Program

We come back on the dynamical properties of k-essential cosmological models and show how the interesting phenomenological features of those models are related to the existence of boundaries in the phase surface. We focus our attention to the branching curves where the energy density has an extremum and the effective speed of sound diverges. We dis- cuss the behaviour of solutions of a general class of cosmological models exhibiting such curves and give two possible interpretations; the most interesting possibility regards the arrow of time that is reversed in trespassing the branching curve. This study teaches to us something new about general FLRW cosmologies where the fluids driving the cosmic evolution have equations of state that are multivalued functions of the energy density and other thermodynamical quantities.

A review of the Scale Invariant Vacuum (SIV) idea will be presented as related to Weyl Integrable Geometry [1]. The main results related to SIV and inflation [2], the growth of the density fluctuations [3], and the application of the SIV to scale-invariant dynamics of Galaxies, MOND, Dark Matter, and the Dwarf Spheroidals [4] will be highlighted.

A longstanding issue is the equivalence between the Jordan and the Einstein frames. Our aim is to tackle this problem from the perspective of the Hamiltonian formalism. For this reason, we will perform the Hamiltonian analysis of the Brans-Dicke theory with Gibbons-Hawking-York boundary term both in the Jordan and the Einstein frames. We will analyze the two cases $\omega\neq-\frac{3}{2}$ and $\omega=-\frac{3}{2}$. We will perform Dirac?s constraint analysis.

The case $\omega\neq-\frac{3}{2}$ [1] exhibits four secondary first class constraints, in the Jordan frame, which have the same constraint algebra as Einstein?s geometro-dynamics. The Weyl (conformal) transformations from the Jordan to the Einstein frame result not to be a (Hamiltonian) canonical transformations. We found a set of canonical transformations which correspond to the strong gravity limit (Carrolian gravity).

Many of these features continue to hold also for the case $\omega=-\frac{3}{2}$ [2]. The main difference, respect to the previous case, is that now the theory has a Weyl (conformal) invariance. This invariance generates a further secondary first class constraint, besides the four secondary first class constraints due to diffeomorphism invariance. The constraint algebra of the secondary five first class constraints is now different in the two frames. This addresses a mathematical inequivalence of the two frames also at classical level. Anyway, the Poisson brackets are defined on the extended phase space where the constraints are not necessarily zero.

We will examine a particular case of a flat FLRW Brans-Dicke [3] mini-superspace model and show that the equations of motions in the Jordan and the Einstein frames are equivalent once the Dirac?s constraints are taken in consideration. This suggests that the same could be true also in the general case of the Hamiltonian Brans-Dicke theory.

I will discuss construction of coherent states in quantum electrodynamics and linearized gravity within the framework of BRST quantization. It will be demonstrated that the field created by an external classical source can be consistently described as a coherent state of the gauge field built around the vacuum of the source-free theory. Implementation of this idea for the case of the cosmological constant amounts to building de Sitter space as a BRST invariant coherent state on top of the Minkowski vacuum.

I will present a brief review of Hubble tension. One way to ameliorate this tension is Early Dark Energy (EDE), which reduces the sound horizon at decoupling, resulting in a larger value of the Hubble constant $H_0$, as inferred from the cosmic microwave background (CMB). Afterwards, I will present a compelling unified model of dark energy and early dark energy (EDE), using a scalar field with a simple exponential runaway potential, in the context of $\alpha$-attractors. I will put emphasis put on concrete predictions of both EDE and dark energy to be tested in the near future, e.g. by the EUCLID or Nancy Grace Roman satellites. This talk is based on [1].

Differing measurements of the expansion rate of the universe have given rise to an observational dilemma in cosmology commonly referred to as the Hubble tension. A possible solution is provided by the model of New Early Dark Energy (NEDE) [1,2,3]. Here, a scalar field’s false vacuum energy plays the role of an early dark energy component that leads to a short repulsive boost close to matter-radiation equality before it decays through a fast, triggered first-order phase transition. I will discuss the phenomenology of NEDE highlighting the role of the trigger mechanism and compare the model to its competitors in the literature.

