Timeless Quantum Mechanics and the Early Universe

Abstract: We discuss the construction and interpretation of observables in quantum theories with worldline diffeomorphism invariance, in which a preferred or absolute time parameter is absent. These theories are also called time-reparametrization invariant, and they can be seen as mechanical toy models of quantum gravity. The interest in these models stems from the necessity of understanding the so-called problem of time in a theory of quantum gravitation: how can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? What is the relevant space of physical states and which operators act on it? How are the quantum states related to probabilities in the absence of a preferred time? We show that the dynamics can be described in terms of relational observables, which are diffeomorphism-invariant extensions of geometrical objects in analogy to gauge-invariant extensions of noninvariant quantities in the usual gauge (Yang-Mills) theories. We take this analogy seriously and use it as a basis of a method of construction of invariant operators in the quantum theory. Furthermore, we discuss how the notion of a physical propagator may be used to define a unitary evolution in the quantum theory, which is to be understood in terms of a generalized clock, as is the classical theory. We also discuss under which circumstances the above mentioned formalism can be related to the use of conditional probabilities in the quantum theory in a generalization of the well-known Page-Wootters approach. Finally, in the interest of making contact with observations, we also examine how our formalism can be adapted to calculations of quantum-gravitational effects in the early Universe.

Close

Working around the non-normalizability of the Lorentzian NBWF

Abstract: The Lorentzian No-Boundary Wavefunction (NBWF) is presented for a free curvature parameter $k$. The choice of the Starobinsky inflation model to be considered for further analysis is motivated. It is shown that the Einstein frame potential of Starobinsky inflation used with the Lorentzian NBWF renders it non-normalizable. Faced with this obstacle, possible workarounds are suggested and supported by heuristic justifications. The breakdown of one of the aforementioned provision is demonstrated, whereas the other provision yields a reasonable pathway to the ensuing slow-roll analysis. Conclusions are drawn on the utility of the tree-level Lorentzian NBWF as a precursor to (Starobinsky) inflation based on the slow-roll analysis in conjunction with a quantum cosmological consistency condition.

Close

From Semiclassical Gravity to Starobinski Model

Abstract: General Relativity and Quantum Mechanics are the foundations of two different descriptions of reality, but incompatible when they work together. We present the attemp to solve that conflict, called “semiclassical" approach, and derive the semiclassical Einstein Equations which renormalise the divergences. Finally, we will apply them to find the new dynamics of the flat homogeneous universe, one of them being the Starobinski model.

Close

Decoherence in quantum mechanics and quantum cosmology

Abstract: How does the classical behaviour emerge in a world that is fundamentally described by quantum theory? The key to the answer is given by a process that was described for the first time in 1970 - decoherence. Decoherence is the irreversible emergence of classical properties of a quantum system through the unavoidable interaction with its environment. In my talk, I give a general introduction into decoherence and present its most important theoretical and experimental applications. I discuss the situation in quantum mechanics including the relevance of decoherence for the interpretation of quantum theory. I then turn to quantum cosmology and explain how the classical appearance of the metric and matter fields can be understood in a fundamental theory of quantum gravity in which arbitary metric superpositions can occur. At the end I address the relevance of decoherence for the origin of the arrow of time.

Close

Witnessing Quantum Gravity via Entanglement in an Atom Chip

Abstract: I will discuss how to witness perturbative quantum aspects of gravity in the far infrared via witnessing entanglement in a low energy scattering diagram. I will discuss how to witness the existence of a graviton in a laboratory by creating Schrödinger cat states in an atom chip. I will explain the ingenuity and the challenges it requires to perform an extra ordinary experiment which will one day shed light on the quantum foundations of space-time and general theory of relativity.

Close

Introduction to holography

Abstract: I will give an introduction to the AdS/CFT correspondence and will discuss some modern topics in that context, such as bulk reconstruction and emergent gravity from entanglement.

Close

Cosmological particle behavior near future sudden singularities

Abstract: We discuss classical and quantum aspects of cosmological models in Brans–Dicke theory. In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In order to have a bouncing solution in classical General Relativity, violation of the energy conditions is required. We present cosmological bounce solutions in the Brans–Dicke theory with radiative fluid that obeys the energy conditions, and with no ghosts. Then we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω < − 3/2, the energy is bounded from below and singularity-free solutions are found. However, in the case ω > − 3/2 we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite. But we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics.

Close

Semi-classical predictions of cosmological wave-packets from ridge-lines

Porting conventional tools to quantum geometrodynamics

Abstract: We introduce the ridge-line approaches to investigate semi-classical predictions from wave-packets with arbitrary width, which is expected to work both for conventional quantum mechanics and the Wheeler–DeWitt quantum cosmology. As the two primary methods, the contour and the stream approaches are applied to the analytic calculation of ridge-lines. Moreover, aspects of these methods are discussed and compared to other scenario and approach, i.e. the narrow WKB wave-packet and the first-derivative test. As the main result, we show that the semi-classical predictions in toy models have more abundant solutions than in the classical theory, and most interestingly they may deviate from classical solutions due to the quantum corrections.

Close

On the Utility of the No-Boundary Wavefunction as a Precursor to Inflation

Abstract: This thesis follows the path integral approach to quantize gravity. The Lorentzian No-Boundary Wavefunction (NBWF) is constructed with a straightforward incorporation of the potential of a single scalar field (to be regarded as the inflaton). The absolute-square of the NBWF is then analyzed for peaks with respect to the scalar field which can be interpreted as the predictions on the initial values of the field. The Starobinsky model of inflation is chosen for further analysis. It is demonstrated that this leads to a non-normalizable NBWF in the region of interest.

Possible provisions to work around the non-normalizability of the NBWF are suggested and supported by heuristic justifications. The breakdown of one of the aforementioned provisions is demonstrated. The other provision, which entails adding a correction to the potential of Starobinsky inflation, allows to continue with the slow-roll analysis. The consequences on the Jordan frame action, of adding such a term in the Einstein frame action are studied carefully. Comparison of the slow-roll analysis results with the Planck results does not rule out this model, whereas the imposition of a quantum cosmological consistency condition suggests that the tree-level Lorentzian NBWF is not a useful precursor to Starobinsky inflation.

Close

Loop Quantum Cosmology- Introduction, k=0 FLRW model, singularity avoidance, and criticism

Abstract: This talk will aim to cover fundamentals of LQC using a simple k=0 FLRW model. In that, it will deal with how quantization is approached in LQC (which is inspired by procedures in LQG) and how it is different from WDW theory. Also the claim of singularity avoidance and its generic nature in LQC will be discussed, by observing the behaviour of expectation values of some Dirac observables, and by looking at the semiclassical behaviour. And finally the criticism of these claims would be briefly discussed to conclude the talk.

Close