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Register a new userQuantum Gravity and Cosmology: an intimate interplay
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Added by
Mairi Sakellariadou
Publication date
2017
fields
Physics
and research's language is
English
Authors
Mairi Sakellariadou
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I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological role of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.
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We briefly discuss new models of an `affine theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einsteins proposal to specify the space-time geometry by use of the Hamilton principle to determine the connection coefficients from a geometric Lagrangian that is an arbitrary function of the generalized Ricci curvature tensor and of other fundamental tensors. Such a theory supplements the standard Einstein gravity with dark energy (the cosmological constant, in the first approximation), a neutral massive (or tachyonic) vector field vecton, and massive (or tachyonic) scalar fields. These fields couple only to gravity and can generate dark matter and/or inflation. The concrete choice of the geometric Lagrangian determines further details of the theory. The most natural geometric models look similar to recently proposed brane models of cosmology usually derived from string theory.
Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.
The main goal of the present work is to analyze the cosmological scenario of the induced gravity theory developed in previous works. Such a theory consists on a Yang-Mills theory in a four-dimensional Euclidian spacetime with $SO(m,n)$ such that $m+n=5$ and $min{0,1,2}$ as its gauge group. This theory undergoes a dynamical gauge symmetry breaking via an Inonu-Wigner contraction in its infrared sector. As a consequence, the $SO(m,n)$ algebra is deformed into a Lorentz algebra with the emergency of the local Lorentz symmetries and the gauge fields being identified with a vierbein and a spin connection. As a result, gravity is described as an effective Einstein-Cartan-like theory with ultraviolet correction terms and a propagating torsion field. We show that the cosmological model associated with this effective theory has three different regimes. In particular, the high curvature regime presents a de Sitter phase which tends towards a $Lambda$CDM model. We argue that $SO(m,n)$ induced gravities are promising effective theories to describe the early phase of the universe.
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for the affine connection in non-Riemannian geometries, for the first time in the literature. A peculiar f(R) case is studied in Chapter 5. This is the conformally (as well as projective invariant) invariant theory f(R)=a R^{2} which contains an undetermined scalar degree of freedom. We then turn our attention to Cosmology with torsion and non-metricity (Chapter 6). In Chapter 7, we formulate the necessary setup for the $1+3$ splitting of the generalized spacetime. Having clarified the subtle points (that generally stem from non-metricity) in the aforementioned formulation we carefully derive the generalized Raychaudhuri equation in the presence of both torsion and non-metricity (along with curvature). This, as it stands, is the most general form of the Raychaudhuri equation that exists in the literature. We close this Thesis by considering three possible scale transformations that one can consider in Metric-Affine Geometry.
We study the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for flat, $k=0$, Friedmann-Robertson-Walker (FRW) universes. When the only matter is a cosmological constant, the nonlinearity can provide a barrier that screens the original Big Bang, leading to the quantum creation of a universe through tunneling just as in the $k=1$ case. When the matter is instead a free massless scalar field, the nonlinearity can again prevent a contracting classical universe from reaching zero size by creating a bounce. Our studies here are self-consistent to leading order in perturbation theory for the nonlinear effects.
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