I will discuss the possibility that the Hubble tension is the signature of a phase transition in the dark sector. Such a phase transition is called New Early Dark Energy (NEDE) and must have taken place just before recombination at the eV scale to resolve the tension fully. After discussing the cosmological NEDE phase transition, I will discuss the details of possible particle physics realizations.

First-order phase transitions can leave relic pockets of false vacua and their particles, that manifest as macroscopic Dark Matter. We compute one predictive model: a gauge theory with a dark quark relic heavier than the confinement scale. During the first-order phase transition to confinement, dark quarks remain in the false vacuum and get compressed, forming Fermi balls that can undergo gravitational collapse to stable dark dwarfs (bound states analogous to white dwarfs) near the Chandrasekhar limit, or to primordial black holes [1]. If time allows, I mention other related works [2].

The acceleration of the expansion of the Universe has no clear explanation yet. Dynamical explanations are not ruled out yet and will be tested in the near future by large scale galaxy surveys. In this talk, we will assume that large scale features can be described effectively by scalar fields and ask the question: could be envisage to detect their influence locally by direct experiments. This is only plausible if screening mechanisms are at play. We will use the example of the unexpected Xenon1T "signal" to describe what screened light scalar fields could imply for direct detection.

In this talk dynamics of the massive minimally coupled scalar field theory in an expanding Friedmann–Lemaître–Robertson–Walker universe is considered. Employing Schwinger-Keldysh diagrammatic technique, infrared loop corrections to the occupation number and anomalous quantum average of the scalar field are computed, and it is shown that these corrections are growing with time. Using these observations, it will be demonstrated that the regularized stress-energy tensor at the distant future acquires substantial quantum corrections which exceed the long known tree-level contributions to the particle flux [1], [2].

The so-called “separate-universe” (SU) approach aims to provide an effective description of cosmological perturbations at large scales [1]. The gauge prescriptions of general relativity are often transposed in SU in order to derive some results valid at large scales, such as the stochastic noise arising from quantum fluctuations [2].

In this talk, we will show that such a procedure for fixing gauges in SU may lead to some results that differ from the full general-relativistic description [3]. We will introduce a geometrical framework in the Hamiltonian framework that may be relevant for obtaining a correct gauge-fixing procedure and a gauge-invariant formulation of the SU approach.

Nearly scale-invariant, Gaussian and adiabatic scalar perturbations from quantum mechanical origin have been extensively tested using CMB and LSS data. Effective field theories aim at providing a systematic way to consider extensions to this adiabatic evolution, incorporating the knowledge of unknown physics in a parametrically controlled manner. In order to grasp the implications of some hidden sector at the quantum level, the formalism needs to incorporate non-unitary effects such as dissipation and decoherence [1]. To achieve this goal, master equations can be a valuable tool. Ubiquitous in quantum optics where they describe the effects of an almost unspecified environment on the evolution of measurable degrees of freedom [2], they rely on assumptions that do not straightforwardly extend to cosmology where the background is dynamical, the Hamiltonian time-dependent and the environment out-of-equilibrium. In this talk, I will present their implementation in cosmology [3] and benchmark their efficiency on solvable models.

At the present state-of-the-art, the simplest inflationary models, based either on scalar fields in General Relativity or on modified $f(R)$ gravity, which produce the best fit to all existing observational data, require only one dimensionless parameter to be taken from observations. These models include the pioneer $R+R^2$ one [1], the Higgs model, and the mixed $R^2$-Higgs model which has been shown to be effectively one-parameter, too. They predict scale-free and close to scale-invariant power spectra of primordial scalar perturbations and gravitational waves generated during inflation. Their target prediction for the tensor-to-scalar ratio is $r=3(1-n_s)^2 = 0.004$, that is still about one order of magnitude less than the present upper bound. Still future observations, in particular the discovery of primordial black holes, may prove that the primordial scalar power spectrum has additional local peaks and depressions that requires at least two new parameters. I discuss mechanisms to produce such features including the recently proposed one which arise in many-field inflation with a large non-minimal kinetic term of an inflaton field leaving inflation before its end [2]. In this case, in addition to PBHs, large peaks in the primordial tensor perturbation spectrum at small scales are generated, too, in the second order of scalar perturbations. As for local non-scale-free features at cosmological scales suggested by features in the CMB temperature anisotropy for l = 2 and in the range l = 20-30, the total present CMB data including CMB polarization do not favor them, but are not able to exclude them completely [3].

