With the start-up of the LHC, we can hope to find evidences for new physics
beyond the Standard Model, and particle candidates for dark matter. Determining
the parameters of the full underlying theory will be a long process requiring
the combination of LHC and ILC data, flavor physics constraints, and
cosmological observations. However, the Very Early Universe properties, from
which the relic particles originate, are poorly known, and the relic density
calculation can be easily falsified by hidden processes. We consider
supersymmetry and show that determining the underlying particle physics
parameters will help understanding the Very Early Universe properties.Comment: 6 pages, 2 figures, contribution to the proceedings of the workshop
  "LC09: e+e- Physics at the TeV Scale and the Dark Matter Connection",
  Perugia, September 21 - 24, 2009, Italy. v2: reference adde

Arbey, A.

Mahmoudi, F.

English

arXiv

International audienceWith the start-up of the LHC, we can hope to find evidences for new physics beyond the Standard Model, and particle candidates for dark matter. Determining the parameters of the full underlying theory will be a long process requiring the combination of LHC and ILC data, flavor physics constraints, and cosmological observations. However, the Very Early Universe properties, from which the relic particles originate, are poorly known, and the relic density calculation can be easily falsified by hidden processes. We consider supersymmetry and show that determining the underlying particle physics parameters will help understanding the Very Early Universe properties

HAL Clermont Université

LHC and ILC Data and the Early Universe Properties

Hal-Diderot

HAL-ENS-LYON

With the start-up of the LHC, we can hope to find evidences for new physics beyond the Standard Model, and particle candidates for dark matter. Determining the parameters of the full underlying theory will be a long process

requiring the combination of LHC and ILC data, flavor physics constraints, and cosmological observations. However, the Very Early Universe properties, from which the relic particles originate, are poorly known, and the relic density calculation can be easily falsified by hidden processes. We consider supersymmetry and show that

determining the underlying particle physics parameters will help understanding the Very Early Universe properties

