We study the dynamics of Friedmann-Lema & icirc;tre-Robertson-Walker models where a dark energy component with a quadratic equation of state (EoS) nonlinearly interacts with cold dark matter. Thus, two energy scales naturally come into play: rho(*) is the scale at which the nonlinearity of the EoS becomes relevant; rho(i) is the energy scale around which the interaction starts to play an important role in the dynamics. Our focus is to understand whether there are parameter ranges for this system that can produce nonsingular bouncing and emergent cosmologies for any initial condition. We complete a dynamical systems analysis, and find the parameter range such that trajectories always expand from a high energy nonsingular de Sitter state. For flat and negative curvature models this de Sitter state is represented by a fixed point, the asymptotic past from which the Universe emerges. We find a subset of positive curvature models that during contraction get arbitrarily close to the de Sitter state, thus having a quasi-de Sitter bounce, then emerge from the bounce and expand, evolving toward spatial flatness. We find that the dimensionless parameter q equivalent to rho(*)/rho(i), which measures the relative strength of the nonlinear terms in the system, plays a crucial role in the topology of the phase space. When q < 3, some trajectories expand toward a singularity, while others evolve toward a low energy cosmological constant at late times, with a subset going through a decelerated matter dominate era before the final acceleration. When q > 3, all trajectories are nonsingular, and evolve toward a late-time cosmological constant. We find a subclass in this case in which all trajectories have at least one decelerated matter dominated phase, and accelerate at late times. Therefore, the nonlinear interacting cosmology presented here allows for a subclass of models that are singularity-free and qualitatively realistic for any initial condition.

Models of interacting dark energy (DE) and dark matter (DM) involving pure momentum exchange are a promising avenue for resolving cosmological tensions. However, the behaviour of these interactions in the theoretically challenging limit where the DE equation of state, w, approaches-1 is not fully understood. We demonstrate that a generic feature of these models is a w-dependent velocity-locking mechanism, which systematically shifts the onset of matter power spectrum suppression to smaller scales as w -> -1. The suppression magnitude depends on the difference in fluid velocities. In this limit, however, the interaction's drag dominates over the DE pressure support and causes the DE velocity to track that of the DM fluid at larger scales. This mechanism provides a physical explanation for the weaker constraints found in the literature when w approximate to -1 in models where the interaction strength does not explicitly depend on w. We also demonstrate that the common approximation of neglecting DE perturbations (ODE = theta DE = 0) fails in this limit. By artificially increasing the velocity difference between the fluids, this simplification incorrectly removes the w-dependent velocity-locking mechanism and erases the shift in power spectrum suppression to smaller scales. This leads to an overestimation of the constraining power of cosmological data on the interaction strength.

Effects of general relativity are usually neglected in the non-linear evolution of structures, where Newtonian N-body simulations are traditionally employed. In the post-Friedmann expansion framework, a weak-field relativistic approximation purpose-built for cosmology, a frame-dragging gravito-magnetic vector potential arises at leading order, sourced by momentum currents. At this order, the vector potential contributes to the metric while leaving the dynamics of the matter fields unaffected, as it does not appear in the Euler equation. It can therefore be extracted a posteriori from standard N-body simulations, where the dynamics is purely Newtonian. Using the Delaunay Tessellation Field Estimator code on the IllustrisTNG simulations, here we extend previous work in order to compute the power spectrum of this vector potential down to galactic scales. The magnitude of the vector potential is two orders of magnitude larger than predicted by perturbation theory, and is a 1 similar to 0.1 effect compared to the non-linear Newtonian scalar gravitational potential. In the redshift range considered here, the gravito-magnetic effect remains sub-dominant, without showing any enhancement during a particular phase in the evolution of structures, aside from the continuous growth of non-linearity at low redshift. Although this seems to suggest that, within the Lambda cold dark matter model, no significant gravito-magnetic effects contribute to the non-linear evolution of cosmic structures, i.e. to the dynamics of massive particles, possible observational consequences, e.g. in lensing, deserve further exploration.