Genesis is an alternative to inflation that can solve the horizon problem [1,2]. In this scenario, the cosmological expansion does not start from the Big Bang, but from Minkowski space. This can be realized in the framework of gravitational theories that allow a strong effective NEC violation [3]. We consider Palatini scalar -tensor theory with a kinetic coupling of the scalar to the Ricci tensor, which ensures NEC violation in situations where Einstein’s theory predicts singular behavior [4]. This model has an Einstein frame in which the scalar is just minimally coupled to gravity [5]. The physical (Jordan) frame of the theory is related to the Einstein frame by invertible disformal transformations that can be solved algebraically for diagonal metrics, such as FRW cosmological models or static spherically symmetric spacetime. The cosmological solution can be constructed analytically and exhibits Genesis type behavior instead of a cosmological singularity. This theory also predicts wormholes instead of black holes in a static spherically symmetric sector [6].

Perturbations generated during inflation are Gaussian with good approximation and deviations from Gaussianities are typically computed using in-in perturbation theory. However, this method is not reliable for unlikely events on the tail of the probability distribution since non-Gaussianities become important. In this talk I will present a way to access this regime with semiclassical methods from [1]: The wavefunction of the Universe can be calculated in the saddle-point approximation in Euclidean space. I will apply this technique to some models of Inflation and connect our results to the calculation of the abundance of primordial black holes.

A rich particle content during inflation is a natural, well motivated outcome of many theories Beyond the Standard Model of particle physics. In this regard, fields known as axions and spin-1 gauge fields may all populate the inflationary zoo. In the presence of axion-gauge field interactions, the classical roll of axion's can “lift” the gauge field fluctuations and enhance their amplitude, leading to an array of interesting signatures in the observable scalar and tensor sector of the theory at both CMB and sub-CMB scales. In this talk, focusing on representative models, I will introduce some exciting imprints of axion-gauge field dynamics during inflation including the generation of scale dependent (chiral) stochastic gravitational wave background (SGWB) of non-vacuum origin and primordial black hole populations. In passing, putting attention on the implementation of a scenario that can generate interesting GW signals at CMB scales, I will discuss theoretical and state of the art observational constraints (by Planck and Bicep/Keck 2018 data releases) on the parameter space of axion-gauge field dynamics during inflation.

I will discuss a framework of natural inflation within supergravity dubbed `inflation by supersymmetry breaking’. The main idea is to identify the inflaton with the superpartner of the goldstino, in the presence of a gauged R-symmetry that may contain the R-parity of the supersymmetric Standard Model.

In this talk I’ll review recent developments in the measurements of intergalactic magnetic fields in the voids of large scale structure with gamma-ray telescopes and by ultra-high energy cosmic ray detectors. In particular, I'll show that the gamma-ray measurement method can be used to detect the primordial magnetic field with a strength of up to $10^{-11}$ G, values interesting for reducing H0 tension. Same magnetic field, if produced at QCD phase transition can be responsible for NANOGrav gravitational wave signal. Also I’ll discuss how one can distinguish magnetic field produced at inflation by simultaneous measurements of extended emission around several nearby TeV blazars. Finally, I'll show upper limit on magnetic field in the void of large scale structure from ultra-high energy cosmic ray measurement in the direction of Perseus-Pisces supercluster.

MS-02 might have discovered in its data a few anti-helium events. To illustrate how problematic these would be, should they be confirmed, we have updated the calculation of the anti-helium cosmic ray fluxes at the Earth from secondary origin. We show that spallation from primary hydrogen and helium nuclei onto the interstellar medium yields an anti-He-3 flux typically one to two orders of magnitude below the sensitivity of AMS-02 after 5 years, and an anti-He-4 flux roughly 5 orders of magnitude below AMS sensitivity. I will present how these secondary anti-helium fluxes have been derived.

I will also comment upon the difficulties of the annihilating dark matter explanation and discuss a recent and exciting proposal.

Then, playing the devil's advocate, I will contemplate the possibility of anti-matter domains in our Galaxy and discuss the constraints set on them by gamma-ray observations. From a theoretical perspective, the presence of anti-matter in the early Universe also raises insuperable problems. I will conclude by a recap of the standard cosmological vision.

