We present a phase-space analysis of the qualitative dynamics cosmologies where dark matter exchanges energy with the vacuum component. We find fixed points corresponding to power-law solutions where the different components remain a constant fraction of the total energy density and given an existence condition for any fixed points with nonvanishing energy transfer. For some interaction models we find novel fixed points in the presence of a third noninteracting fluid with constant equation of state, such as radiation, where the interacting vacuum+matter tracks the evolution of the third fluid, analogous to tracker solutions previously found for self-interacting scalar fields. We illustrate the phase-plane behavior, determining the equation of state and stability of the fixed points in the case of a simple linear interaction model, for interacting vacuum and dark matter, including the presence of noninteracting radiation. We give approximate solutions for the equation of state in matter- or vacuum-dominated solutions in the case of small interaction parameters.
We propose a large class of nonsingular cosmologies of arbitrary spatial curvature whose cosmic history is determined by a primeval dynamical $Λ(t)$-term. For all values of the curvature, the models evolve between two extreme de Sitter phases driven by the relic time-varying vacuum energy density. The transition from inflation to the radiation phase is universal and points to a natural solution of the graceful exit problem regardless of the values of the curvature parameter. The flat case recovers the scenario recently discussed in the literature (Perico et al., Phys. Rev. D88, 063531, 2013). …
In the context of Horndeski cosmologies, we consider a dynamical adjustment mechanism able to screen any value of the vacuum energy of the matter fields leading to a fixed de Sitter geometry. Thus, we present the most general scalar-tensor cosmological models without higher than second order derivatives in the field equation that have a fixed spatially flat de Sitter critical point for any kind of material content or vacuum energy. These models allow us to understand the current accelerated expansion of the universe as the result of the evolution towards the critical point when it is an attrac…
We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, $ρ_Λ \propto H$, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses ($M \gtrsim 10^{14} M_{\odot}h^{-1}$) when compared to the standard $Λ$CDM model. Since these models are no…
The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $Λ$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the h…
We investigate the qualitative evolution of (D+1)-dimensional cosmological models in f(R) gravity for the general case of the function f(R). The analysis is specified for various examples, including the (D+1)-dimensional generalization of the Starobinsky model, models with polynomial and exponential functions. The cosmological dynamics are compared in the Einstein and Jordan representations of the corresponding scalar-tensor theory. The features of the cosmological evolution are discussed for Einstein frame potentials taking negative values in certain regions of the field space.
We investigate the cosmological production of gravitational waves in a nonsingular flat cosmology powered by a "running vacuum" energy density described by $ρ_Λ\equivρ_Λ(H)$, a phenomenological expression potentially linked with the renormalization group approach in quantum field theory in curved spacetimes. The model can be interpreted as a particular case of the class recently discussed by Perico et al. (Phys. Rev. D {\bf 88}, 063531, 2013) which is termed complete in the sense that the cosmic evolution occurs between two extreme de Sitter stages (early and late time de Sitter phases). {The …
We investigate the dynamics of the FLRW flat cosmological models in which the vacuum energy varies with redshift. A particularly well motivated model of this type is the so-called quantum field vacuum, in which both kind of terms $H^{2}$ and constant appear in the effective dark energy density affecting the evolution of the main cosmological functions at the background and perturbation levels. Specifically, it turns out that the functional form of the quantum vacuum endows the vacuum energy of a mild dynamical evolution which could be observed nowadays and appears as dynamical dark energy. Int…
In this letter we point out the existence of solutions to General Relativity with a negative cosmological constant in four dimensions, which contain solitons as well as traversable wormholes. The latter connect two asymptotically locally AdS$_{4}$ spacetimes. At every constant value of the radial coordinate the spacetime is a spacelike warped AdS$_{3}$. We compute the dual energy momentum tensor at each boundary showing that it yields different results. We also show that these vacuum wormholes can have more than one throat and that they are indeed traversable by computing the time it takes for…
We investigate the virialization of cosmic structures in the framework of flat FLRW cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, "turn around" and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, $Λ=Λ(H)$. A particularly well motivated model of this type is the so-called quantum field vacuum, in which $Λ(H)$ is a quadratic function, $Λ(H)=n_0+n_2\…
We examine the growth of structure in three different cosmological models with interacting dark matter and vacuum energy. We consider the case of geodesic dark matter with zero sound speed, where the relativistic growing mode in comoving-synchronous gauge coincides with the Newtonian growing mode at first order in $Λ$CDM. We study corrections to the linearly growing mode in the presence of interactions and the linear matter growth rate, $f_1$, contrasting this with the velocity divergence, $f_{rsd}σ_8$, observed through redshift-space distortions. We then derive second-order density perturbati…
