Loop quantum cosmology: Recent progress

Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is sensitive to the quantum regime. As a consequence, the structure of and the approach to classical singularities are very different from general relativity. The quantum theory is free of singularities, and there are new phenomenological scenarios for the evolution of the very early universe such as inflation. We give an overview of the main effects, focussing on recent results obtained by different groups.     

Noncommutative quantum cosmology

We consider noncommutative quantum cosmology in the case of the low-energy string effective theory. Exact solutions are found and compared with the commutative case.     

A phenomenology analysis of the tachyon warm inflation in loop quantum cosmology

We investigate the warm inflation condition in loop quantum cosmology. In our consideration, the system is described by a tachyon field interacted with radiation. The exponential potential function, V(?)=V₀e−α?$V(?)=V_0{e}^{-\alpha ?}$, with the same order parameters V₀$V_0$ and α, is taken as an example of this tachyon warm inflation model. We find that, for the strong dissipative regime, the total number of e-folds is less than the one in the classical scenario, and for the weak dissipative regime, the beginning time of the warm inflation will be later than the tachyon (cool) inflation.     

Loop quantum cosmology: an overview

A brief overview of loop quantum cosmology of homogeneous isotropic models is presented with emphasis on the origin of and subtleties associated with the resolution of big bang and big crunch singularities. These results bear out the remarkable intuition that John Wheeler had. Discussion is organized at two levels. The the main text provides a bird’s eye view of the subject that should be accessible to non-experts. Appendices address conceptual and technical issues that are often raised by experts in loop quantum gravity and string theory.     

A definition for time in quantum cosmology

A definition for the intrinsic time co-ordinate is proposed, using the phase of the wave function of the universe. This definition generalizes the notion of time co-ordinate which arises in the semiclassical cosmology. It also leads to acceptable results for the evaluation of expectation values of physical variables.     

A supersymmetric Vista for quantum cosmology

A brief overview on the subject of Supersymmetric Quantum Cosmology (SQC) is presented here. Different approaches are described, all of them being inspired by the search of a square root of (quantum) General Relativity. Some new ideas in the form of a list of (still!) open problems and an extensive bibliography are included.     

Loop quantum cosmology and slow roll inflation

In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. Rather than growing unboundedly in the past, the Hubble parameter vanishes at the bounce and attains a finite universal maximum   at the end of super-inflation. These novel features lead to an unforeseen implication: in presence of suitable potentials all LQC dynamical trajectories are funneled to conditions which virtually guarantee slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to certain results in general relativity, where it is argued that the a priori probability of obtaining a slow roll with 68 or more e-foldings is suppressed by a factor e−204$e^{-204}$.     

Tomographic representation of minisuperspace quantum cosmology and noether symmetries

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select “observable” universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters.     

Dust and radiation quantum perfect fluid cosmology: selection of time variable

We studied the expectation value of the scale factor in radiation and dust quantum perfect fluid cosmology. We used Schutzs variational formalism to describe the perfect fluid and selected the conjugate coordinate of the perfect fluid to be the dynamical variable. After quantization and solving the Wheeler-DeWitt equation we obtained an exact solution. By superposition of exact solutions, we obtained one wave packet and used it to compute the expectation value of the scale factor. We found that if one selects a different dynamical variable being the time variable in each of these two systems, the expectation value of the scale factor of these two systems can fit in with the prediction of General Relativity. Therefore we thought that the selection of a reference time can be different for different quantum perfect fluid systems.     

