The robustness of slow contraction and the shape of the scalar field potential

We use numerical relativity simulations to explore the conditions for a canonical scalar field $\phi$ minimally coupled to Einstein gravity to generate an extended phase of slow contraction that robustly smooths the universe for a wide range of initial conditions and then sets the conditions for a graceful exit stage. We show that to achieve robustness it suffices that the potential $V(\phi)$ is negative and $M_{\rm Pl}|V_{,\phi}/V|\gtrsim5$ during the smoothing phase. We also show that, to exit slow contraction, the potential must have a minimum. Beyond the minimum, we find no constraint on the uphill slope including the possibility of ending on a positive potential plateau or a local minimum with $V_{\rm min}>0$. Our study establishes ultralocality for a wide range of potentials as a key both to robust smoothing and to graceful exit

Nearly scale-invariant curvature modes from entropy perturbations during graceful exit

In this Letter, we describe how a spectrum of entropic perturbations generated during a period of slow contraction can source a nearly scale-invariant spectrum of curvature perturbations on length scales larger than the Hubble radius during the transition from slow contraction to a classical non-singular bounce (the `graceful exit' phase). The sourcing occurs naturally through higher-order scalar field kinetic terms common to classical (non-singular) bounce mechanisms. We present a concrete example in which, by the end of the graceful exit phase, the initial entropic fluctuations have become negligible and the curvature fluctuations have a nearly scale-invariant spectrum with an amplitude consistent with observations

A general mechanism for producing scale-invariant perturbations and small non-Gaussianity in ekpyrotic models

We explore a new type of entropic mechanism for generating density perturbations in a contracting phase in which there are two scalar fields, but only one has a steep negative potential. This first field dominates the energy density and is the source of the ekpyrotic equation of state. The second field has a negligible potential, but its kinetic energy density is coupled to the first field with a non-linear sigma-model type interaction. We show that for any ekpyrotic equation of state it is possible to choose the potential and the kinetic coupling such that exactly scale-invariant (or nearly scale-invariant) entropy perturbations are produced. The corresponding background solutions are stable, and the bispectrum of the entropy perturbations vanishes as no non-Gaussianity is produced during the ekpyrotic phase. Hence, the only contribution to non-Gaussianity comes from the non-linearity of the conversion process during which entropic perturbations are turned into adiabatic ones, resulting in a local non-Gaussianity parameter $f_{NL} \sim 5$

The Effects of Multiple Modes and Reduced Symmetry on the Rapidity and Robustness of Slow Contraction

We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry. Particularly significant are shear effects that only become possible when variations are allowed along two or more spatial dimensions. Based on the numerical results, we conjecture that the counterintuitive enhancement occurs because more degrees of freedom are activated which drive spacetime away from an unstable Kasner fixed point and towards the stable Friedmann-Robertson-Walker fixed point

Ultralocality and Slow Contraction

We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction

Dynamical attractors in contracting spacetimes dominated by kinetically coupled scalar fields

We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear sigma model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann- Robertson-Walker (FRW) geometry for a wide range of inhomogeneous and anisotropic initial conditions. Ultimately, we find, the kinetic coupling causes the evolution to deflect away from flat FRW and towards a novel Kasner-like stationary point, but in general this occurs on time scales that are too long to be observationally relevant

Inflationary schism

Classic inflation, the theory described in textbooks, is based on the idea that, beginning from typical initial conditions and assuming a simple inflaton potential with a minimum of fine-tuning, inflation can create exponentially large volumes of space that are generically homogeneous, isotropic and flat, with nearly scale-invariant spectra of density and gravitational wave fluctuations that are adiabatic, Gaussian and have generic predictable properties. In a recent paper, we showed that, in addition to having certain conceptual problems known for decades, classic inflation is for the first time also disfavored by data, specifically the most recent data from WMAP, ACT and Planck2013. Guth, Kaiser and Nomura and Linde have each recently published critiques of our paper, but, as made clear here, we all agree about one thing: the problematic state of classic inflation. Instead, they describe an alternative inflationary paradigm that revises the assumptions and goals of inflation, and perhaps of science generally

Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry

We deform the action and the supersymmetry transformations of the d = 10 and d = 4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d = 6 vector branes related to chiral (2,0) supergravity, which we denote as 'Vp-branes'. We use a space-filling V5 superbrane for the d = 6 model and a V3 superbrane for the d = 4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d = 10 and 4, and half-maximal 8+8 supersymmetries in d = 6 and 4.</p