Dragging of inertial frames by matter and waves

In this paper, we review and analyze four specific general-relativistic problems in which gravitomagnetism plays an important role: the dragging of magnetic fields around rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves. We demonstrate how the quantum detection of inertial frame dragging can be accomplished by using the Unruh–DeWitt detectors. Finally, we shall briefly show how “instantaneous Machian gauges” can be useful in the cosmological perturbation theory.

Enlightening the CSL model landscape in inflation

We propose a novel realization for the natural extrapolation of the continuous spontaneous localization (CSL) model, in order to account for the origin of primordial inhomogeneities during inflation. This particular model is based on three main elements: (i) the semiclassical gravity framework, (ii) a collapse-generating operator associated to a relativistic invariant scalar of the energy-momentum tensor, and (iii) an extension of the CSL parameter(s) as a function of the spacetime curvature. Furthermore, employing standard cosmological perturbation theory at linear order, and for a reasonable range within the parameter space of the model, we obtain a nearly scale invariant power spectrum consistent with recent observational CMB data. This opens a vast landscape of different options for the application of the CSL model to the cosmological context, and possibly sheds light on searches for a full covariant version of the CSL theory.

Backreaction in Cosmology

In this review, we investigate the question of backreaction in different approaches to cosmological perturbation theory, and with a special focus on quantum theoretical aspects. By backreaction we refer here to the effects of matter field or cosmological inhomogeneities on the homogeneous dynamical background degrees of freedom of cosmology. We begin with an overview of classical cosmological backreaction which is ideally suited for physical situations in the late time Universe. We then proceed backwards in time, considering semiclassical approaches such as semiclassical or stochastic (semiclassical) gravity which take quantum effects of the perturbations into account. Finally, we review approaches to backreaction in quantum cosmology that should apply to the very early Universe where classical and semiclassical approximations break down. The main focus is on a recently proposed implementation of backreaction in quantum cosmology using a Born–Oppenheimer inspired method.

Gauge invariant perturbation theory via homotopy transfer

We show that the perturbative expansion of general gauge theories can be expressed in terms of gauge invariant variables to all orders in perturbations. In this we generalize techniques developed in gauge invariant cosmological perturbation theory, using Bardeen variables, by interpreting the passing over to gauge invariant fields as a homotopy transfer of the strongly homotopy Lie algebras encoding the gauge theory. This is illustrated for Yang-Mills theory, gravity on flat and cosmological backgrounds and for the massless sector of closed string theory. The perturbation lemma yields an algorithmic procedure to determine the higher corrections of the gauge invariant variables and the action in terms of these.

Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

We construct an approximate solution to the cosmological perturbation theory around Einstein–de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the metric, from which follows that the model density forms an infinite, cubic lattice. To verify the convergence of the perturbative construction, we express the resulting metric as a polynomial in the perturbative parameter and calculate the exact Einstein tensor. In our model, it seems that physical quantities averaged over large scales overlap with the respective Einstein–de Sitter prediction, while local observables could differ significantly from their background counterparts. As an example, we analyze the behavior of the local measurements of the Hubble constant and compare them with the Hubble constant of the homogeneous background model. A difference between these quantities is important in the context of a current Hubble tension problem.

One-loop corrections to the primordial tensor spectrum from massless isocurvature fields

We study one-loop corrections to the two-point correlation function of tensor perturbations in primordial cosmology induced by massless spectator matter fields. Using the Schwinger-Keldysh formalism in cosmological perturbation theory, we employ dimensional regularization and cutoff regularization to study the finite quantum corrections at one-loop arising from isocurvature fields of the massless scalar, fermion and abelian gauge field which are freely propagating on the FRW spacetime. For all cases, we find a logarithmic running of the form $$ \frac{C}{q^3}\frac{H^4}{M_p^4} $$ C q 3 H 4 M p 4 log $$ \left(\frac{H}{\mu}\right) $$ H μ where C is a negative constant related to the beta function, H is the Hubble parameter at horizon exit and μ is the renormalization scale.