Brane-world cosmology and inflation

There has been substantial progress in brane-world cosmology in recent years. Much attention has been particularly paid to the second Randall-Sundrum (RS2) scenario in which a single positive-tension brane is embedded in a five-dimensional space-time, called the bulk, with a negative cosmological constant. This brane-world scenario is quite attractive because of the non-trivial geometry in the bulk and because it successfully gives four-dimensional general relativity in the low energy limit. After reviewing basic features of the RS2 scenario, we consider a brane-world inflation model driven by the dynamics of a scalar field living in the five-dimensional bulk, the so-called bulk inflaton model. An intriguing feature of this model is that the projection of the bulk inflaton on the brane behaves just like an ordinary inflaton in four dimensions in the low energy regime,H ² l ² « 1, whereH is the Hubble expansion rate of the brane andl is the curvature radius of the bulk. We then discuss the cosmological perturbation on superhorizon scales in this model. We find that, even under the presence of spatial inhomogeneities, the model is indistinguishable from the standard four-dimensional inflation toO(H ² l ²). That is, the difference may appear only atO(H ¹⁴ l ⁴).     

Simple quantum cosmology: vacuum energy and initial state

A static non-singular 10-dimensional closed Friedmann universe of Planck size, filled with a perfect fluid with equation of state p = – , can arise spontaneously by a quantum fluctuation from nothing in 11-dimensional spacetime. A quantum transition from this state can initiate the inflationary quantum cosmology outlined in [Gen. Relativ. Gravit. 33, 1415 (2001)]. With no fine-tuning, that cosmology predicts about 60 e-folds of inflation and a vacuum energy density depending only on the number of extra space dimensions (seven), G,, c and the ratio between the strength of gravity and the strength of the strong force. The fraction of the total energy in the universe represented by this vacuum energy depends on the Hubble constant H₀. Estimates of H₀ from WMAP, SDSS, the Hubble Key Project, and Sunyaev-Zeldovich and X-ray flux measurements range from 60 to 72 km s^–1 Mpc^–1. Using a mid-range value of H₀ = 65 km s^–1 Mpc^–1, the model in [Gen. Relativ. Gravit. 33, 1415 (2001)] predicts 0.7.     

Tomographic entropy and cosmology

The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free pointlike particle and repulsive oscillator are considered. The notion of tomographic entropy and its properties are used to find some inequalities for the tomographic probability determining the quantum state of the universe. The sense of the inequality as a lower bound for the entropy is clarified.     

Higgs boson cosmology

The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition one nanosecond after the big bang, on to the end of the present-day universe through vacuum decay. Higgs physics is wide ranging, and gives an impetus to go beyond the Standard Models of particle physics and cosmology to explore the physics of ultra-high energies and quantum gravity.     

斯塔罗宾斯基与暴胀宇宙学

俄罗斯国家科学院院士阿里可塞·斯塔罗宾斯基(Alexei Starobinsky)教授是现代宇宙学暴胀模型的最早提出者之一,文中回顾了他在暴胀模型形成初期的具体贡献,并表达了他对暴胀模型和宇宙学未来发展的最新看法。     

Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.     

Observational constraints on loop quantum cosmology

In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.     

On the consistent histories approach to quantum mechanics

We review the consistent histories formulations of quantum mechanics developed by Griffiths, Omnès, and Gell-Mann and Hartle, and describe the classification of consistent sets. We illustrate some general features of consistent sets by a few simple lemmas and examples. We consider various interpretations of the formalism, and examine the new problems which arise in reconstructing the past and predicting the future. It is shown that Omnès' characterization of true statements—statements which can be deduced unconditionally in his interpretation—is incorrect. We examine critically Gell-Mann and Hartle's interpretation of the formalism, and in particular their discussions of communication, prediction, and retrodiction, and conclude that their explanation of the apparent persistence of quasiclassicality relies on assumptions about an as-yetunknown theory of experience. Our overall conclusion is that the consistent histories approach illustrates the need to supplement quantum mechanics by some selection principle in order to produce a fundamental theory capable of unconditional predictions.     

Quantum cosmology in Ashtekar variables with non-minimally coupled scalar-tensor theory

Using non-minimally coupled scalar-tensor theory in homogeneous and isotropic cosmological model, quantum cosmology has been developed for Ashtekar variables. The wave function has been evaluated by solving the Wheeler-Dewitt (WD) equation and also using path integral formulation. Semi-classical limit using WKB approximation has also been discussed. Finally, the quantum Bohmian trajectories has been studied in detail.