This paper investigates the manner in which classical universes are obtained in the no-boundary quantum state. In this context, universes can be characterised as classical (in a WKB sense) when the wavefunction is highly oscillatory, i.e. when the ratio of the change in the amplitude of the wavefunction becomes small compared to the change in the phase. In the presence of a positive or negative exponential potential, the WKB condition is satisfied in proportion to a factor $e^{-(ε- 3)N/(ε-1)},$ where $ε$ is the (constant) slow-roll/fast-roll parameter and $N$ designates the number of e-folds. Thus classicality is reached exponentially fast in $N$, but only when $ε< 1$ (inflation) or $ε> 3$ (ekpyrosis). Furthermore, when the potential switches off and the ekpyrotic phase goes over into a phase of kinetic domination, the level of classicality obtained up to that point is preserved. Similar results are obtained in a cyclic potential, where a dark energy plateau is added. Finally, for a potential of the form $-ϕ^n$ (with $n=4,6,8$), where the classical solution becomes increasingly kinetic-dominated, there is an initial burst of classicalisation which then quickly levels off. These results demonstrate that inflation and ekpyrosis, which are the only dynamical mechanisms known for smoothing the universe, share the perhaps even more fundamental property of rendering space and time classical in the first place.
The results from Planck2015, when combined with earlier observations from WMAP, ACT, SPT and other experiments, were the first observations to disfavor the "classic" inflationary paradigm. To satisfy the observational constraints, inflationary theorists have been forced to consider plateau-like inflaton potentials that introduce more parameters and more fine-tuning, problematic initial conditions, multiverse-unpredictability issues, and a new 'unlikeliness problem.' Some propose turning instead to a "postmodern" inflationary paradigm in which the cosmological properties in our observable unive…
The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of "ekpyrotic instanton", which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark en…
We present a new class of complex instantons in the context of ekpyrotic cosmological theories. These instantons, which satisfy the "no-boundary" boundary conditions, describe the emergence of a classical, contracting universe out of nothing. The ekpyrotic attractor is essential in guaranteeing an evolution towards a real, Lorentzian history of the universe. In the context of the no-boundary proposal, the relative probability for such ekpyrotic histories compared to inflationary ones is very high -- in fact, assuming a bounce can be incorporated, these new instantons currently describe the mos…
I will discuss the development of inflationary theory and its present status, as well as some recent attempts to suggest an alternative to inflation. In particular, I will argue that the ekpyrotic scenario in its original form does not solve any of the major cosmological problems. Meanwhile, the cyclic scenario is not an alternative to inflation but rather a complicated version of inflationary theory. This scenario does not solve the flatness and entropy problems, and it suffers from the singularity problem. We describe many other problems that need to be resolved in order to realize a cyclic …
Ekpyrotic instantons describe the emergence of classical contracting universes out of the no-boundary quantum state. However, up to now these instantons ended in a big crunch singularity. We remedy this by adding a higher-derivative term, allowing a ghost condensate to form. This causes a smooth, non-singular bounce from the contracting phase into an expanding, kinetic-dominated phase. Remarkably, and although there is a non-trivial evolution during the bounce, the wavefunction of the universe is "classical" in a WKB sense just as much after the bounce as before. These new non-singular instant…
Both inflationary and ekpyrotic scenarios can account for the origin of the large scale structure of the universe. It is often said that detecting primordial gravitational waves is the key to distinguish both scenarios. We show that this is not true if the gauge kinetic function is present in the ekpyrotic scenario. In fact, primordial gravitational waves sourced by the gauge field can be produced in an ekpyrotic universe. We also study scalar fluctuations sourced by the gauge field and show that it is negligible compared to primordial gravitational waves. This comes from the fact that the fas…
We examine the processes of quantum squeezing and decoherence of density perturbations produced during a slowly contracting ekpyrotic phase in which entropic perturbations are converted to curvature perturbations before the bounce to an expanding phase. During the generation phase, the entropic fluctuations evolve into a highly squeezed quantum state, analogous to the evolution of inflationary perturbations. Subsequently, during the conversion phase, quantum coherence is lost very efficiently due to the interactions of entropy and adiabatic modes. Moreover, while decoherence occurs, the adiaba…
We study density perturbations in several cosmological models motivated by string theory. The evolution and the spectra of curvature perturbations ${\cal R}$ are analyzed in the Ekpyrotic scenario and nonsingular string cosmologies. We find that these string-inspired models generally exhibit blue spectra in contrast to standard slow-roll inflationary scenarios. We also clarify the parameter range where ${\cal R}$ is enhanced on superhorizon scales.