Independent pieces of astronomical data, indicating to noticeable population of our Galaxy by different kind of antimatter, are reviewed, in particular, observations of cosmic positrons, antinuclej and possibly antistars. A old model which leads to prediction of all these phenomena is described.

he tentative detection of a few anti-Helium nuclei [1] is presently revitalizing the discussion on the existence of baryonic antimatter in the Universe. As "the discovery of a single anti-helium nucleus in the cosmic ray flux would definitely point toward the existence of stars and even of entire galaxies made of anti-matter" [2] it has been proposed that the anti-Helium nuclei could originate from anti-clouds or anti-stars in the solar vicinity [3].

We discuss possible entities of antimatter in the Universe that would be probed through ordinary matter, with annihilation-radiation providing indirect evidence for their presence [4]. The observations of high energy ($\sim$ 100 MeV) gamma-rays sets limits on the fraction of nuclear antimatter contained in our local and Galactic neighborhood. Redshifted annihilation radiation, measured in the MeV range, constrains matter-antimatter domain boundaries in the dense early Universe. If matter-antimatter domains existed prior to recombination, annihilations at domain interfaces should have left their signature as distortions of the Planckian spectrum of the Cosmic Microwave Background. We review recent gamma-ray [5] and and sub-mm observation that set stringent upper limits on those emissions.

The gradient expansion is a very useful approximation that allow us to study the long wavelength limit of inflationary inhomogeneities in a non-perturbative (in terms of their amplitude) way , however, the initial conditions for the inhomogeneities are not well defined in this approach. In this talk I will show how the stochastic approach of inflation solves this problem by introducing noises to the equations of motion of gradient expansion [1].

Probing dark energy with gravitational waves distances} Cosmological distances provide a powerful tool to test the evolution of the Universe since they depend directly on its dynamics. However, the distances we measure are always inferred through the detection of a signal, whether an electromagnetic one or a gravitational wave, hence they also depend on its propagation history and the theory of gravity considered. For instance, in scalar-tensor theories of gravity aimed at modeling dark energy, gravitational waves can suffer extra damping while propagating which affects our distance inference, while photons dynamics is left unaffected. With the aim of testing these alternative dark energy proposals, in this talk I will describe how gravitational waves luminosity and angular diameter distances change, though preserving the distance-duality relation, in the subset of scalar-tensor theories where they propagate at the speed of light. I will also show how it is possible to detect dark energy scalar field fluctuations by exploiting the difference between electromagnetic and gravitational signals. Finally, I will discuss the detectability of the scalar wave in light of screening mechanism, feature of all viable scalar-tensor theories which suppresses the fifth force carried by the scalar field in high density regions where General Relativity has passed every test performed.

Primordial scalar perturbations are always considered as a source in the study of large-scale structures. Being the dominant ones at first order in perturbation theory, they have also encouraged the study of generation of second order gravitational waves from them. We seek to investigate the opposite effect, i.e. if gravitational waves can have an observable contribution on the matter power spectrum in the second order. For this, we consider gravitational waves with broken scale-invariance, which happens in some models of inflation. Our results are positive about having a significant effect, and we notice a crucial characteristic of this new effect, unlike the standard matter perturbation, it does not induce CMB temperature anisotropy on the large scales, although on smaller scales it can be said that it mimics the linear one.

Primordial black holes, which could form in the early universe, before the stars were born, can make up all or part of dark matter. They can also account for some of the observed gravitational wave signals, can provide seeds of supermassive black holes, and can contribute to synthesis of heavy elements by disrupting neutron stars. I will review the formation scenarios [1,2], astrophysical manifestations [3], and the ongoing search for primordial black holes [4].

We define `third derivative' General Relativity, by promoting the integration measure in Einstein-Hilbert action to be an arbitrary $4$-form field strength. We project out its local fluctuations by coupling it to another $4$-form field strength. This ensures that the gravitational sector contains only the usual massless helicity-2 propagating modes. Adding the charges to these $4$-forms allows for discrete variations of the coupling parameters of conventional General Relativity: $G_N, \Lambda, H_0$, and even $\langle {\tt Higgs }\rangle$ are all variables which can change by jumps. Hence de Sitter is unstable to membrane nucleation. Using this instability we explain how the cosmological constant problem can be solved.