We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type M(p+1) x R x T(D-p-2) depending on a single coordinate. In the absence of fluxes, the solutions include flat space and Kasner-like vacua that break all supersymmetries. In the presence of a symmetric flux, there are three families of solutions that are characterized by a pair of boundaries and have a singularity at one of them, the origin. The first family comprises supersymmetric vacua, which capture a universal limiting behavior at the origin. The first and second families also cont…
The idea that the cosmological term, Lambda, should be a time dependent quantity in cosmology is a most natural one. It is difficult to conceive an expanding universe with a strictly constant vacuum energy density, namely one that has remained immutable since the origin of time. A smoothly evolving vacuum energy density that inherits its time-dependence from cosmological functions, such as the Hubble rate or the scale factor, is not only a qualitatively more plausible and intuitive idea, but is also suggested by fundamental physics, in particular by quantum field theory (QFT) in curved space-t…
We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type M(p+1) x R x T(10-p-2) depending on a single coordinate. In the absence of fluxes and for p<8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Th…
We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of p…
We evaluate the two-point functions of the electromagnetic field in (D+1) -dimensional spatially flat Friedmann-Robertson-Walker universes with a power-law scale factor, assuming that the field is prepared in the Bunch-Davies vacuum state. The range of powers are specified in which the two-point functions are infrared convergent and the Bunch-Davies vacuum for the electromagnetic field is a physically realizable state. The two-point functions are applied for the investigation of the vacuum expectation values of the field squared and the energy-momentum tensor, induced by a single and two paral…
We propose a new framework for studying the cosmology of $f(R)$ gravity which completely avoids using the reconstruction programme. This allows us to easily obtain a qualitative feel of how much the $Λ$CDM model differs from other $f(R)$ theories of gravity at the level of linear perturbation theory for theories that share the same background dynamics. This is achieved by using the standard model independent cosmographic parameters to develop a new dynamical system formulation of $f(R)$ gravity which is free from the limitation of having to first specify the functional form of $f(R)$. By consi…
We examine the dynamics of FLRW 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 …
We study the evolution of spatially flat Friedmann-Lemaître-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a non-singular bounce as in loop quantum cosmology, but with far more complex modified Friedmann dynamics with higher order than quadratic terms in energy density. For the kinetic energy dominated bounce, we obtain analytical solutions using different approximations and compare with numerical evolution for various physical variables. The relative error turns out to be less than $0.3\%$ in the b…
The problem of matching different regions of spacetime in order to construct inhomogeneous cosmological models is investigated in the context of Lagrangian theories of gravity constructed from general analytic functions f(R), and from non-analytic theories with f(R)=R^n. In all of the cases studied, we find that it is impossible to satisfy the required junction conditions without the large-scale behaviour reducing to that expected from Einstein's equations with a cosmological constant. For theories with analytic f(R) this suggests that the usual treatment of weak-field systems as perturbations…
Contracting cosmologies are known to be flawed with a shear instability, where the contribution from the anisotropic stress to the overall energy density grows as $a^{-6}$, with $a$ the scale factor. Classically, whether or not this contribution becomes important before the bounce depends on its initial value, which can always be sufficiently fine tuned to make it irrelevant. However, vacuum quantum fluctuations inevitably provide a non-vanishing source of anisotropic stress. In this work, we compute the minimum amount of shear that is obtained if one assumes that it vanishes initially, but le…
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of c…
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
Well-tempering is a promising classical method of dynamically screening an arbitrarily large vacuum energy and generating a late-time, low energy de Sitter vacuum state. In this paper, we study for the first time self-tuning in teleparallel gravity and obtain well-tempered cosmological models in the teleparallel gravity analogue of Horndeski theory. This broadens the scope of well-tempered cosmology and teases the potentially far richer cosmological dynamics that could be anchored on teleperallel gravity. We expand the well-tempered recipe to its most general form so far and use it to search f…