It is shown that the squeezed limit of inflationary expectation values follows from reparametrization invariance of the wavefunction of the universe. This translates into a constraint on the longitudinal modes of functional derivatives of the wavefunction. Thus, the local non-Gaussianity induced by single field inflation is purely a gauge artifact, and should not yield a physically measurable effect. We focus on Einstein gravity in de Sitter space and single field inflation, although the formalism only relies on the diffeomorphism invariance of the theory, and thus applies to any theory of gra…
We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a `bounce' to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation am…
New Ekpyrotic Cosmology is an alternative scenario of the early universe which relies on a phase of slow contraction before the big bang. We calculate the 3-point and 4-point correlation functions of primordial density perturbations and find a generically large non-Gaussian signal, just below the current sensitivity level of CMB experiments. This is in contrast with slow-roll inflation, which predicts negligible non-Gaussianity. The model is also distinguishable from alternative inflationary scenarios that yield large non-Gaussianity, such as DBI inflation and the simplest curvaton-like models…
We explore the effect of initial conditions on the inflationary wavefunction and their consequences for the observed spectrum of primordial fluctuations. In a class of models with a sudden transition into inflation we find that, for a reasonable set of assumptions about the reheat temperature and the number of e-foldings, it is possible for initial conditions set by a pre-inflationary epoch to have an observable effect.
We show that curvature perturbations acquire a scale invariant spectrum for any constant equation of state, provided the fluid has a suitably time-dependent sound speed. In order for modes to exit the physical horizon, and in order to solve the usual problems of standard big bang cosmology, we argue that the only allowed possibilities are inflationary (albeit not necessarily slow-roll) expansion or ekpyrotic contraction. Non-Gaussianities offer many distinguish features. As usual with a small sound speed, non-Gaussianity can be relatively large, around current sensitivity levels. For DBI-like …
We study the emergence of anisotropic (Bianchi IX) inflationary universes with no-boundary conditions in the path integral approach to quantum gravity. In contrast to previous work, we find no evidence for any limit to how large the anisotropies can become, although for increasing anisotropies the shape of the instantons becomes significantly different from Hawking's original no-boundary instanton. In all cases an inflationary phase is reached, with the anisotropies decaying away. Larger anisotropies are associated with a much larger imaginary part of the action, implying that the highly aniso…
The alternative scalar field dark sector of the Universe: Cosmological inflation, quintessence and ekpyrotic model in the framework of scalar-tensor cosmology
We respond to the criticisms by Kallosh, Kofman and Linde concerning our proposal of the ekpyrotic universe scenario. We point out a number of errors in their considerations and argue that, at this stage, the ekpyrotic model is a possible alternative to inflationary cosmology as a description of the very early universe.
We argue that the preferred classical variables that emerge from a pure quantum state are determined by its entanglement structure in the form of redundant records: information shared between many subsystems. Focusing on the early universe, we ask how classical metric perturbations emerge from vacuum fluctuations in an inflationary background. We show that the squeezing of the quantum state for super-horizon modes, along with minimal gravitational interactions, leads to decoherence and to an exponential number of records of metric fluctuations on very large scales, $λ/λ_{\rm Hubble}>Δ_ζ^{-2/3}…
It has been pointed out by several groups that ekpyrotic and cyclic models generate significant non-gaussianity. In this paper, we present a physically intuitive, semi-analytic estimate of the bispectrum. We show that, in all such models, there is an intrinsic contribution to the non-gaussianity parameter f_{NL} that is determined by the geometric mean of the equation of state w_{ek} during the ekpyrotic phase and w_{c} during the phase that curvature perturbations are generated and whose value is O(100) or more times the intrinsic value predicted by simple slow-roll inflationary models, f_{NL…
By considering a simplified but exact model for realizing the ekpyrotic scenario, we clarify various assumptions that have been used in the literature. In particular, we discuss the new ekpyrotic prescription for passing the perturbations through the singularity which we show to provide a spectrum depending on a non physical normalization function. We also show that this prescription does not reproduce the exact result for a sharp transition. Then, more generally, we demonstrate that, in the only case where a bounce can be obtained in Einstein General Relativity without facing singularities an…
We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, that can be entirely described using 4d effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modelled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtaine…
We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter space. We focus on theories which spontaneously break dS boost symmetries and can produce significant non-Gaussianities. The corresponding inflationary correlators are (approximately) scale invariant, but are not invariant under the full conformal group. We derive cutting rules and dispersion formulas for the late-time wavefunction coefficients by using factorization and analyticity properties of the dS bulk-to-bulk propagator. This gives a unitarity method which is valid at tree-level for general $n$-p…
We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe. The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations without invoking superluminal expansion (inflation). The scenario relies, instead, on physical phenomena that arise naturally in theories based on extra dimensions and branes. As an example, we present our scenario predominantly w…
We derive an analogue of the Berry phase associated with inflationary cosmological perturbations of quantum mechanical origin by obtaining the corresponding wavefunction. We have further shown that cosmological Berry phase can be completely envisioned through the observable parameters, viz. spectral indices. Finally, physical significance of this phase is discussed from the point of view of theoretical and observational aspects with some possible consequences of this quantity in inflationary cosmology.