We study black hole (BH) formation from the nonlinear growth and collapse of primordial perturbations during the matter-dominated era. Modelling cold dark matter (CDM) as pressureless dust, we describe the collapse in a fully nonlinear relativistic framework using the Lemaître-Tolman-Bondi (LTB) and quasi-spherical Szekeres solutions as exact perturbations of a spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) ΛCDM background. At first order in relativistic scalar perturbation theory, the growing mode of any relevant quantity can be expressed in terms of the conserved gauge-invariant curvature perturbation ℛ_c, which acts as a potential for the 3-curvature of hypersurfaces orthogonal to the matter 4-velocity. We use this result to express the active gravitational mass and curvature functions of the LTB and Szekeres models in terms of the initial values of ℛ_c and its spatial derivatives. From these initial curvature data we derive: (i) the turn-around, collapse, and apparent-horizon formation times, and (ii) the regularity conditions required for BH formation. We show that sinusoidal and Gaussian profiles do not provide viable BH-forming channels, whereas broad compensated curvature peaks, naturally predicted by peak theory, do. We then estimate the formation times of 10^3-10^6 M_⊙ massive BH seeds produced by the direct collapse of primordial CDM curvature peaks, finding full BH formation at redshifts z>5, with core collapse beginning at 10 ≲ z ≲ 16. Finally, we characterize the local dynamics and singularity type of the collapse (point-like, cigar-like, or pancake-like) directly from the initial comoving curvature data, clarifying the role of the initial shear in selecting the collapse end-state.

The ΛCDM model provides a rudimentary but adequate description of the Universe governed by the Friedmann-Lemaˆıtre-Robertson-Walker metric. However, increasing observational precision has revealed tensions between observations and model. In particular, ΛCDM struggles to accurately explain DESI type Ia supernova observations, Cosmic-Microwave-Background anisotropies and Baryon-acoustic-oscillation distance scales; whilst it’s model of constant dark energy offers no explanation for cosmic coincidence or the Hubble tension. Therefore, in this work we model the dark energy component as an interacting affine fluid coupled across the dark sector, with dynamical and Λ-like constant components that evolve independently, naturally alleviating many of these issues. Using dynamical system theory techniques, we study the evolution of four models of linear and non-linear interactions between dark matter and energy, across a range of interaction strengths. By treating the model as an autonomous closed differential system, we redefine our model in terms of dimensionless variables that are solved using python packages, ensuring ΛCDM-like dynamics at present time via PLANCK observations as well as enhancing the dynamical freedom of the system from which evolving equations of state can be plotted. Furthermore, by analysing the system in phase space we observe natural scaling solutions as well as Fixed Point solutions that alleviate coincidence without the explicit need for fine tuned initial conditions; along with altered cosmological histories mitigating the Hubble tension. Finally, we assess the physical viability of each interaction model with parameter ranges by comparing the predicted expansion history with DESI supernova constraints and PLANCK density fraction observations. All models produce the necessary ΛCDM late time solutions whilst displaying a wide range of dynamical flexibility across expansion history that helps to reconcile the Hubble tension; therefore proving that interacting affine models of dark energy provide necessary extensions to the standard cosmological model.

Models of interacting dark energy and dark matter offer a possible solution to cosmological tensions. In this work, we examine a pure momentum-exchange model with a time-dependent coupling strength ξ(z) that could help to alleviate the S_8 tension. We perform Fisher forecasting and MCMC analysis to constrain the coupling strength of this interaction for different redshift bins 0.0<z<2.1, using the specifications of upcoming DESI-like surveys. For this analysis, we examine both a model with a constant equation of state w=-0.9, as well as a thawing dark energy model with an evolving w(z). We show that, for a constant equation of state, ξ(z) can be well constrained in all redshift bins. However, due to a weaker effect at early times, the constraints are significantly reduced at high redshifts in the case of a thawing w(z) model.

