Supersymmetry signals of supercritical string cosmology at the Large Hadron ColliderBhaskar Dutta,1Alfredo Gurrola,1Teruki Kamon,1Abram Krislock,1A. B. Lahanas,2N. E. Mavromatos,3and D. V. Nanopoulos1,4,51Department of Physics, Texas A&M University, College Station, Texas 77843-4242, USA2Physics Department, Nuclear and Particle Physics Section, University of Athens, GR-157 71, Athens, Greece3King’s College London, Department of Physics, University of London, Strand WC2R 2LS, London, United Kingdom4Astroparticle Physics Group, Houston Advanced Research Center (HARC), Mitchell Campus, Woodlands, Texas 77381, USA5Division of Natural Sciences, Academy of Athens, 28 Panepistimiou Avenue, Athens 10679, Greece(Received 20 August 2008; published 4 March 2009)We investigate the minimal supergravity signals at the Large Hadron Collider in the context ofsupercritical string cosmology (SSC). In this theory, the presence of a time dependent dilaton providesus with a smoothly evolving dark energy and modifies the dark matter allowed region of the minimalsupergravity model with standard cosmology. Such a dilaton dilutes the supersymmetric dark matterdensity (of neutralinos) by a factor Oð10Þ and consequently the regions with too much dark matter in thestandard scenario are allowed in the SSC. The final states expected at the Large Hadron Collider in thisscenario, unlike the standard scenario, consist of Z bosons, Higgs bosons, and/or high energy taus. Weshow how to characterize these final states and determine the model parameters. Using these parameters,we determine the dark matter content and the neutralino-proton cross section. All these techniques canalso be applied to determine model parameters in SSC models with different supersymmetry breakingscenarios.DOI: 10.1103/PhysRevD.79.055002 PACS numbers: 12.60.Jv, 04.65.+e, 98.80.CqI. INTRODUCTIONThe recent WMAP data [1] have determined the contentof the Universe very precisely. The dark matter and darkenergy compose about 23% and 73% of the total energydensity of the Universe, respectively.The origin of dark matter can be explained in supersym-metry (SUSY) models, where the lightest SUSY particle,the neutralino (in most SUSY models) [2], is the darkmatter candidate. SUSY, combined with supergravitygrand unification (SUGRA GUT) [3], resolves a numberof the problems inherent in the standard model (SM). TheSUGRA GUT model not only solves the gauge hierarchyproblem and predicts grand unification at the GUT scaleMG 1016GeV but also allows for the spontaneous break-ing of SUGRA at the MGscale in a hidden sector, leadingto an array of soft breaking masses. The renormalizationgroup equations then show that this breaking of SUGRAleads naturally to the breaking of SUð2ÞUð1Þ of the SMat the electroweak scale [4]. SUSY breaking masses arounda TeV for most of the SUSY parameter space are allowedby other experimental constraints. It is also very interestingto note that achieving the WMAP relic density requiresthe annihilation cross section of the lightest neutralino (~01)in these SUSY models to be of order 1 pb with M~01Oð100 GeVÞ. Such a mass scale is reachable at the CERNLHC.The origin of dark energy is not well understood. Thesimplest proposal is to add a cosmological constant inEinstein’s equation. However, the reason why the darkmatter content is comparable to the dark energy contentat the present time remains a puzzle. Another proposal isthat a quintessence scalar field is responsible for darkenergy [5]. However, this requires the field to have a verysmall mass and is not well motivated in particle physicsmodels. In the context of string theory, the dilaton can playthe role of dark energy [6,7]. One also finds proposalswhich involve, for example, modifications to general rela-tivity, braneworld scenarios, or topological defects, whichare invoked to explain this fundamental issue.In this paper, we will investigate experimental signaturesof SUSY as consequences of a rolling dilaton in theQ-cosmology scenario [6] which offers an alternativeframework that establishes the supercritical (or noncritical)string cosmology (or SSC). In the SSC framework, the darkenergy has two components: One component arises fromthe dilaton, , and the other arises from the Q2which isassociated with the central charge deficit. Both Q and thedilaton have time dependent pieces. It was shown that theSSC scenario [8] is consistent with the smoothly evolvingdark energy at least for the last 10  109yr (0 <z<1:6),in accordance with the very recent observations on super-novae [9].The presence of this time dependent dilaton affects therelic density calculation since it modifies the Boltzmannequation in the following way:dndtþ 3Hn þh viðn2 neq2Þ _n ¼ 0. The relic density is given byPHYSICAL REVIEW D 79, 055002 (2009)1550-7998=2009=79(5)=055002(15) 055002-1 Ó 2009 The American Physical Societyh2¼ R ðh2Þ0(1)where R  exp½Rxfx0ð_H 1=xÞdx and ðh2Þ0denotes therelic density that is obtained by ordinary cosmology. It ispossible to determine R by solving for  from the fieldequations for this SSC scenario. The value of R is about 0.1in order to satisfy the recent observation of the evolution ofdark energy in the range 0 <z<1:6. This new factorchanges the profile of the dark matter allowed region inSUSY models.To investigate the SUSY signatures we use the minimalSUGRA (mSUGRA) model and calculate the dark mattercontent in the context of the SSC framework. We note thatthe low-energy limit of string theory is certainly muchmore complicated than mSUGRA, and there are manydifferent effective theories, depending on the details ofcompactification and SUSY breaking [10]. The relevantdark matter phenomenological analyses are highly modeldependent [11]. In some cases, such as the orbifold-compactified heterotic models [10], there might be situ-ations in which the couplings of matter with stabilizeddilatons lead to nonthermal dark matter, thus leading tocompletely different phenomenology.However, the SSC framework is characterized by a non-stabilized dilaton which runs in cosmic time [8]. In thiscontext, it is possible to have thermalization of weaklyinteracting dark matter, such as the mSUGRA lightestneutralino (~01) which couples to the dilaton. In this sense,the mSUGRA framework provides a sufficiently nontrivialand generic pilot study of the novel effects the runningdilaton has on the abundance of thermal dark matter