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different patches. Working in the saddle point approximation and in minisuperspace we compute quantum transitions connecting inflationary histories across a de Sitter like throat or a singularity. This supplies probabilities for how an inflating universe, when evolved backwards, transitions and branches into an ensemble of histories on the opposite side of a quantum bounce.…
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 no…
We study some gravitational instanton solutions that offer a natural realization of the spontaneous creation of inflationary universes in the brane world context in string theory. Decoherence due to couplings of higher (perturbative) modes of the metric as well as matter fields modifies the Hartle-Hawking wavefunction for de Sitter space. Generalizing this new wavefunction to be used in string theory, we propose a principle in string theory that hopefully will lead us to the particular vacuum we live in, thus avoiding the anthropic principle. As an illustration of this idea, we give a phenomen…
In this paper we establish dualities between inflationary, cyclic/ekpyrotic, and phantom cosmologies within the patch formalism approximating high-energy effects in scenarios with extra dimensions. The exact dualities relating the four-dimensional spectra are broken in favour of their braneworld counterparts; the dual solutions display new interesting features because of the modification of the effective Friedmann equation on the brane. We then address some qualitative issues about phantomlike cosmologies without phantom matter.
We study the Wigner function for the inflationary tensor perturbation defined in the real phase space. We compute explicitly the Wigner function including the contributions from the cubic self-interaction Hamiltonian of tensor perturbations. Then we argue that it is no longer an appropriate description for the probability distribution in the sense that quantum nature allows negativity around vanishing phase variables. This comes from the non-Gaussian wavefunction in the mixed state as a result of the non-linear interaction between super- and sub-horizon modes. We also show that this is related…
We employ Riesz's fractional derivative into the Wheeler--DeWitt equation for a closed de Sitter geometry and obtain the no-boundary and tunneling wavefunctions. From the corresponding probability distributions, the event horizon of the nucleated universe can be a fractal surface with dimensions between $2\leq D<3$. Concretely, the tunneling wavefunction favors fractal dimensions less than $2.5$ and an accelerated power-law phase. Differently, the no-boundary proposal conveys fractal dimensions close to $3$, with the universe instead entering a decelerated phase. Subsequently, we extend our di…
When inflationary perturbations refuse to classicalise: the role of non-Gaussianity in Wigner negativity
Leinweber Institute for Theoretical Physics, Stanford University（莱因韦伯理论物理研究所，斯坦福大学）；Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，法国国家科学研究中心，PSL大学，索邦大学，巴黎西岱大学）
We elucidate the nature of the correction to the Hartle-Hawking wavefunction presented in hep-th/$0505104$ and hep-th/$0406107$. The correction comes from the quantum fluctuation of the metric that spontaneously breaks the classical deSitter symmetry. This converts the tunneling from nothing to a deSitter-like universe via a $S^{4}$ instantion to that via a barrel instanton, which is bounded from below. Its generalization to 10 dimensional spacetime allows us to find the preferred sites in the stringy cosmic landscape. We comment on how some of the problems of the Hartle-Hawking wavefunction a…
In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inflation is realized--- is highly constrained, with use of the Hamilton--Jacobi equations. In multi-field holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wavefunctions contain no oscillatory phases independent of the momenta). We show that this result is exact, independe…
Possibly, the most general action in the background of isotropic and homogeneous space-time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective Hamiltonian operator in the presence of curvature squared terms suggests unitary time evolution of the quantum states, assuring conservation of probability. The oscillatory behaviour of the semi-classical wavefunction around a de-Sitter solution signals that the theory is classically allowed, and the universe enters an inflationary regime just after Planck's era.…
The 2015 Planck data release has placed tight constraints on the class of in ationary models allowed. The current best fit region favors concave downwards in ationary potentials, since they produce a suppressed tensor to scalar index ratio r. Concave downward potentials have a negative curvature V"<0, therefore a tachyonic mass square that drives fluctuations. Furthermore, their use can become problematic if the field rolls in a part of the potential away from the extrema, since the semiclassical approximation of quantum cosmology, used for deriving the most probable wavefunction of the univer…
Proposing smooth initial conditions is one of the most important tasks in quantum cosmology. On the other hand, the low-energy effective action, appearing in the semiclassical path integral, can get nontrivial quantum corrections near classical singularities due to specific quantum gravity proposals. In this article, we combine the well-known no-boundary proposal for the wavefunction of the universe with quantum modifications coming from loop quantum cosmology (LQC). Remarkably, we find that the restriction of a `slow-roll' type potential in the original Hartle-Hawking proposal is considerably…
Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parame…
We interpret the Holographic Conjecture in terms of quantum bits (qubits). N-qubit states are associated with surfaces that are punctured in N points by spin networks' edges labeled by the spin-1/2 representation of SU(2), which are in a superposed quantum state of spin "up" and spin "down". The formalism is applied in particular to de Sitter horizons, and leads to a picture of the early inflationary universe in terms of quantum computation. A discrete micro-causality emerges, where the time parameter is being defined by the discrete increase of entropy. Then, the model is analysed in the fram…
