We present first results from a novel numerical relativity code based on a tetrad formulation of the Einstein-scalar field equations combined with recently introduced gauge/frame invariant diagnostics. The results provide support for the argument that inflation does not solve the homogeneity and isotropy problem beginning from generic initial conditions following a big bang.

United States

David Garfinkle

Anna Ijjas

Paul J. Steinhardt

Initial conditions problem in cosmological inflation revisited

We track the evolution of entropy and black holes in a cyclic universe that undergoes repeated intervals of expansion followed by slow contraction and a smooth (non-singular) bounce. In this kind of cyclic scenario, there is no big crunch and no chaotic mixmaster behavior. We explain why the entropy following each bounce is naturally partitioned into near-maximal entropy in the matter-radiation sector and near-minimal in the gravitational sector, satisfying the Weyl curvature conditions conjectured to be essential for a cosmology consistent with observations. As a result, this kind of cyclic universe can undergo an unbounded number of cycles in the past and/or the future.

Germany

Entropy, black holes, and the new cyclic universe

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.

Frans Pretorius

Andrew P. Sullivan

The effects of multiple modes and reduced symmetry on the rapidity and robustness of slow contraction

Performing a fully non-perturbative analysis using the tools of numerical general relativity, we demonstrate that a period of slow contraction is a “supersmoothing” cosmological phase that homogenizes, isotropizes and flattens the universe both classically and quantum mechanically and can do so far more robustly and rapidly than had been realized in earlier studies.

William G. Cook

Iryna A. Glushchenko

Supersmoothing through slow contraction

In the Ijjas-Steinhardt cyclic model, the universe passes through phases dominated by radiation, matter, and a dark energy scalar field, with the value of the scale factor increasing with each cycle. Since each cycle terminates in a finite time, it is straightforward to calculate the fraction of time that the universe spends in a state for which the matter and dark energy densities have comparable magnitudes; when this fraction is large, it can be taken as a solution of the coincidence problem. This solution of the coincidence problem requires a relatively short lifetime for each cycle, but unlike in the case of phantom models, there is no fixed upper bound on this lifetime. However, scalar field models satisfying the Swampland conjectures yield sufficiently short lifetimes to provide a satisfactory resolution of the coincidence problem.

Robert J. Scherrer

The coincidence problem and the Swampland conjectures in the Ijjas-Steinhardt cyclic model of the universe

Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically, but the scale factor grows by an exponential factor from one cycle to the next. The resulting cosmology not only resolves the homogeneity, isotropy, flatness and monopole problems and generates a nearly scale invariant spectrum of density perturbations, but it also addresses a number of age-old cosmological issues that big bang inflationary cosmology does not. There may also be wider-ranging implications for fundamental physics, black holes and quantum measurement.

A new kind of cyclic universe

We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order L4 Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.

Fully stable cosmological solutions with a non-singular classical bounce

In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space–times always decreases while in contracting space–times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, i.e. , without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this letter, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show that mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein–Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. We also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.

Justin Ripley

NEC violation in mimetic cosmology revisited

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.