One-loop effective scalar-tensor gravity
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Regular Article - Theoretical Physics
One-loop effective scalar-tensor gravity Boris Latosh1,2,a 1 2
Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia Dubna State University, Universitetskaya str. 19, Dubna 141982, Russia
Received: 18 May 2020 / Accepted: 16 August 2020 © The Author(s) 2020
Abstract Non-minimal interactions are proven to be generated at the one-loop level in simple scalar-tensor gravity models. The John interaction from the Fab Four class is generated. The interaction affects the speed of gravitational waves in the contemporary Universe. Its role in low-energy phenomenology is discussed. Brans-Dicke-like interaction is generated in a non-minimal model. An opportunity to generate a dynamic low-energy Newton constant is addressed.
1 Introduction Effective field theory framework provides a tool to study quantum effects in gravity models [1–5]. Within the effective theory generated by general relativity some verifiable predictions were obtained. For instance, corrections for the Newton potential were studied [2,6,7] together with PPN parameters [8,9]. Various implementations of effective theory for gravity models is widely covered in literature [10–18]. The effective theory for general relativity is constructed as follows [1–5]. First of all, the theory is confined to an energy region below the Planck scale, as it marks the limit of applicability of general relativity. Secondly, a normalization scale μ is chosen below the Planck mass. At this scale a microscopic action A is defined. Finally, the theory is extended below the normalization scale via loop corrections and its description is given by an effective action Γ . An effective theory constructed by this algorithm cannot be considered fundamental. The theory is confined to an energy region below the normalization scale μ which, in turn, is smaller then the Planck scale. There are no reasons to expect that the theory will be applicable outside this domain. A similar logic holds for the microscopic action A. It can only be viewed as an approximation of the fundamental theory at μ. The fundamental theory itself lies beyond the scope of the effective field theory framework. In such a way the a e-mail:
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framework allows one to study quantum effects without a detailed knowledge about the fundamental theory. The microscopic action A defined at the normalization scale can be non-renormalizable within the standard quantum field theory. Firstly, as the theory is not fundamental there are no reasons to impose the renormalizability condition. Secondly, loop corrections can generate operators missing from the microscopic action A. The corresponding infinite contributions can be safely normalized at the scale μ [2,19]. The fundamental theory, no matter if it will be renormalizable in the standard sense or not, should contain a suitable regularization mechanism. Therefore all divergences appearing in the effective theory will be regularized. The finite contributions ge
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