In the Emergent scenario, the Universe should evolve from a nonsingular state replacing the typical singularity of General Relativity, for any initial condition. For the scalar field model by Ellis and Maartens [Class. Quantum Grav. 21 (2003) 223] we show that only a set of measure zero of trajectories leads to emergence, either from a static state (an Einstein model), or from a de Sitter state. Assuming a scenario based on CDM interacting with a Dark Energy fluid, we show that in general flat and open models expand from a nonsingular unstable de Sitter state at high energies; for some closed models this state is a transition phase with a bounce, other closed models are cyclic. A subset of these models are qualitatively in agreement with the observable Universe, accelerating at high energies, going through a matter-dominated decelerated era, then accelerating toward a de Sitter phase.

We analyse three interacting vacuum dark energy models with the aim of exploring whether the H0 and σ8 tensions can be simultaneously resolved in such models. We present the first ever derivation of the covariant gauge-invariant perturbation formalism for the interacting vacuum scenario, and, for the sub-class of geodesic cold dark matter models, connect the evolution of perturbation variables in this approach to the familiar cosmological observables. We show how H0 and σ8 evolve in three interacting vacuum models: firstly, a simple linear coupling between the vacuum and cold dark matter; secondly, a coupling which mimics the behaviour of a Chaplygin gas; and finally a coupling which mimics the Shan–Chen fluid dark energy model. We identify, if any, the regions of parameter space which would correspond to a simultaneous resolution of both tensions in these models. When constraints from observational data are added, we show how all the models described are constrained to be close to their ΛCDM limits.

We use numerical relativity simulations to describe the spacetime evolution during nonlinear structure formation in $\Lambda$CDM cosmology. Fully nonlinear initial conditions are set at an initial redshift $z\approx 300$, based directly on the gauge invariant comoving curvature perturbation $\mathcal{R}_c$ commonly used to model early-universe fluctuations. Assigning a simple 3-D sinusoidal structure to $\mathcal{R}_c$, we then have a lattice of quasi-spherical over-densities representing idealised dark matter halos connected through filaments and surrounded by voids. This structure is implemented in the synchronous-comoving gauge, using a pressureless perfect fluid (dust) description of CDM, and then it is fully evolved with the Einstein Toolkit code. With this, we look into whether the Top-Hat spherical and homogeneous collapse model provides a good description of the collapse of over-densities. We find that the Top-Hat is an excellent approximation for the evolution of peaks, where we observe that the shear is negligible and collapse takes place when the linear density contrast reaches the predicted critical value $\delta^{(1)}_C =1.69$. Additionally, we characterise the outward expansion of the turn-around boundary and show how it depends on the initial distribution of matter, finding that it is faster in denser directions, incorporating more and more matter in the infalling region. Using the EBWeyl code [1] we look at the distribution of the electric and magnetic parts of the Weyl tensor, finding that they are stronger along and around the filaments, respectively. We introduce a method to dynamically classify different regions in Petrov types. With this, we find that the spacetime is of Petrov type I everywhere, as expected, but we can identify the leading order type, finding a transition between different types as non-linearity grows, with production of gravitational waves.

In order to invariantly characterise spacetimes resulting from cosmological simulations in numerical relativity, we present two different methodologies to compute the electric and magnetic parts of the Weyl tensor, $E_{αβ}$ and $B_{αβ}$, from which we construct scalar invariants and the Weyl scalars. The first method is geometrical, computing these tensors in full from the metric, and the second uses the 3+1 slicing formulation. We developed a code for each method and tested them on five analytic metrics, for which we derived $E_{αβ}$ and $B_{αβ}$ and the various scalars constructed from them with computer algebra software. We find excellent agreement between the analytic and numerical results. The slicing code outperforms the geometrical code for computational convenience and accuracy; on this basis we make it publicly available in github with the name EBWeyl [ https://github.com/robynlm/ebweyl ]. We emphasize that this post-processing code is applicable to numerical spacetimes in any gauge.