Using three-dimensional simulations, we study the dynamics and final structure of merging solitonic cores predicted to form in ultra-light axion dark matter halos. The classical, Newtonian equations of motion of a self-gravitating scalar field are described by the Schrödinger-Poisson equations. We investigate mergers of ground state (boson star) configurations with varying mass ratios, relative phases, orbital angular momenta and initial separation with the primary goal to understand the mass loss of the emerging core by gravitational cooling. Previous results showing that the final density pr…
We show that a CP-violating interaction induced by a derivative coupling between the running vacuum and a non-conserving baryon current may dynamically break CPT and trigger baryogenesis through an effective chemical potential. By assuming a non-singular class of running vacuum cosmologies which provides a complete cosmic history (from an early inflationary de Sitter stage to the present day quasi-de Sitter acceleration), it is found that an acceptable baryon asymmetry is generated for many different choices of the model parameters. It is interesting that the same ingredient (running vacuum en…
We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to q…
After decades of successful hot big-bang paradigm, Cosmology still lacks a framework in which the early inflationary phase of the universe smoothly matches the radiation epoch and evolves to the present `quasi' de Sitter spacetime. No less intriguing is that the current value of the effective vacuum energy density is vastly smaller than the value that triggered inflation. In this Essay we propose a new class of cosmologies capable of overcoming, or highly alleviating, some of these acute cosmic puzzles. Powered by a decaying vacuum energy density, the spacetime emerges from a pure nonsingular …
We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wave…
(abridged) We used a suite of numerical cosmological simulations in order to investigate the effect of gas cooling and star formation on the large scale matter distribution. The simulations follow the formation of cosmic structures in five different Dark Energy models: the fiducial $Λ$CDM cosmology and four models where the Dark Energy density is allowed to have a non-trivial redshift evolution. For each cosmology we have a control run with dark matter only, in order to allow a direct assessment of the impact of baryonic processes. We found that the power spectra of gas and stars, as well as t…
Massive gravity is a theory which has a tremendous amount of freedom to describe different cosmologies; but at the same time the various solutions one encounters must fulfill some rather nontrivial constraints. Most of the freedom comes not from the Lagrangian, which contains only a small number of free parameters (typically 3 depending on counting conventions), but from the fact that one is in principle free to choose the background reference metric almost arbitrarily --- which effectively introduces a non-denumerable infinity of free parameters. In the current paper we stress that although c…
Recent measurements of the Cosmic Microwave Anisotropies power spectra measured by the Planck satellite show a preference for a closed universe at more than $99 \%$ Confidence Level. Such a scenario is however in disagreement with several low redshift observables, including luminosity distances of Type Ia Supernovae. Here we show that Interacting Dark Energy (IDE) models can ease the discrepancies between Planck and Supernovae Ia data in a closed Universe. Therefore IDE cosmologies remain as very appealing scenarios, as they can provide the solution to a number of observational tensions in dif…
We construct the cosmological model to explain the cosmological constant problem. We built the extension of the standard cosmological model $Λ$CDM by consideration of decaying vacuum energy represented by the running cosmological term. From the principles of quantum mechanics one can find that in the long term behavior survival probability of unstable states is a decreasing function of the cosmological time and has the inverse power-like form. This implies that cosmological constant $ρ_{\text{vac}} = Λ(t) = Λ_{\text{bare}} + \fracα{t^2}$ where $Λ_{\text{bare}}$ and $α$ are constants. We invest…
We consider a scalar field with a bottom-less potential, such as $g^3 ϕ$, finding that cosmologies unavoidably end up with a crunch, late enough to be compatible with observations if $g \lesssim 1.2 H_0^{2/3} M_{\rm Pl}^{1/3}$. If rebounces avoid singularities, the multiverse acquires new features; in particular probabilities avoid some of the usual ambiguities. If rebounces change the vacuum energy by a small enough amount, this dynamics selects a small vacuum energy and becomes the most likely source of universes with anthropically small cosmological constant. Its probability distribution co…
Within the quantum mechanical treatment of the decay problem one finds that at late times $t$ the survival probability of an unstable state cannot have the form of an exponentially decreasing function of time $t$ but it has an inverse power-like form. This is a general property of unstable states following from basic principles of quantum theory. The consequence of this property is that in the case of false vacuum states the cosmological constant becomes dependent on time: $Λ- Λ_{\text{bare}}\equiv Λ(t) -Λ_{\text{bare}} \sim 1/t^{2}$. We construct the cosmological model with decaying vacuum en…
We study the matter-coupled equations of motion for cosmological NS massless fields including all $α'$ corrections in an O$(d,d)$ duality invariant approach, with emphasis on the Kalb-Ramond two-form field $B_{(2)}$ and its source. Solutions for the vacuum and matter case are found and the corresponding Einstein frame cosmologies are discussed. We also show that the ansatz for $B_{(2)}$ required by the duality invariant framework implies that the two-form is non-isotropic.
