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The cosmological evolution of the equation of state w Q ≡ p Q /ρ Q for the scalar field Q is 

The cosmological evolution of the equation of state w Q ≡ p Q /ρ Q for the scalar field Q is 

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Recent data point in the direction of a cosmological constant dominated universe. We investigate the role of supersymmetric QCD with Nf<Nc as a possible candidate for a dynamical cosmological constant (“quintessence”). When Nf>1, the multiscalar dynamics is fully taken into account, showing that a certain degree of flavor symmetry in the initial co...

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... Fig.2 we plot the scalar field equation of state, w Q , for the corresponding solutions of The cosmological evolution of the equation of state w Q ≡ p Q /ρ Q for the scalar field Q is plotted as a function of red-shift. ...

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... 3. On the other hand, our results almost entirely rule out the quintessence models in which initially w>−1 and w decreases as the scalar rolls down the potential ("cooling" models), which occupy most of the region w 0 >−1, w a >0 (see Barger et al. 2006). These typically arise in models of dynamical supersymmetry breaking (Binetruy 1999;Masiero et al. 2000) and supergravity (Brax & Martin 1999;Copeland et al. 2000), including the "freezing" models in Caldwell & Linder (2005) in which the potential has a minimum at f = ¥. 4. For "phantom" models with w 0 <−1 (see Caldwell 2002), our constraint w a −3/4−(w 0 +3/2) excludes a major portion of the parameter space that corresponds to models for which the equation of state crossed the phantom divide line w=−1 from a higher value. ...
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We compare the maximal abundance of massive systems predicted in different dynamical dark energy (DDE) models at high redshifts z = 4-7 with the measured abundance of the most massive galaxies observed to be already in place at such redshifts. The aim is to derive constraints for the evolution of the dark energy equation of state parameter w which are complementary to existing probes. We adopt the standard parametrization for the DDE evolution in terms of the local value w_0 and of the look-back time derivative w_a of the equation of state. We derive constraints on combinations (w_0, w_a) in the different DDE models by using three different, independent probes: (i) the observed stellar mass function of massive objects at z = 6 derived from the CANDELS survey; (ii) the estimated volume density of massive halos derived from the observation of massive, star-forming galaxies detected in the submillimeter range at z = 4; (iii) The rareness of he most massive system (estimated gas mass exceeding 3 10^11} M_sun) observed to be in place at z = 7, a far-infrared-luminous object recently detected in the South Pole Telescope (SPT) survey. Finally, we show that the combination of our results from the three above probes excludes a sizable fraction of the DDE parameter space w_a > -3/4 - (w_0 + 3/2) presently allowed (or even favored) by existing probes.
... The first piece of the potential (2) is obtained when one deals with R 2 gravity in the Einstein Frame [20], and the tail, which is the same used in [1], comes from SUSY QED [21]. ...
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... Models involving multiple quintessence fields have been previously presented in the literature; see for example [38][39][40][41][42][43][44][45]. Many-field models with a connection to Early Universe inflation, as in our set-up, are less common (although not absent [43,45]), as are embeddings in more fundamental theories. ...
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A bstract We present a two-field model that realises inflation and the observed density of dark energy today, whilst solving the fine-tuning problems inherent in quintessence models. One field acts as the inflaton, generically driving the other to a saddle-point of the potential, from which it acts as a quintessence field following electroweak symmetry breaking. The model exhibits essentially no sensitivity to the initial value of the quintessence field, naturally suppresses its interactions with other fields, and automatically endows it with a small effective mass in the late Universe. The magnitude of dark energy today is fixed by the height of the saddle point in the potential, which is dictated entirely by the scale of electroweak symmetry breaking.
... This potential can be computed from the Affleck-Dine-Seiberg superpotential [36,46]. The scalar potential in global supersymmetry (SUSY) for a canonically normalised meson field φ 2 ≡ QQ is given by V = |W φ | 2 , where W φ = ∂W/∂φ [38,47], representing the lightest meson field corresponding to a pseudo-Goldstone boson. It is worth noticing that the ADS superpotential W is exact (it receives no radiative corrections) and the resulting scalar potential V is stable against quantum corrections [36]. ...
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... This potential can be computed from the Affleck-Dine-Seiberg superpotential [36,46]. The scalar potential in global supersymmetry (SUSY) for a canonically normalised meson field φ 2 ≡ QQ is given by V = |W φ | 2 , where W φ = ∂W/∂φ [38,47], representing the lightest meson field corresponding to a pseudo-Goldstone boson. It is worth noticing that the ADS superpotential W is exact (it receives no radiative corrections) and the resulting scalar potential V is stable against quantum corrections [36]. ...