We explore the dynamics of FLRW cosmologies which consist of dark matter, radiation and dark energy with a quadratic equation of state. Standard cosmological singularities arise due to energy conditions which are violated by dark energy, therefore we focus our analysis on non-singular bouncing and cyclic cosmologies, in particular focusing on the possibility of closed models always having a bounce for any initial conditions. We analyse the range of dynamical behaviour admitted by the system, and find a class of closed models that admit a non-singular bounce, with early- and late-time accelerated expansion connected by a decelerating phase. In all cases, we find the bouncing models are only relevant when dark matter and radiation appear at a certain energy scale, and so require a period such as reheating. We then investigate imposing an upper bound on the dark matter and radiation, such that their energy densities cannot become infinite. We find that bounces are always the general closed model, and a class of models exist with early- and late-time acceleration, connected by a decelerating phase. We also consider parameter values for the dark energy component, such that the discrepancy between the observed value of Λ and the theoretical estimates of the contributions to the effective cosmological constant expected from quantum field theory would be explained. However, we find that the class of models left does not allow for an early- and late-time accelerated expansion, connected by a decelerating period where large-scale structure could form. Nonetheless, our qualitative analysis serves as a basis for the construction of more realistic models with realistic quantitative behaviour.

ABSTRACT In this paper, we introduce a novel class of interacting vacuum models, based on recasting the equation of state originally developed in the context of lattice kinetic theory by Shan & Chen as the coupling between the vacuum and cold dark matter (CDM). This coupling allows the vacuum to evolve and is non-linear around a characteristic energy scale ρ*, changing into a linear coupling with a typical power-law evolution at scales much lower and much higher than ρ*. Focusing on the simplest sub-class of models where the interaction consists only of an energy exchange and the CDM remains geodesic, we first illustrate the various possible models that can arise from the Shan–Chen coupling, with several different behaviours at both early and late times depending on the values of the model parameters selected. We then place the first observational constraints on this Shan–Chen interacting vacuum scenario, performing an MCMC analysis to find those values of the model and cosmological parameters which are favoured by observational data. We focus on models where the non-linearity of the coupling is relevant at late times, choosing for the reference energy scale ρ*, the critical energy density in ΛCDM. We show that the observational data we use are compatible with a wide range of models which result in different cosmologies. However, we also show that ΛCDM is preferred over all of the Shan–Chen interacting vacuum models that we study, and comment on the inability of these models to relax the H0 and σ8 tensions.

We examine the dynamics of Friedmann-Lemaitre-Robertson-Walker cosmologies in which the vacuum interacts with a perfect fluid through an energy exchange, focusing on the exploration of nonsingular configurations, including cyclic and bouncing models. We consider two specific choices for the energy transfer. In the first case, the energy transfer is proportional to a linear combination of the vacuum and fluid energy densities which makes the conservation equations exactly integrable. The resulting Friedmann equation can be interpreted as an energy constraint equation with an effective potential for the scale factor that may include an infinite barrier forcing a bounce at small values of the scale factor, as well as a potential well allowing for cycling solutions. In the second case, the energy transfer is a nonlinear combination of the vacuum and fluid energy densities. Nonetheless even in this case the dynamics can be partially integrated, leading to a first integral, reducing the number of degrees of freedom. We show that also in this nonlinear case bouncing and cycling cosmologies may arise. In both cases the structure of the resulting phase space allows for nonsingular orbits with an early accelerated phase around a single bounce, connected via a decelerated matter-dominated era to a late-time accelerated phase dominated by an effective cosmological constant.

The current cosmological probes have provided a fantastic confirmation of the standard Λ Cold Dark Matter cosmological model, which has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity, a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in part the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the 4.4σ tension between the Planck estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting models of new physics that could solve this tension and discuss how the next decade’s experiments will be crucial.

