Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling solutions and weak gravity in dark energy with energy and momentum couplings
170
0
0.0
(
0
)
Authors
Luca Amendola
Ask ChatGPT about the research
No Arabic abstract
We argue that the $Lambda$CDM tensions of the Hubble-Lemaitre expansion rate $H_0$ and the clustering normalization $sigma_8$ can be eased, at least in principle, by considering an interaction between dark energy and dark matter in such a way to induce a small and positive early effective equation of state and a weaker gravity. For a dark energy scalar field $phi$ interacting with dark matter through an exchange of both energy and momentum, we derive a general form of the Lagrangian allowing for the presence of scaling solutions. In a subclass of such interacting theories, we show the existence of a scaling $phi$-matter-dominated-era ($phi$MDE) which can potentially alleviate the $H_0$ tension by generating an effective high-redshift equation of state. We also study the evolution of perturbations for a model with $phi$MDE followed by cosmic acceleration and find that the effective gravitational coupling relevant to the linear growth of large-scale structures can be smaller than the Newton gravitational constant $G$ at low redshifts. The momentum exchange between dark energy and dark matter plays a crucial role for realizing weak gravity, while the energy transfer is also required for the existence of $phi$MDE.
rate research
Read More
In cubic-order Horndeski theories where a scalar field $phi$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(phi)$, we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant $Q$ including the case of vanishing coupling, the corresponding Lagrangian reduces to the form $L=Xg_2(Y)-g_3(Y)square phi$, where $X=-partial_{mu}phipartial^{mu}phi/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{lambda phi}$ with constant $lambda$. We obtain the fixed points of the scaling Lagrangian for constant $Q$ and show that the $phi$-matter-dominated-epoch ($phi$MDE) is present for the cubic coupling $g_3(Y)$ containing inverse power-law functions of $Y$. The stability analysis around the fixed points indicates that the $phi$MDE can be followed by a stable critical point responsible for the cosmic acceleration. We propose a concrete dark energy model allowing for such a cosmological sequence and show that the ghost and Laplacian instabilities can be avoided even in the presence of the cubic coupling.
We investigate a dark energy scenario in which a canonical scalar field $phi$ is coupled to the four velocity $u_{c}^{mu}$ of cold dark matter (CDM) through a derivative interaction $u_{c}^{mu} partial_{mu} phi$. The coupling is described by an interacting Lagrangian $f(X, Z)$, where $f$ depends on $X=-partial^{mu} phi partial_{mu} phi/2$ and $Z=u_{c}^{mu} partial_{mu} phi$. We derive stability conditions of linear scalar perturbations for the wavelength deep inside the Hubble radius and show that the effective CDM sound speed is close to 0 as in the standard uncoupled case, while the scalar-field propagation speed is affected by the interacting term $f$. Under a quasi-static approximation, we also obtain a general expression of the effective gravitational coupling felt by the CDM perturbation. We study the late-time cosmological dynamics for the coupling $f propto X^{(2-m)/2}Z^m$ and show that the gravitational coupling weaker than the Newton constant can be naturally realized for $m>0$ on scales relevant to the growth of large-scale structures. This allows the possibility for alleviating the tension of $sigma_8$ between low- and high-redshift measurements.
We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the torsion pseudo-trace provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions representing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard $L$CDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state parameters over different redshift ranges. In spite of being weakly dynamic, the dark energy component differs significantly from the cosmological constant, both in characteristics and features, for e.g. it interacts with the cosmological (dust) fluid in the Einstein frame, and crosses the phantom barrier in the Jordan frame. We also obtain the upper bounds on the torsion mode parameters and the lower bound on the effective Brans-Dicke parameter. The latter turns out to be fairly large, and in agreement with the local gravity constraints, which therefore come in support of our analysis.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades there has been a huge theoretical and observational effort into improving our understanding of the Universe. The cosmological equations describing the dynamics of a homogeneous and isotropic Universe are systems of ordinary differential equations, and one of the most elegant ways these can be investigated is by casting them into the form of dynamical systems. This allows the use of powerful analytical and numerical methods to gain a quantitative understanding of the cosmological dynamics derived by the models under study. In this review we apply these techniques to cosmology. We begin with a brief introduction to dynamical systems, fixed points, linear stability theory, Lyapunov stability, centre manifold theory and more advanced topics relating to the global structure of the solutions. Using this machinery we then analyse a large number of cosmological models and show how the stability conditions allow them to be tightly constrained and even ruled out on purely theoretical grounds. We are also able to identify those models which deserve further in depth investigation through comparison with observational data. This review is a comprehensive and detailed study of dynamical systems applications to cosmological models focusing on the late-time behaviour of our Universe, and in particular on its accelerated expansion. In self contained sections we present a large number of models ranging from canonical and non-canonical scalar fields, interacting models and non-scalar field models through to modified gravity scenarios. Selected models are discussed in detail and interpreted in the context of late-time cosmology.
Non-canonical scalar fields with the Lagrangian ${cal L} = X^alpha - V(phi)$, possess the attractive property that the speed of sound, $c_s^{2} = (2,alpha - 1)^{-1}$, can be exceedingly small for large values of $alpha$. This allows a non-canonical field to cluster and behave like warm/cold dark matter on small scales. We demonstrate that simple potentials including $V = V_0coth^2{phi}$ and a Starobinsky-type potential can unify dark matter and dark energy. Cascading dark energy, in which the potential cascades to lower values in a series of discrete steps, can also work as a unified model. In all of these models the kinetic term $X^alpha$ plays the role of dark matter, while the potential term $V(phi)$ plays the role of dark energy.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
