Covariant Quantum Gravitational Corrections to Scalar and Tensor Field Models
Sandeep Aashish
备注：
130 pages, 2 figures; PhD thesis (Indian Institute of Science Education and Research Bhopal, April 2020) based on previously published works in arxiv:1803.10157, arxiv:1806.08194, arxiv:1903.11364, arxiv:1905.12249 and arxiv:2001.07350
Recent and upcoming experimental data as well as the possibility of rich phenomenology have spiked interest in studying the quantum effects in cosmology at low (inflation-era) energy scales. One of the approaches to find covariant quantum corrections is the DeWitt-Vilkovisky's (DV) covariant effective action formalism that is gauge invariant and background field invariant. We use the DeWitt-Vilkovisky method to study formal and cosmological aspects of quantum fields in curved spacetime, and take initial steps towards studying quantum gravitational corrections in cosmological setting. The thesis comprises of mainly two parts. We first study the formal aspects of rank-2 antisymmetric tensor field which appear in the low energy limit of superstring models and are thus relevant in the early universe, in particular the quantization and quantum equivalence properties, for the case with and without spontaneous Lorentz violation. The effective action is generalized for gauge theories whose gauge parameters possess additional symmetries. When used in the case of spontaneously Lorentz violating antisymmetric tensor field model, it is found that classical equivalence with a vector theory breaks down at one-loop level due to the presence of Lorentz violating terms. The final chapter of this thesis is devoted to taking first steps towards exploring applications of DV method in early universe cosmology. We calculate perturbatively the covariant one-loop quantum gravitational effective action for a scalar field model inspired by the recently proposed nonminimal natural inflation model. The effective potential is evaluated taking into account the finite corrections, and an order-of-magnitude estimate of the one-loop corrections reveals that gravitational and non-gravitational corrections have same or comparable magnitudes.
We investigate the correspondence between generally covariant higher derivative scalar-tensor theory and spatially covariant gravity theory. The building blocks are the scalar field and spacetime curvature tensor together with their generally covariant derivatives for the former, and the spatially covariant geometric quantities together with their spatially covariant derivatives for the later. In the case of a single scalar degree of freedom, they are transformed to each other by gauge fixing and recovering procedures, of which we give the explicit expressions. We make a systematic classificat…
We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and shown to be in accord with the requirements of conformal invariance.
We study the particle content of higher derivative theories of gravity built with contractions of the Riemann tensor and its covariant derivatives. In the absence of the latter, there is a family of theories exhibiting an Einsteinian spectrum known as generalized quasi-topological gravities. In turn, we present a no-go result for the construction of Einsteinian gravities involving covariant derivatives of the Riemann tensor. We find evidences suggesting that (truncated series) finite order Lagrangians with covariant derivatives of the Riemann tensor generically present ghosts in their spectrum…
We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with derivatives of the scalar field up to the third order and with the Riemann tensor up to the quadratic order. We build two types of linear spaces. One is the set of linearly independent generally covariant scalar-tensor monomials, the other is the set of linearly independent spatially covariant gravity monomials. We argue that these two types of linear space are isomorphic to each other in the sense of gauge fixing/recovering procedures. We then identify the subspaces in the spatially covariant gravity, which a…
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Unimodular gravity (UG) is an interesting theory that may explain why the cosmological constant is extremely small, in contrast to general relativity (GR). The theory has only the transverse diffeomorphism invariance and this causes lots of debate as to the equivalence of UG to GR in the covariant quantization. We study the covariant BRST quantization of UG by gauge fixing only the transverse diffeomorphism and show that the remaining physical degrees of freedom are two, the same number as GR. This is achieved by using antisymmetric tensor ghost fields which automatically satisfy the transvers…
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We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescription and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's extension to the ordinary Schwinger-DeWitt approach. For complete…
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Covariant quantization of rank-2 antisymmetric fields is non-trivial due to additional symmetries of the gauge parameters. We present an intuitive way to deal with this additional symmetry of gauge parameters in terms of geometrical understanding of field space. We generalize the DeWitt-Vilkovisky covariant effective action formalism for quantization of such theories. As an application, we quantize a massive rank-2 antisymmetric field using the covariant effective action approach and reproduce previously obtained results.
A necessary condition for a generally covariant scalar-tensor theory to be ghostfree is that it contains no extra degrees of freedom in the unitary gauge, in which the Lagrangian corresponds to the spatially covariant gravity. Comparing with analysing the scalar-tensor theory directly, it is simpler to map the spatially covariant gravity to the generally covariant scalar-tensor theory using the gauge recovering procedures. In order to ensure the resulting scalar-tensor theory to be ghostfree absolutely, i.e., no matter if the unitary gauge is accessible, a further covariant degeneracy/constrai…
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The scalar-tensor theories have become popular recently in particular in connection with attempts to explain present accelerated expansion of the universe, but they have been considered as a natural extension of general relativity long time ago. The Horndeski scalar-tensor theory involving four invariantly defined Lagrangians is a natural choice since it implies field equations involving at most second derivatives. Following the formalisms of defining covariant global quantities and conservation laws for perturbations of spacetimes in standard general relativity we extend these methods to the …
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Covariant eigenmode overlap formalism for gravitational wave signals in electromagnetic cavities
Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology（高能物理研究所（IFAE），巴塞罗那科学与技术研究院）；Universität Hamburg（汉堡大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所（DESY））
We calculate the covariant one-loop quantum gravitational effective action for a scalar field model inspired by the recently proposed nonminimal natural inflation model. Our calculation is perturbative, in the sense that the effective action is evaluated in orders of background field, around a Minkowski background. The effective potential has been evaluated taking into account the finite corrections. An order-of-magnitude estimate of the one-loop corrections reveals that gravitational and non-gravitational corrections have same or comparable magnitudes.
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Bi-scalar-tensor theory: a spatially covariant gravity approach
School of Physics, Sun Yat-sen University（中山大学物理学院）；Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing, Sun Yat-sen University（中山大学广东省量子计量与传感重点实验室）；Department of Physics, Rikkyo University（立教大学物理系）
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