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What’s even more surprising it’s the fact that, according to the latest PLANCK results\cite{Ade_2014} , Dark Energy constitutes around the 68\% of the known universe with the remainder being around 5\% baryons and 27\% dark matter.  The latter is a name used to describe a form of non-relativistic matter that interacts very weakly with standard matter particles. Its existence was postulated by Vera Rubin in the 70’s \cite{Rubin_1970} that inferred its presence from the gravitational effects it exerted on visible matter allowing her to explain the shape of rotational curves in the observed galaxies.\\  It is now well known that Dark Matter plays a crucial role for the growth of large scale structure in the universe because it can cluster by gravitational instability creating the perfect environment for galaxy formation.  The formation of structure in the universe begins when the pressureless dark matter starts to dominate the total energy density of the universe, during this era the energy density of dark energy needs to be strongly suppressed to allow sufficient growth of large scale structures.\\ structures.  While the energy density of dark matter evolves as $\rho_m \propto a^{-3}$ where a is the scale factor of an expanding universe, the dark energy density remains constant in time and eventually catches up with the former and starts to dominate and accelerate the expansion history of the universe.\\ universe \cite{dodelson2003modern}.\\  This evolution history rises two main theoretical weak points for the Cosmological Constant [Weinberg] \cite{Weinberg_1989}  : \begin{itemize}  \item The Fine Tuning Problem: from the viewpoint of particle physics, the cosmological constant can be interpreted as vacuum energy density, but summing up zero-point energies it’s estimated to be around $10^{74}$ Gev$^4$, much larger than the observed value of $10^{-47}$ Gev$^4$, so a novel mechanism is needed to obtain the tiny value of LAMBDA consistent with observations.  \item The Coincidence Problem: Dark Energy started to dominate the expansion history of the universe relatively close to the present epoch, allowing just the right time for galaxies to form. 
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A current of thought argues that these are indeed the only conditions that allow the development of life as we know it, but this anthropic explanations is highly controversial.  That’s why a lot of effort has been put in increasing the complexity of the concordance LCDM model.   A first approch is to add additional degrees of freedom to the standard model as a way to parametrize our ignorance about the fundamental nature of Dark Energy with a few parameters that quantify possible deviations from the LCDM behavior.  The first class of models falling into this category still describes Dark Energy as an homogeneous field in a universe described by the Friedmann-Lemaitre-Robertson-Walker metric [ ]: \cite{Baldi_2012}:  \begin{equation} ds^2 = -c^2dt^2 + a(t)\{ \delta_{ij}dx^i dx^j \} \end{equation}  whose time dependence is all described by the scale factor $a(t)$. The background evolution so it’s usually described by the Hubble function $H(a) \equiv \dot{a}/a$ that describes how the expansion rate changes as a function of time. This in turn is related to the abundance of different constituents in the universe through the Friedmann equation:  \begin{equation} \frac{H^2(a)}{H_0^2} = \Omega_M a^{-3} + \Omega_r a^{-4} + \Omega_K a^{-2} + \Omega_{DE} \text{exp} \left \{ -3 \int_1^a \frac{1+w(a')}{a'}da' \right \} \end{equation}  Where the $\Omega$’s are the energy densities of respectively matter, radiation, curvature and Dark Energy.\\  The equation of state parameter $w(a)$ quantifies the ratio between pressure and energy density of the Dark Energy component. For a cosmological constant this parameter is constant and has a value $w = -1$ but we can readily see how just by allowing this parameter to be time dependant we can obtain a completely new expansion history.   