We study 1-loop corrections to the primordial stochastic background of gravitational waves produced during inflation. While in single-clock, at the leading order in slow-roll, quantum corrections keep the amplitude scale-free this is not the case when the pattern of symmetry breaking is different. In particular, when spatial diffeomorphisms are also broken during inflation as for solid inflation, a log-running in the external momentum is generated.

I will give an overview of different line of sight effects that are expected to distort a gravitational wave signal emitted by an astrophysical source at cosmological distance. I will in particular focus on kinematic effects due to the motion of the source with respect to the observer rest frame. I will show that (the components of) peculiar velocities transverse to the line of sight give a bias in the reconstruction of both wave polarisations and source position. I will present forecasts for current and next generation gravitational wave detectors.

Effective potentials of a few scalar-tensor gravity models are considered. The structure of the scalar field potential induced by loop corrections is studied. Our aim is to look for possibilities to get modified gravity models (e.g. Horndeski theories) from minimal scalar-tensor actions based on some symmetry assumptions. For the minimal model without self-interactions of the scalar field at the tree level, we get the set of operators providing the leading contribution and preserving the second order of field equations [1].

One-loop effective potential of scalar-tensor gravity with a quartic scalar field self-interaction is evaluated up to the first post-Minkowskian order [2]. The potential develops an instability in the strong-field regime as expected for an effective theory. Depending on model parameters the instability region can be pushed exponentially far in the strong field region. For a specific model with non-linear symmetry realization, it is shown that loop corrections lead to the appearance of anomalous terms which do not preserve the symmetries of the initial Lagrangian [3]. It is shown that such models have room for a natural inflation similar to the well-known case of the Starobinsky inflation. The possibility to have screening of the Lambda term due to loop corrections is also discussed.

We present a simple class of mechanical models where a canonical degree of freedom interacts with another one with a negative kinetic term, i.e., with a ghost. We prove analytically that the classical motion of the system is completely stable for all initial conditions, notwithstanding that the conserved Hamiltonian is unbounded from below and above. This is fully supported by numerical computations. Systems with negative kinetic terms often appear in modern cosmology, quantum gravity, and high energy physics and are usually deemed as unstable. Our result demonstrates that for mechanical systems this common lore can be too naive and that living with ghosts can be stable.

An inflation scenario in the observable sector of heterotic M-theory is reviewed. The particle spectrum of a consistent anomalous $U(1)$ hidden sector is presented. The masses of the hidden sector spectrum and Kahler moduli are analyzed, as well as their interactions with themselves and with fields in the observable sector. The possible role of hidden sector particles and moduli as dark matter is discussed.

We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modeled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution for a 1-dimensional perturbation. We study how these models are affected by small anisotropic perturbations within the BIX potential. For the spherical collapse case, we found that the model is equivalent to a closed FLRW Universe filled with matter and two perfect fluids representing the anisotropic contributions. From the linear evolution up to the turnaround, the anisotropies effectively shift the value of the FLRW spatial curvature, because the fluids have effective Equation of State (EoS) parameters $w \approx 1/3$. Then we estimate the impact of such anisotropies on the number density of haloes using the Press-Schechter formalism. If a fluid description of the anisotropies is still valid after virialization, the averaged over time EoS parameters are $w\approx1/3$. Using this and demanding hydrostatic equilibrium, we find a relation between the mass $M$, the average radius $R$ and the pressure $p$ of the virialized final structure. When we consider perturbations of the Zeldovich solution, our qualitative analysis suggests that the so called pancakes exhibit oscillatory behavior, as would be expected in the case of a vacuum BIX spacetime.

Motivated by the correspondence between the Relativistic Zel’dovich Approximation (RZA) and Szekeres exact solutions [1], we propose a generalization of RZA that includes the entire Szekeres family. In contrast with RZA, which retains a global cosmological background, the proposed scheme contains a space-dependent scale factor, resulting from a Friedmann-like reference model. The overall approach is then interpreted as the evolution of a deformation field on the reference model. This method, by construction, contains the most relevant exact cosmological solutions as particular cases. We implement illustrative numerical examples and estimate the error from the violation of the constraint equations.

