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Register a new userInfluence functionals, decoherence and conformally coupled scalars
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Some of the simplest modifications to general relativity involve the coupling of additional scalar fields to the scalar curvature. By making a Weyl rescaling of the metric, these theories can be mapped to Einstein gravity with the additional scalar fields instead being coupled universally to matter. The resulting couplings to matter give rise to scalar fifth forces, which can evade the stringent constraints from local tests of gravity by means of so-called screening mechanisms. In this talk, we derive evolution equations for the matrix elements of the reduced density operator of a toy matter sector by means of the Feynman-Vernon influence functional. In particular, we employ a novel approach akin to the LSZ reduction more familiar to scattering-matrix theory. The resulting equations allow the analysis, for instance, of decoherence induced in atom-interferometry experiments by these classes of modified theories of gravity.
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In the first part of this paper we critically examine the ultra-violet implications of theories that exhibit Vainshtein screening, taking into account both the standard Wilsonian perspective as well as more exotic possibilities. Aspects of this discussion draw on results from the second part of the paper in which we perform a general study of derivatively coupled scalar theories using non-perturbative exact renormalisation group techniques, which are of interest independently of their application to modified gravity. In this context, we demonstrate the suppression of quantum corrections within the Vainshtein radius and discuss the potential relation with the classicalisation conjecture. We question whether the latter can be considered a realistic candidate for UV completion of large-scale modifications of gravity on account of a dangerously low classicalisation/strong coupling scale.
We study the decoherence of a renormalised quantum field theoretical system. We consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. Using out-of-equilibrium field theory techniques at finite temperatures, we show that the Gaussian von Neumann entropy for a pure quantum state asymptotes to the interacting thermal entropy. The decoherence rate can be well described by the single particle decay rate in our model. Connecting to electroweak baryogenesis scenarios, we moreover study the effects on the entropy of a changing mass of the system field. Finally, we compare our correlator approach to existing approaches to decoherence in the simple quantum mechanical analogue of our field theoretical model. The entropy following from the perturbative master equation suffers from physically unacceptable secular growth.
We discuss the hybrid inflation model where the inflaton field is nonminimally coupled to gravity. In the Jordan frame, the potential contains $phi^4$ term as well as terms in the original hybrid inflation model. In our model, inflation can be classified into the type (I) and the type (II). In the type (I), inflation is terminated by the tachyonic instability of the waterfall field, while in the type (II) by the violation of slow-roll conditions. In our model, the reheating takes place only at the true minimum and even in the case (II) finally the tachyonic instability occurs after the termination of inflation. For a negative nonminimal coupling, inflation takes place in the vacuum-dominated region, in the large field region, or near the local minimum/maximum. Inflation in the vacuum dominated region becomes either the type (I) or (II), resulting in blue or red spectrum of the curvature perturbations, respectively. Inflation around the local maximum can be either the type (I) or the type (II), which results in the red spectrum of the curvature perturbations, while it around the local minimum must be the type (I), which results in the blue spectrum. In the large field region, to terminate inflation, potential in the Einstein frame must be positively tilted, always resulting in the red spectrum. We then numerically solve the equations of motion to investigate the whole dynamics of inflaton and confirm that the spectrum of curvature perturbations changes from red to blue ones as scales become smaller.
We construct black hole solutions in four-dimensional quadratic gravity, supported by a scalar field conformally coupled to quadratic terms in the curvature. The conformal matter Lagrangian is constructed with powers of traces of a conformally covariant tensor, which is defined in terms of the metric and a scalar field, and has the symmetries of the Riemann tensor. We find exact, neutral and charged, topological black hole solutions of this theory when the Weyl squared term is absent from the action functional. Including terms beyond quadratic order on the conformally covariant tensor, allows to have asymptotically de Sitter solutions, with a potential that is bounded from below. For generic values of the couplings we also show that static black hole solutions must have a constant Ricci scalar, and provide an analysis of the possible asymptotic behavior of both, the metric as well as the scalar field in the asymptotically AdS case, when the solutions match those of general relativity in vacuum at infinity. In this frame, the spacetime fulfils standard asymptotically AdS boundary conditions, and in spite of the non-standard couplings between the curvature and the scalar field, there is a family of black hole solutions in AdS that can be interpreted as localized objects. We also provide further comments on the extension of these results to higher dimensions.
We construct the gauge invariant free action for cosmological perturbations for the nonminimally coupled inflaton field in the Jordan frame. For this the phase space formalism is used, which keeps track of all the dynamical and constraint fields. We perform explicit conformal transformations to demonstrate the physical equivalence between the Jordan and Einstein frames at the level of quadratic perturbations. We show how to generalize the formalism to the case of a more complicated scalar sector with an internal symmetry, such as Higgs inflation. This work represents a first step in developing gauge invariant perturbation theory for nonminimally coupled inflationary models.
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