential is protected from radiative corrections by a discrete shift symmetry., Comment: Journal version, includes kinetic steepening possibility

We examine the effects of cosmic strings on structure formation and on the ionization history of the universe. While Gaussian perturbations from inflation are known to provide the dominant contribution to the large scale structure of the universe, density perturbations due to strings are highly non-Gaussian and can produce nonlinear structures at very early times. This could lead to early star formation and reionization of the universe. We improve on earlier studies of these effects by accounting for high loop velocities and for the filamentary shape of the resulting halos. We find that for string energy scales G\mu > 10^{-7} the effect of strings on the CMB temperature and polarization power spectra can be significant and is likely to be detectable by the Planck satellite. We mention shortcomings of the standard cosmological model of galaxy formation which may be remedied with the addition of cosmic strings, and comment on other possible observational implications of early structure formation by strings., Comment: 22 pages, 10 figures. References added

We argue that classical transitions can be the key to explaining the long standing puzzle of the fast A-B phase transition observed in superfluid Helium 3 while standard theory expects it to be unobservably slow. Collisions between domain walls are shown to be capable of reaching phases inaccessible through homogenous nucleation on the measured timescales. We demonstrate qualitative agreements with prior observations and provide a definite, distinctive prediction that could be verified through future experiments or, perhaps, a specific analysis of existing data., Comment: 27 pages, 9 figures

We investigate the recent suggestion that a Minkowski vacuum is either absolutely stable, or it has a divergent decay rate and thus fails to have a locally Minkowski description. The divergence comes from boost integration over momenta of the vacuum bubbles. We point out that a prototypical example of false-vacuum decay is pair production in a uniform electric field, so if the argument leading to the divergence is correct, it should apply to this case as well. We provide evidence that no catastrophic vacuum instability occurs in a constant electric field, indicating that the argument cannot be right. Instead, we argue that the boost integration that leads to the divergence is unnecessary: when all possible fluctuations of the vacuum bubble are included, the quantum state of the bubble is invariant under Lorentz boosts., Comment: 12 pages, 1 figure

Within the framework of flux compactifications, we construct an instanton describing the quantum creation of an open universe from nothing. The solution has many features in common with the smooth 6d bubble of nothing solutions discussed recently, where the spacetime is described by a 4d compactification of a 6d Einstein-Maxwell theory on S^2 stabilized by flux. The four-dimensional description of this instanton reduces to that of Hawking and Turok. The choice of parameters uniquely determines all future evolution, which we additionally find to be stable against bubble of nothing instabilities., Comment: 19 pages, 6 figures

Using a new parallel computing technique, we have run the largest cosmic string simulations ever performed. Our results confirm the existence of a long transient period where a non-scaling distribution of small loops is produced at lengths depending on the initial correlation scale. As time passes, this initial population gives way to the true scaling regime, where loops of size approximately equal to one-twentieth the horizon distance become a significant component. We observe similar behavior in matter and radiation eras, as well as in flat space. In the matter era, the scaling population of large loops becomes the dominant component; we expect this to eventually happen in the other eras as well., Comment: 23 pages, 10 figures, 2 tables. V2: combine 3 figures, add 1 table, better discussion + citation of prev. work

We develop a "semi-parallel" simulation technique suggested by Pretorius and Lehner, in which the simulation spacetime volume is divided into a large number of small 4-volumes which have only initial and final surfaces. Thus there is no two-way communication between processors, and the 4-volumes can be simulated independently without the use of MPI. This technique allows us to simulate much larger volumes than we otherwise could, because we are not limited by total memory size. No processor time is lost waiting for other processors. We compare a cosmic string simulation we developed using the semi-parallel technique with our previous MPI-based code for several test cases and find a factor of 2.6 improvement in the total amount of processor time required to accomplish the same job for strings evolving in the matter-dominated era., Comment: 22 pages, 7 figures, 3 tables

We construct instanton solutions describing the decay of flux compactifications of a $6d$ gauge theory by generalizing the Kaluza-Klein bubble of nothing. The surface of the bubble is described by a smooth magnetically charged solitonic brane whose asymptotic flux is precisely that responsible for stabilizing the 4d compactification. We describe several instances of bubble geometries for the various vacua occurring in a $6d$ Einstein-Maxwell theory namely, AdS_4 x S^2, R^{1,3} x S^2, and dS_4 x S^2. Unlike conventional solutions, the bubbles of nothing introduced here occur where a {\em two}-sphere compactification manifold homogeneously degenerates., Comment: 31 pages, 15 figures