In my talk I will present some of the constituents of the modern cosmology, the structure formation process [1] and the spatial curvature estimates (2], focusing on the methods of modelling gravitational instability evolution and calculating its statistical outcome. These formalisms are based on the Buchert scalar averaging formalism, with the Zel'dovich approximation serving as a closure condition and the silent universe models (Einstein equations with no rotation and no energy transfer). Both of these methods are utilizing Einstein's theory of general relativity and reveal substantial differences compared with the standard Newtonian or post-Newtonian treatments. The resulting, relativistic mass functions of galaxy clusters will be presented. Possible applications and improvements will be briefly discussed.

Cosmological data is typically analysed under the model assumptions of exact spatial homogeneity and isotropy in the space-time description of our Universe. However, such symmetries are in reality broken due to the presence of cosmic structure. I will present cosmographic strategies [1,2,3] for analysing data while remaining agnostic about the form of the metric of space-time and the determining field equations.

I will discuss standardisable objects and redshift drift signals as model-independent probes of the kinematics of our Universe. The developed frameworks allow for consistent analyses of anisotropic features in cosmological data.

The $\Lambda$CDM model implicitly assumes infiniteness of the spatial sections of our Universe. However, the observation map of the CMB temperature anisotropies presents a lack of correlation at large angular scale in the 2-point correlation function (2-pcf), i.e. beyond 60$^{\circ}$.

In my talk I shall present another CMB signature, statistical, compatible with the multi-connectedness of the universe, the $3-$torus topological manifold. In addition, this new signature $\rho$ leads to a size of our Universe of L $\sim$ 3 Hubble lengths. Also, I discuss the linearity of the law L=f($\rho$).

I shall illustrate my talk with results obtained over large ensembles of CMB simulation maps, in the infinite $\Lambda$CDM Universe model and 5 different sizes of universe with $3-$toroidal topology.

Cosmology is transitioning from a theoretical discipline towards one with increased focus on observations, resulting in a massive surge of data that demands increasingly more sophisticated methods to glean meaningful information. In a related development, geometry and topology have witnessed a tilt from purely theoretical fields towards strong focus on application. A foray into “big data” quickly brings to front two of the central statistical challenges of our times – detection and classification of structure in extremely large, high-dimensional, data sets. Among the most intriguing new approaches to this challenge is “TDA,” or “topological data analysis,” the primary aim of which is providing topologically informative pre-analyses of data, which serve as input to more quantitative analyses at a later stage. Algebraic and computational topology at the level of homology and persistent homology are the foundational pillars of TDA [1].

In the first part of my talk, I will a summary of the theoretical and computational aspects of topological data analysis. In the second part of the talk, I will present an analysis of the topological properties of the temperature and polarization maps of the Cosmic Microwave Background (CMB) radiation obtained by the Planck satellite. I will also discuss some of the anomalies that the temperature and polarization maps exhibit with respect to the simulations based on the standard cosmological model, which assumes the initial fluctuation field to be an instance of an isotropic and homogeneous Gaussian random field [2,3].

I will apply the Dirac procedure for constrained systems to the ADM formalism for cosmological perturbation theory in the Bianchi I universe. I will carefully discuss the issue of gauge-fixing, gauge transformations and spacetime reconstruction. I will find the so called Kuchar parametrization to be well suited for this purpose. Then I will shift my attention to the peculiarities of cosmological perturbations in anisotropic backgrounds such as the evolution of the plane wave wavefronts and the couplings between gravitational waves and matter perturbations. I will show that there exist coordinate systems in which (a polarization mode of) a gravitational wave is represented by the density metric perturbation.

I will discuss the general problem of parallax measurement in general relativity. The parallax effect can be used to define the parallax distance, one of possible distance measures to distant objects in GR. I will show how the tiny difference between the angular diameter distance and the parallax distance can be used to measure the matter content along the line of sight and how the sign of this difference is related to the null energy condition. I will also briefly discuss possible applications of these results to astrometry and cosmology. The talk is based on [1-3].

