V. A. Rubakov’s research while affiliated with Lomonosov Moscow State University and other places

A bstract We construct a concrete model of Horndeski bounce with strong gravity in the past. Within this model we show that the correct spectra of cosmological perturbations may be generated at early contracting epoch, with mild fine-tuning ensuring that the scalar spectral tilt n S and tensor-to-scalar ratio r are consistent with observations. The smallness of r is governed by the smallness of the scalar sound speed. Arbitrarily small values of r are forbidden in our setup because of the strong coupling in the past. Nevertheless, we show that it is possible to generate perturbations in a controllable way, i.e. in the regime where the background evolution and perturbations are legitimately described within classical field theory and weakly coupled quantum theory.

We consider the issue of stability at the linearized level for static, spherically symmetric wormhole solutions within a subclass of scalar-tensor theories of beyond Horndeski type. In this class of theories we derive a set of stability conditions ensuring the absence of ghosts and both radial and angular gradient instabilities about a static, spherically-symmetric background. This set of constraints extends the existing one and completes the stability analysis for high energy modes in both parity odd and parity even sectors, while "slow" tachyonic instabilities remain unconstrained. We give an example of beyond Horndeski Lagrangian admitting a wormhole solution which complies with all stability constraints for the high energy modes.

The geometric concept of geodesic completeness depends on the choice of the metric field or “metric frame”. We develop a frame-invariant concept of “generalised geodesic completeness” or “time completeness”. It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave functions for particles with varying mass permit the derivation of generalised geodesics and the associated notion of completeness. Time completeness involves aspects of particle physics and is no longer a purely geometric concept.

The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of physical time defined by counting oscillations for some physically allowed process. Oscillating solutions of wave functions for particles with varying mass permit the derivation of generalised geodesics and the associated notion of completeness. Time completeness involves aspects of particle physics and is no longer a purely geometric concept.

We construct a concrete model of Horndeski bounce with strong gravity in the past. Within this model we show that the correct spectra of cosmological perturbations may be generated at early contracting epoch, with mild fine-tuning ensuring that the scalar spectral tilt $n_S$ and tensor-to-scalar ratio r are consistent with observations. The smallness of r is governed by the smallness of the scalar sound speed. Arbitrarily small values of r are forbidden in our setup because of the strong coupling in the past. Nevertheless, we show that it is possible to generate perturbations in a controllable way, i.e. in the regime where the background evolution and perturbations are legitimately described within classical field theory and weakly coupled quantum theory.

In scalar-tensor Horndeski theories, nonsingular cosmological models—bounce and genesis—are problematic because of potential ghost and/or gradient instabilities. One way to get around this obstacle is to send the effective Planck mass to zero in the asymptotic past (“strong gravity in the past”). One may suspect that this feature is a signal of a strong coupling problem at early times. However, the classical treatment of the cosmological background is legitimate, provided that the strong coupling energy scale remains at all times much higher than the scale associated with the classical evolution. We construct various models of this sort, namely (i) bouncing Universe which proceeds through inflationary epoch to kination (expansion within general relativity, driven by massless scalar field); (ii) bouncing Universe with kination stage immediately after bounce; (iii) combination of genesis and bounce, with the Universe starting from flat space-time, then contracting and bouncing to the expansion epoch; (iv) “standard” genesis evading the strong coupling problem in the past. All these models are stable, and perturbations about the backgrounds are not superluminal.

In scalar-tensor Horndeski theories, non-singular cosmological models - bounce and genesis - are problematic because of potential ghost and/or gradient instabilities. One way to get around this obstacle is to send the effective Planck mass to zero in the asymptotic past ("strong gravity in the past"). One may suspect that this feature is a signal of strong coupling problem at early times. However, the classical treatment of the cosmological background is legitimate, provided that the strong coupling energy scale remains at all times much higher than the scale associated with the classical evolution. We construct various models of this sort, namely (i) bouncing Universe which proceeds through inflationary epoch to kination (expansion within GR, driven by massless scalar field); (ii) bouncing Universe with kination stage immediately after bounce; (iii) combination of genesis and bounce, with the Universe starting from flat space-time, then contracting and bouncing to the expansion epoch; (iv) "standard" genesis evading the strong coupling problem in the past. All these models are stable, and perturbations about the backgrounds are not superluminal.

A bstract We consider DHOST Ia theory interacting gravitationally with an additional conventional scalar field minimally coupled to gravity. At the linearized level of perturbations about cosmological background, we find that in the presence of a slowly rolling extra scalar field, one of the modes generically propagates at superluminal speed. This result is valid for any stable cosmological background. We identify a subclass of DHOST Ia theories in which this superluminality property is absent, and all modes may propagate (sub)luminally. We discuss possible implications for the interacting DHOST Ia theories.

A bstract Genesis within the Horndeski theory is one of possible scenarios for the start of the Universe. In this model, the absence of instabilities is obtained at the expense of the property that coefficients, serving as effective Planck masses, vanish in the asymptotics t → −∞ , which signalizes the danger of strong coupling and inconsistency of the classical treatment. We investigate this problem in a specific model and extend the analysis of cubic action for perturbations (arXiv:2003.01202) to arbitrary order. Our study is based on power counting and dimensional analysis of the higher order terms. We derive the latter, find characteristic strong coupling energy scales and obtain the conditions for the validity of the classical description. Curiously, we find that the strongest condition is the same as that obtained in already examined cubic case.