We construct a simple AdS_4 x S^1 flux compactification stabilized by a complex scalar field winding the extra dimension and demonstrate an instability via nucleation of a bubble of nothing. This occurs when the Kaluza -- Klein dimension degenerates to a point, defining the bubble surface. Because the extra dimension is stabilized by a flux, the bubble surface must be charged, in this case under the axionic part of the complex scalar. This smooth geometry can be seen as a de Sitter topological defect with asymptotic behavior identical to the pure compactification. We discuss how a similar construction can be implemented in more general Freund -- Rubin compactifications., Comment: 16 pages, 5 figures References added

We demonstrate that possession of a single negative mode is not a sufficient criterion for an instanton to mediate exponential decay. For example, de Sitter space is generically stable against decay via the Coleman-De Luccia instanton. This is due to the fact that the de Sitter Euclidean action is bounded below, allowing for an approximately de Sitter invariant false vacuum to be constructed., Comment: 4 pages, 5 figures Added discussion of density of states. Submitted to PRL

We analyze the gravitational wave signatures of a network of metastable cosmic strings. We consider the case of cosmic string instability to breakage, with no primordial population of monopoles. This scenario is well motivated from GUT and string theoretic models with an inflationary phase below the GUT/string scale. The network initially evolves according to a scaling solution, but with breakage events resulting from confined monopoles (beads) being pair produced and accelerated apart. We find these ultra-relativistic beads to be a potent source of gravitational waves bursts, detectable by Initial LIGO, Advanced LIGO, and LISA. Indeed, Advanced LIGO could observe bursts from strings with tensions as low as $G\mu \sim 10^{-12}$. In addition, we find that ultra-relativistic beads produce a scale-invariant stochastic background detectable by LIGO, LISA, and pulsar timing experiments. The stochastic background is scale invariant up to Planckian frequencies. This phenomenology provides new constraints and signatures of cosmic strings that disappear long before the present day., Comment: 37 pages, 7 figures Typos corrected, References added

Motivated by the possibility of a string landscape, we reexamine tunneling of a scalar field across single/multiple barriers. Recent investigations have suggested modifications to the usual picture of false vacuum decay that lead to efficient and rapid tunneling in the landscape when certain conditions are met. This can be due to stringy effects (e.g. tunneling via the DBI action), or by effects arising due to the presence of multiple vacua (e.g. resonance tunneling). In this paper we discuss both DBI tunneling and resonance tunneling. We provide a QFT treatment of resonance tunneling using the Schr\"odinger functional approach. We also show how DBI tunneling for supercritical barriers can naturally lead to conditions suitable for resonance tunneling. We argue using basic ideas from percolation theory that tunneling can be rapid in a landscape where a typical vacuum has multiple decay channels and discuss various cosmological implications. This rapidity vacuum decay can happen even if there are no resonance/DBI tunneling enhancements, solely due to the presence of a large number of decay channels. Finally, we consider various ways of circumventing a recent no-go theorem for resonance tunneling in quantum field theory., Comment: 47 pages, 16 figures. Acknowledgements added

Stringy effects on vacuum transitions are shown to include surprisingly large decay rates through very high potential barriers. This simple, yet counter-intuitive result will drastically modify the measure on the landscape of string vacua., Comment: 4 pages, 2 figures, changes made to 'including gravity' section

The unique, conical spacetime created by cosmic strings brings about distinctive gravitational lensing phenomena. The variety of these distinctive phenomena is increased when the strings have non-trivial mutual interactions. In particular, when strings bind and create junctions, rather than intercommute, the resulting configurations can lead to novel gravitational lensing patterns. In this brief note, we use exact solutions to characterize these phenomena, the detection of which would be strong evidence for the existence of complex cosmic string networks of the kind predicted by string theory-motivated cosmic string models. We also correct some common errors in the lensing phenomenology of straight cosmic strings., Comment: 11 Pages, 6 Figures

In an analysis of the gravitational lensing by two relativistic cosmic strings, we argue that the formation of closed time-like curves proposed by Gott is unstable in the presence of particles (e.g. the cosmic microwave background radiation). Due to the attractor-like behavior of the closed time-like curve, we argue that this instability is very generic. A single graviton or photon in the vicinity, no matter how soft, is sufficient to bend the strings and prevent the formation of closed time-like curves. We also show that the gravitational lensing due to a moving cosmic string is enhanced by its motion, not suppressed., Comment: 26 pages, 9 figures

It was pointed out that brane-anti-brane inflation without warped geometry is not viable due to compactification effects (in the simplified scenario where the inflaton is decoupled from the compactification moduli). We show that the inflationary scenario with branes at a small angle in this simplified scenario remains viable. We also point out that brane-anti-brane inflation may still be viable under some special conditions. We also discuss a way to treat potentials in compact spaces that should be useful in the analysis of more realistic brane inflationary scenarios., Comment: 17 pages, 1 figure