Addressing cosmological questions exclusively based on observations requires a formulation on the past lightcone of the cosmic observer. In this talk, the question of how to define gravitational energy associated with the past lightcone of a cosmic observer is studied by introducing Hawking’s quasi-local energy as a tentative energy measure of the observable Universe. The Hawking energy phenomenologically quantifies energy in terms of light bending. This talk will mainly focus on the relation of the Hawking energy to cosmological observables within linear perturbation theory on an FLRW background.

Universe heating in $R^2$ gravity is studied. It is shown that the energy density of matter drops down with time much slower than in conventional cosmology. This reopens the possibility for SUSY-type particles with very high masses to form cosmological dark matter. The concrete results depend upon the dominant decay mode of the scalaron.

Black Holes of primordial origin (PBHs) can constitute a large fraction of dark matter (DM) in the Universe. If light enough, they can emit a sizeable amount of Hawking radiation, which may be detected by dark matter experiments and be used to set constraints on the fraction of PBHs as DM components. In this talk, I will present and discuss constraints on Hawking radiation of PBHs, in the context of general standard spinning black holes, as well as for non-standard black holes with extra-dimensions or arising from loop quantum gravity. I will also present the BlackHawk program, which is an open-source code to compute Hawking radiation for different black hole models.}

Primordial black holes are black holes that may have formed in the early Universe. In principle, they could exist on a large mass range — from as low as the Planck scale up to many orders of magnitude above the solar mass. They could account for dark matter as well as provide seeds for supermassive black holes in galactic centres. Even though not confirmed yet, there are numerous hints for their existence. Numerous are also their proposed formation scenarios, most of which suffer from strong coupling and (exponential) fine tuning. After an introduction and a general discussion on primordial black holes, I will elaborate on one particular mechanism which is not affected by those issues. Here, primordial black hole formation is induced by confinement of heavy quarks. I will discuss phenomenological features of the new mechanism.

This talk is based on Reference [1] (see also References [2, 3] for recent reviews on primordial black holes).

The spectacular discovery of gravitational waves provides a strong impetus to understand black hole binary systems. Being intrinsically relativistic, these systems destroy the simplicity of the starting point in classical mechanics, the Kepler problem. Our aim will be to investigate relativistic corrections in a more general setting that involves charged black holes. The inclusion of a scalar field (originally introduced by Nordstrom) allows one to violate the no-hair theorem. We will discuss how the relativistic corrections can cancel out in this system, thus regaining the simplicity (and analytical traction) of the Kepler problem while describing black holes.

We will point out the importance of the quantum nature of the gravitational interaction with matter in a linearized theory of quantum gravity induced entanglement of masses (QGEM). We will show how the quantum interaction entangles the steady states of a closed system (eigenstates) of two test masses placed in the harmonic traps, and how such a quantum matter-matter interaction emerges from an underlying quantum gravitational field. We will rely upon quantum perturbation theory highlighting the critical assumptions for generating a quantum matter-matter interaction and showing that a classical gravitational field does not render such an entanglement. We will consider two distinct examples; one where the two harmonic oscillators are static and interact via an exchange of a virtual spin-2 and spin-0 components of the graviton, and the other where the harmonic oscillators are non-static and interact with a virtual graviton corresponding to the gravitational wave beside the static components of the graviton propagator. The quantum nature of the gravitons interacting with the harmonic oscillators are responsible for creating an entangled state with the ground and the excited states of harmonic oscillators as the Schmidt basis. We will compute the concurrence as a criterion for the above entanglement and compare the two ways of entangling the two harmonic oscillators.

The extra-dimensional paradigm facilitates a solution to a variety of problems and plays a significant role in the modern physics and cosmology. The inhomogeneous extra dimensions widen capabilities of this idea. In this talk I discuss evolution of D-dimensional space from the sub-Planckian energies down to the electroweak scale and lower; the relation between the main cosmological parameters and a metric of extra space; role of scalar field distribution inside extra space and its effect on the 4-dimensional observational parameters.

It is shown that an application of inhomogeneous extra dimensions points the way to solving the Hierarchy problem. The set of such metrics has the cardinality of the continuum and contains metrics that satisfy observational data.