We investigate the inherently nonlinear transverse modes of the gravitational and velocity fields in ΛCDM cosmology, based on a high-resolution simulation performed using the adaptive-mesh refinement general-relativistic N -body code GRAMSES. We study the generation of vorticity in the dark matter velocity field at low redshift, providing power-law fits to the shape and evolution of its power spectrum from large sub-horizon scales to deeply nonlinear scales. By analysing the gravitomagnetic vector potential, a purely relativistic vector mode of the gravitational field that is absent in Newtonian simulations of structure formation, in dark matter haloes with masses ranging from ∼ 10 h−1M to ∼ 10 h−1M , we find that the magnitude of this vector correlates with the halo mass, peaking in the inner regions and decreasing towards their outskirts. Nevertheless, on average, its ratio against the scalar gravitational potential remains fairly constant inside the haloes, below percent level, decreasing roughly linearly with redshift at z < 3 and showing a weak dependence on halo mass. Furthermore, we show that the gravitomagnetic acceleration in dark matter haloes peaks towards the core and reaches almost 10−10 h cm/s in the most massive halo of the simulation. However, regardless of the halo mass, the ratio between the magnitudes of the gravitomagnetic force and the standard gravitational force is typically at around the 10−3 level in the innermost parts of the haloes and drops by up to one order of magnitude at the outskirts. This ratio shows a very weak dependence on redshift. This result confirms that the gravitomagnetic field has a negligible effect on cosmic structure formation, even for the most massive structures, although its behaviour in low density regions such as voids remains to be explored. In addition, its effects on photons and therefore observations remains to be understood in detail in the future.

The standard $\Lambda$ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few tensions and anomalies became statistically significant with the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension of the Planck data with weak lensing measurements and redshift surveys, about the value of the matter energy density $\Omega_m$, and the amplitude or rate of the growth of structure ($\sigma_8,f\sigma_8$). We list a few interesting models for solving this tension, and we discuss the importance of trying to fit with a single model a full array of data and not just one parameter at a time.

The standard Λ Cold Dark Matter cosmological model provides an amazing description of a wide range of astrophysical and astronomical data. However, there are a few big open questions, that make the standard model look like a first-order approximation to a more realistic scenario that still needs to be fully understood. In this Letter of Interest we will list a few important goals that need to be addressed in the next decade, also taking into account the current discordances present between the different cosmological probes, as the Hubble constant H0 value, the σ8S8 tension, and the anomalies present in the Planck results. Finally, we will give an overview of upgraded experiments and next-generation space-missions and facilities on Earth that will be of crucial importance to address all these questions.

A precise measurement of the curvature of the Universe is of prime importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early-Universe scenarios. Recent observations, while broadly consistent with a spatially flat standard A Cold Dark Matter (ACDM) model, show tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99% confidence level. While new physics could be at play, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat ACDM model. (C) 2021 Elsevier B.V. All rights reserved.

A precise measurement of the curvature of the Universe is of primeval importance for cosmology since it could not only confirm the paradigm of primordial inflation but also help in discriminating between different early Universe scenarios. The recent observations, while broadly consistent with a spatially flat standard Λ Cold Dark Matter (ΛCDM) model, are showing tensions that still allow (and, in some cases, even suggest) a few percent deviations from a flat universe. In particular, the Planck Cosmic Microwave Background power spectra, assuming the nominal likelihood, prefer a closed universe at more than 99% confidence level. While new physics could be in action, this anomaly may be the result of an unresolved systematic error or just a statistical fluctuation. However, since a positive curvature allows a larger age of the Universe, an accurate determination of the age of the oldest objects provides a smoking gun in confirming or falsifying the current flat ΛCDM model.

We perform a reconstruction of the coupling function between vacuum energy and geodesic cold dark matter using the latest observational data. We bin the interaction in seventeen redshift bins but use a correlation prior to prevent rapid, unphysical oscillations in the coupling function. This prior also serves to eliminate any dependence of the reconstruction on the binning method. We use two different forms of the correlation prior, finding that both give similar results for the reconstruction of the dark matter–dark energy interaction. Calculating the Bayes factor for each case, we find no meaningful evidence for deviation from the null interacting case, i.e. ΛCDM, in our reconstruction.