Abstract
The Starobinsky model of inflation remains consistent with observation, forty years after its introduction. It provides a well motivated origin for the scalar inflaton, the "scaleron" with a mass of $O(10^{13})$ GeV, emerging as a graviton degree of freedom from $R^2$ corrections to Einstein-Hilbert gravity. However the coupling of such a heavy state to the BEH ("Higgs") scalar is problematic as its quantum loop corrections can induce an unacceptably large contribution to the radiatively induced BEH scalar mass. The calculation of these corrections is normally done by Weyl transforming to the Einstein frame, yet at the quantum level Weyl transformations are fraught with ambiguities. However the recent realization that there exist "gravitational contact interactions" largely sidesteps these ambiguities. Such contact terms are necessarily present, coming from t-channel graviton exchange interactions, and they show that the theory defined in the "Jordan Frame" is identical to the theory in the Einstein frame, with additional Planck-scale suppressed interactions that take on the form of a Weyl transformation. This avoids ambiguous nonlinear field redefinitions, and reliable loop calculations are possible leading to a consistent low energy theory in an expansion in $1/M^2$. Taking account of the contact terms we study the radiative corrections to the BEH mass in the mixed Higgs/$R^2$ model with explicit scale breaking, and in an extension of the model in which exact scale symmetry is spontaneously broken.
Highlights
There has been considerable interest in recent years in the fundamental role of scale symmetry with gravity and the cosmological evolution of the early universe
Equivalently Weyl invariance, offers a class of models in which cosmic inflation, the origin of the Planck mass as a dynamical scale symmetry breaking, and potentially large hierarchies seen in nature, can arise as a unified phenomenon
In the present paper we focus on a leading candidate quantum field theory of inflation known as the Starobinsky Model [1] both in its original form with explicit scale breaking, and in an extension of the model in which exact scale symmetry is spontaneously broken
Summary
There has been considerable interest in recent years in the fundamental role of scale symmetry with gravity and the cosmological evolution of the early universe. We write down a generic set of relevant operators, match their coefficients at M to the Starobinsky potential, and compute the evolution of their couplings into the infrared with conventional RG equations This is similar to a second order phase transition in condensed matter physics, where there is approximate scale invariance and sensitivity to the complicated short-distance physics is erased, leading to universal low energy results. We will analyse a Weyl invariant version of the Starobinsky model including the BEH scalar in which the fundamental mass scales arise by spontaneous symmetry breaking [11] This requires an additional scalar field and forms the basis of the modern Weyl invariant field theory approach [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. We emphasize that the contact terms are not a Weyl transformation and preserve the original metric, though formally the resulting structure of the theory is that of the Weyl transformation
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
