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Register a new userLayzer-Irvine equation: new perspectives and the role of interacting dark energy
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We derive the Layzer-Irvine equation in the presence of a homogeneous (or quasi-homogeneous) dark energy component with an arbitrary equation of state. We extend the Layzer-Irvine equation to homogeneous and isotropic universes with an arbitrary number of dimensions and obtain the corresponding virial relation for sufficiently relaxed objects. We find analogous equations describing the dynamics of cosmic string loops and other p-branes of arbitrary dimensionality, discussing the corresponding relativistic and non-relativistic limits. Finally, we generalize the Layzer-Irvine equation to account for a non-minimal interaction between dark matter and dark energy, discussing its practical use as a signature of such an interaction.
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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 different fiducial cosmologies. The results presented here strongly favour broader analyses of cosmological data, and suggest that relaxing the usual flatness and vacuum energy assumptions can lead to a much better agreement among theory and observations.
The immediate observational consequence of a non-trivial spatial topology of the Universe is that an observer could potentially detect multiple images of radiating sources. In particular, a non-trivial topology will generate pairs of correlated circles of temperature fluctuations in the anisotropies maps of the cosmic microwave background (CMB), the so-called circles-in-the-sky. In this way, a detectable non-trivial spatial topology may be seen as an observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological dark energy (DE) equation of state (EOS) parameters. We show that the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of reducing the degeneracies in the DE EOS parameters. We concretely illustrate the topological role by assuming, as an exanple, a Poincar{e} dodecahedral space topology and reanalyzing the constraints on the parameters of a specific EOS which arise from the supernovae type Ia, baryon acoustic oscillations and the CMB plus the statistical topological contribution.
We investigate the impacts of dark energy on constraining massive (active/sterile) neutrinos in interacting dark energy (IDE) models by using the current observations. We employ two typical IDE models, the interacting $w$ cold dark matter (I$w$CDM) model and the interacting holographic dark energy (IHDE) model, to make an analysis. To avoid large-scale instability, we use the parameterized post-Friedmann approach to calculate the cosmological perturbations in the IDE models. The cosmological observational data used in this work include the Planck cosmic microwave background (CMB) anisotropies data, the baryon acoustic oscillation data, the type Ia supernovae data, the direct measurement of the Hubble constant, the weak lensing data, the redshift-space distortion data, and the CMB lensing data. We find that the dark energy properties could influence the constraint limits of active neutrino mass and sterile neutrino parameters in the IDE models. We also find that the dark energy properties could influence the constraints on the coupling strength parameter $beta$, and a positive coupling constant, $beta>0$, can be detected at the $2.5sigma$ statistical significance for the IHDE+$ u_s$ model by using the all-data combination. In addition, we also discuss the Hubble tension issue in these scenarios. We find that the $H_0$ tension can be effectively relieved by considering massive sterile neutrinos, and in particular in the IHDE+$ u_s$ model the $H_0$ tension can be reduced to be at the $1.28sigma$ level.
Recently, the Planck collaboration has released the first cosmological papers providing the high resolution, full sky, maps of the cosmic microwave background (CMB) temperature anisotropies. It is crucial to understand that whether the accelerating expansion of our universe at present is driven by an unknown energy component (Dark Energy) or a modification to general relativity (Modified Gravity). In this paper we study the coupled dark energy models, in which the quintessence scalar field nontrivially couples to the cold dark matter, with the strength parameter of interaction $beta$. Using the Planck data alone, we obtain that the strength of interaction between dark sectors is constrained as $beta < 0.102$ at $95%$ confidence level, which is tighter than that from the WMAP9 data alone. Combining the Planck data with other probes, like the Baryon Acoustic Oscillation (BAO), Type-Ia supernovae ``Union2.1 compilation and the CMB lensing data from Planck measurement, we find the tight constraint on the strength of interaction $beta < 0.052$ ($95%$ C.L.). Interestingly, we also find a non-zero coupling $beta = 0.078 pm 0.022$ ($68%$ C.L.) when we use the Planck, the ``SNLS supernovae samples, and the prior on the Hubble constant from the Hubble Space Telescope (HST) together. This evidence for the coupled dark energy models mainly comes from a tension between constraints on the Hubble constant from the Planck measurement and the local direct $H_0$ probes from HST.
We place observational constraints on two models within a class of scenarios featuring an elastic interaction between dark energy and dark matter that only produces momentum exchange up to first order in cosmological perturbations. The first one corresponds to a perfect-fluid model of the dark components with an explicit interacting Lagrangian, where dark energy acts as a dark radiation at early times and behaves as a cosmological constant at late times. The second one is a dynamical dark energy model with a dark radiation component, where the momentum exchange covariantly modifies the conservation equations in the dark sector. Using Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO), and Supernovae type Ia (SnIa) data, we show that the Hubble tension can be alleviated due to the additional radiation, while the $sigma_8$ tension present in the $Lambda$-Cold-Dark-Matter model can be eased by the weaker galaxy clustering that occurs in these interacting models. Furthermore, we show that, while CMB+BAO+SnIa data put only upper bounds on the coupling strength, adding low-redshift data in the form of a constraint on the parameter $S_8$ strongly favours nonvanishing values of the interaction parameters. Our findings are in line with other results in the literature that could signal a universal trend of the momentum exchange among the dark sector.
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