We review the concept of purely virtual particle, or “fakeon", based on a new diagrammatics, and its uses in quantum gravity, primordial cosmology and collider physics. Quantum gravity propagates the graviton, a massive scalar field (the inflaton) and a massive spin-2 fakeon, and leads to a constrained primordial cosmology, which predicts the tensor-to-scalar ratio $r$ in the window $0.4 \stackrel{<}{\sim} 1000r \stackrel{<}{\sim} 3.5$. The interpretation of inflation as a cosmic RG\ flow allows us to calculate the perturbation spectra to high orders in the presence of the Weyl squared term. In models of new physics beyond the standard model, fakeons evade various phenomenological bounds. The fakeon mass is the scale of the violation of microcausality, while the fakeon width is the “peak uncertainty", which reveals that it is impossible to get too close to the fakeon peak.

The neutron lifetime problem (the dependence of the lifetime on the measurement method) can be explained by the neutron $n$ mixing with a sterile neutron $n'$ from dark mirror sector. I discuss implications of $n-n'$ mixing for neutron stars and for the gravitational mergers in the neutron star binaries.

We review some results about the consistent interactions of massless, partially massless and massive spin-2 fields in maximally-symmetric spacetimes. We also consider the possible couplings of these fields to a multiplet of vector fields.

It has been argued recently that black hole properties are not specific to gravity but rather are universal for class of objects, called saturons, that saturate a certain universal upper bound on the microstate degeneracy. This bound sets a maximal entropy permitted by unitarity. In this talk we show that saturons appear in a simple calculable model of Gross-Neveu. We show that saturated bound states in this theory share all the properties that are ordinarily attributed to black holes. In particular, they carry the area-law entropy, evaporate thermally ala Hawking, exhibit the Page's time of information retrieval and saturate unitarity in scattering amplitudes. These findings shed very different light on black holes, indicating that their properties originate from universal phenomenon of saturation that goes far beyond gravity.

In this talk, based on [1], I will argue that black holes admit vortex structure. This is based both on a graviton-condensate description of a black hole as well as on a correspondence between black holes and generic objects with maximal entropy compatible with unitarity, so-called saturons. Due to vorticity, a Q-ball-type saturon of a calculable renormalisable theory obeys the same extremality bound on the spin as the black hole. Correspondingly, a black hole with extremal spin emerges as a graviton condensate with vorticity. Next, I will comment on the possible phenomenological consequences.

Primordial black holes (PBHs) with a wide mass distribution imprinted by the thermal history of the Universe, which naturally produces a high peak at the solar mass scale, could explain the gravitational-wave events seen by LIGO/Virgo and up to the totality of the dark matter. We show that compared to monochromatic or log-normal mass functions, the gravitational wave backgrounds (GWBs) from early PBH binaries and from late binaries in clusters are strongly enhanced at low frequency and could even explain the NANOGrav observations. This enhancement comes from binaries with very low mass ratios, involving solar-mass and intermediate-mass PBHs at low frequency, solar-mass and subsolar-mass at high frequency. LISA could distinguish the various models, while in the frequency band of ground-based detectors, we find that the GWB from early binaries is just below the current LIGO/Virgo limits and above the astrophysical background, if they also explain black hole mergers. The GWB from binaries in clusters is less boosted but has a different spectral index than for neutron stars, astrophysical black holes or early PBH binaries. It is detectable with Einstein Telescope or even with the LIGO/Virgo design sensitivity [1].

Primordial Black Holes (PBHs) are a fascinating candidate for the dark matter in the universe. We discuss about their formation in the early universe and focus on their possible detectability at present and future gravitational-wave experiments.

Adopting a spatial decomposition [1] of Faraday's (covariant) equation at the magnetohydrodynamic (MHD) limit, we bring it in a solvable form. Its solution shows that the magnetic field generally grows/decays in proportion to the inverse cube law [2] of the scale factor–associated with the continuous (volume) contraction/expansion of a highly conducting fluid. Applying the aforementioned law allows us firstly to derive the evolution formulae of (magnetized) Bianchi I spacetime; secondly, to establish a non-collapse criterion [3] predicting that magnetized gravitational contraction is impeded when the tidal tensor (electric Weyl) along the magnetic force-lines overwhelms the magnetic energy density.