Common phenomenological parametrizations of the equation of state parameter are the Chevallier-Polarski-Linder parametrization [70 71 baldi ] : \cite{CHEVALLIER_2001, Linder_2003}:  \begin{equation} w(a) = w_0 + w_a (1-a) \end{equation}  based on the behavior of w(a) at low redshifts, and the early dark energy parametrization [ look at fontanot ] \cite{Wetterich_2004}  \begin{equation} w(a) = \frac{w_0}{1+b \text{ln}(1/a)}\end{equation}  where $b$ is a parameter dependant on the the abundance of Dark Energy at early times.\\  Another class of widely studied scenarios views Dark Energy as a scalar field whose dynamical evolution is driven by a parametrized potential, the representative models of this class are Quintessence [b], k-essence[b], Phantom[b], \cite{Wetterich_1988, Ratra_1988}, k-essence \cite{Armendariz_Picon_2001}, Phantom \cite{Caldwell_2002},  Quintom [b] \cite{Feng_2005}  and perfect fluid [] \cite{Kamenshchik_2001}  Dark Energy models. For Quintessence models the most common choices of potentials include slowly varying runaway potentials such as an inverse power law [ b]: \cite{Ratra_1988}:  \begin{equation} V(\phi) = A \phi^{-\alpha} \end{equation}  or an exponential [b]: \cite{Wetterich_1988}:  \begin{equation} V(\phi) = A e^{-\alpha \phi} \end{equation}  or SUGRA potentials arising within supersymmetric theories of gravity [b] \cite{Brax_1999}  : \begin{equation} V(\phi) = A \phi^{-\alpha}e^{\phi^2/2}\end{equation}  in k-essence models instead it’s the scalar field kinetic energy that drives the acceleration.  In the perfect fluid models such as Chaplygin gas model [45 book ] \cite{Kamenshchik_2001}  Dark Energy is modeled as a perfect fluid with a specific equation of state.\\ A first extension to those models can be done by letting the Dark Energy field interact with the matter species via a parametrized coupling like in the extended quintessence models []. \cite{Pettorino_2008}.  For these scenarios the strength of the coupling must be suppressed in high density environments to satisfy solar system test of gravity. That’s why recently models with species-dependent coupling have been developed, examples are the Coupled Dark Energy models [ Badli ] \cite{Wetterich:1994bg, Amendola_2000}  or the Growing Neutrino Models [ ]. \cite{Amendola_2008}.  In these scenarios the coupling with baryons is highly suppressed so that the model can be easily satisfy solar system tests while still allowing for an interesting range of modification of the structure formation process [].\\ \cite{Baldi_2012}.\\  Another approach along these lines is that of a slowly running cosmological constant that arises as an effective vacuum energy density in Quantum field theory in a curved space time, time \cite{parker2009quantum},  this idea, based on the possibility that quantum effects in curved space time can be responsible for the renormalization group running of the vacuum energy, leading to an energy density that evolves with the Hubble rate \begin{equation} \rho_\Lambda(H) = \rho_{\Lambda0} + \frac{3\nu}{8\pi}(H^2-H_0^2) \end{equation}  this can be coupled to the running of newton gravitational constant  \begin{equation} G(H) = \frac{G_0}{1+\nu ~ \text{ln}(H^2/H_0^2)} \end{equation}  to allow for the conservation of the energy-momentum tensor. tensor \cite{Grande_2011}.  This model known as the "Running FLRW model" is so able to describe completely new expansion history from first principles.\\ A further step these lines is to drop the assumption that General Relativity is valid on the largest scales and construct what are now known as Modified Gravity models.\\  A way to accomplish this is to take the Lagrangian density of the LCDM model $f(R) = R - 2\Lambda$ and modify it by adding non linear terms in $R$, obtaining what are now known as f(R)-Gravity models [ ]. \cite{Sotiriou_2010, Carroll_2004}.  Scalar tensor theories instead couple the Ricci scalar $R$ to a scalar field, examples of those are the Brans-Dicke theory [ ] and Dilaton gravity [ ]. A different approach instead is that of the braneworld models proposed by Dvali, Gabadaze, Porrati (DGP) [ ] where the late time acceleration of the universe is realized as a result of the gravitational leakage from a 3-dimensional surface to a 5th extra dimension on Hubble distances.\\  All this models are able to satisfy local gravity constraints as well as conditions set by the epochs preceding the matter domination epoch and provide the acceleration of the universe without resorting to unknown forms of matter.