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... Applications to cosmic acceleration go under the name K-essence , and were first considered within the context of cosmological inflation [145,146]. There have also been efforts to embed quintessence in some more fundamental theory; for example supersymmetry [147][148][149][150][151] or string theory [152][153][154][155][156][157][158][159][160]. ...
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After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond \Lambda, or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests. We begin by reviewing attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must screen themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives become important, and those for which second derivatives are important. Examples of the first class, such as f(R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories. We describe experimental tests, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. We discuss future tests which will be sensitive to different signatures of new physics in the gravitational sector. Parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.
... For the freezing (tracker) type, a quintessence field moves fast in the early Universe, then "freezes" at some later time to realize its equation of state w X close to −1. A typical example of potentials in this category is the inverse power law potential [5,6,[17][18][19][20][21][22]. For such a potential, it is well known that the quintessence field exhibits a tracking behavior where it traces the equation of state of the dominant background fluid (e.g., radiation and matter). ...
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... One of the earliest proposed, simplest, and most widely investigated of the scalar field quintessence models is the pure inverse power law (IPL) model, originally introduced by Ratra and Peebles [1]. This model was originally put forward to mimic a time-varying cosmological constant undergoing dissipationless decay and is motivated by supersymmetric QCD (see [16] and references therein). More recently, this potential has been reanalyzed ( [12,13]) in the context of a scalar field potential driving the current epoch of cosmic acceleration. ...
... The quantities V 0 and α are the two free parameters in the potential. In some supersymmetric QCD realizations of the IPL model [16], α is also related to the number of flavors and colors, and can take on a continuous range of values α > 0 [19]. For α → ∞ (but with ρ φ still subdominant), the scalar field energy density scales like that of the dominant background. ...
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We report on the results of a Markov Chain Monte Carlo (MCMC) analysis of an inverse power law (IPL) quintessence model using the Dark Energy Task Force (DETF) simulated data sets as a representation of future dark energy experiments. We generate simulated data sets for a Lambda-CDM background cosmology as well as a case where the dark energy is provided by a specific IPL fiducial model and present our results in the form of likelihood contours generated by these two background cosmologies. We find that the relative constraining power of the various DETF data sets on the IPL model parameters is broadly equivalent to the DETF results for the w_{0}-w_{a} parameterization of dark energy. Finally, we gauge the power of DETF "Stage 4" data by demonstrating a specific IPL model which, if realized in the universe, would allow Stage 4 data to exclude a cosmological constant at better than the 3-sigma level. Comment: 15 pages, including 13 figures
... See Peebles & Vilenkin (1999), Perrotta & Baccigalupi (1999) and Giovannini (1999) for a specific model and observational consequences of this scenario. A potential ∝ φ −α could arise in a number of high energy particle physics models, see, e.g., Binétruy (1999), Kim (1999), Barr (1999), Choi (1999), Banks, Dine, & Nelson (1999), Brax & Martin (1999), Masiero, Pietroni, & Rosati (1999), and Bento & Bertolami (1999) for specific examples. It is conceivable that such a setting might provide an explanation for the needed form of the potential, as well as for the needed very weak coupling of φ to other fields (RP ;Carroll 1998;Kolda & Lyth 1999, but see Periwal 1999and Garriga, Livio, & Vilenkin 1999 for other possible explanations for the needed present value of Λ). ...
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The energy density of a scalar field ϕ\phi with potential V(ϕ)ϕαV(\phi) \propto \phi^{-\alpha}, α>0\alpha > 0, behaves like a time-variable cosmological constant that could contribute significantly to the present energy density. Predictions of this spatially-flat model are compared to recent Type Ia supernovae apparent magnitude versus redshift data. A large region of model parameter space is consistent with current observations. (These constraints are based on the exact scalar field model equations of motion, not on the widely used time-independent equation of state fluid approximation equations of motion.) We examine the consequences of also incorporating constraints from recent measurements of the Hubble parameter and the age of the universe in the constant and time-variable cosmological constant models. We also study the effect of using a non-informative prior for the density parameter. Comment: Accepted for publication in ApJ