Scientific Open-access Literature Archive and Repository

DOI 10.1393/ncc/i2010-10593-1Colloquia: LC09IL NUOVO CIMENTO Vol. 33 C, N. 2 Marzo-Aprile 2010LHC and ILC data and the Early Universe propertiesA. Arbey(1)(2)(3)(4) and F. Mahmoudi(5)(1) Universite´ de Lyon - Lyon F-69000, France(2) Universite´ Lyon 1 - Villeurbanne F-69622, France(3) Centre de Recherche Astrophysique de Lyon, Observatoire de LyonCNRS, UMR 5574 - 9 avenue Charles Andre´, Saint-Genis-Laval cedex F-69561, France(4) Ecole Normale Supe´rieure de Lyon - Lyon F-69342, France(5) Clermont Universite´, Universite´ Blaise Pascal, CNRS/IN2P3, LPC - BP 1044863000 Clermont-Ferrand, France(ricevuto il 15 Febbraio 2010; approvato il 23 Marzo 2010; pubblicato online il 3 Giugno 2010)Summary. — With the start-up of the LHC, we can hope to find evidences fornew physics beyond the Standard Model, and particle candidates for dark matter.Determining the parameters of the full underlying theory will be a long processrequiring the combination of LHC and ILC data, flavor physics constraints, andcosmological observations. However, the Very Early Universe properties, from whichthe relic particles originate, are poorly known, and the relic density calculation canbe easily falsified by hidden processes. We consider supersymmetry and show thatdetermining the underlying particle physics parameters will help understanding theVery Early Universe properties.PACS 11.30.Pb – Supersymmetry.PACS 95.35.+d – Dark matter (stellar, interstellar, galactic, and cosmological).PACS 98.80.Cq – Particle-theory and field-theory models of the early Universe (in-cluding cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe,etc.).1. – IntroductionThe present and future high-energy colliders will hopefully allow the discovery ofnew particles. Many new physics models beyond the Standard Model propose particlecandidates for dark matter, within the reach of the LHC and ILC. Should a stable, neutraland weakly interacting new particle be found, it would be a candidate for dark matter.Through particle physics computation of annihilation and co-annihiliation diagrams, itis possible to compute the dark matter relic density [1]. This relic density is then oftencompared to the dark matter density deduced from cosmological observations in order toconstrain new physics parameters. If the computed relic density is compatible with thecosmologically inferred dark matter density, the cosmological model will be reinforced byc© Societa` Italiana di Fisica 151152 A. ARBEY and F. MAHMOUDIthis new particle discovery. However, in case of disagreements, two possible paths canopen: either the new physics particle model is not correctly designed, or the cosmologicalmodel is missing ingredients, such as quintessence [2] or reheating [3]. In [4,5], we showedthat such dark components can modify the computed relic density by several orders ofmagnitudes, and we introduced parametrizations to characterize the Very Early Universeproperties. Using this kind of parametrizations, and combining with particle physics data,it will therefore be possible to determine the Very Early Universe properties beyond thestandard cosmological scenario. In the following we will consider Supersymmetry (SUSY)as an example and discuss the use of relic density to constrain cosmological properties.2. – Relic density calculationThe density number of supersymmetric particles is determined by the Boltzmannequation and takes the form(1)dndt= −3Hn− 〈σv〉(n2 − n2eq),where n is the number density of supersymmetric particles, 〈σv〉 is the thermally averagedannihilation cross-section, H is the Hubble expansion rate and neq is the supersymmet-ric particle equilibrium number density. The expansion rate H is determined by theFriedmann equation(2) H2 =8πG3(ρrad + ρD).ρrad is the radiation energy density, which is considered to be dominant before BBN inthe standard cosmological model. ρD is introduced in eq. (2) to parametrize the expan-sion rate modification [4] and can be interpreted either as an additional energy densitymodifying the expansion (e.g., quintessence), or as an effective energy density which canaccount for other phenomena affecting the expansion rate (e.g., extra-dimensions).The entropy evolution can also be altered beyond the standard cosmological model.In presence of entropy fluctuations we give the entropy evolution equation:(3)dsdt= −3Hs +ΣD,where s is the total entropy density. ΣD in the above equation parametrizes effectiveentropy fluctuations due to unknown properties of the Early Universe, and is temperaturedependent.The parameters ρD and ΣD can be regarded as independent. Entropy and energyalterations are considered here as effective effects, and can be generated by curvature,phase transitions, extra-dimensions, or other phenomena in the Early Universe. In aspecific physical scenario, these parameters can be related, as for example in reheatingmodels [3].The radiation energy and entropy densities can be written as usual:(4) ρrad = geff(T )π230T 4, srad = heff(T )2π245T 3.LHC AND ILC DATA AND THE EARLY UNIVERSE PROPERTIES 153We split the total entropy density into two parts: radiation entropy density and effectivedark entropy density, s ≡ srad + sD. Using eq. (3) the relation between sD and ΣD canthen be derived:(5) ΣD =√4π3G5√1 + ρ˜DT 2[√geffsD − 13heffg1/2∗TdsDdT],with(6) g1/2∗ =heff√geff(1 +T3heffdheffdT).Following the standard relic density calculation method [1], Y ≡ n/s is introduced, andeq. (1) yields(7)dYdx=−mlspx2√π45Gg1/2∗(1 + s˜D√1 + ρ˜D)[〈σv〉(Y 2−Y 2eq)+Y ΣD(heff(T ) 2π245 T3)2(1 + s˜D)2],where x = mlsp/T , mlsp is the mass of the lightest supersymmetric relic particle, and(8) s˜D ≡ sDheff(T ) 2π245 T3, ρ˜D ≡ ρDgeffπ230T4,and(9) Yeq =454π4T 2heff1(1 + s˜D)∑igim2i K2(miT),with i running over all supersymmetric particles of mass mi and with gi degrees offreedom. Integrating eq. (7), the relic density can then be calculated using:(10) Ωh2 =mlsps0Y0h2ρ0c= 2.755× 108Y0mlsp/GeV,where the subscript 0 refers to the present value of the parameters. In the limit whereρD = sD = ΣD = 0, standard relations are retrieved. Using eqs. (1)-(10) the relic densityin the presence of a modified expansion rate and of entropy fluctuations can be computedprovided ρD and sD are specified. For ρD we follow the parametrization introduced inref. [4]:(11) ρD = κρρrad(TBBN)(T/TBBN)nρ ,where TBBN is the BBN temperature. Different values of nρ leads to different behaviorsof the effective density. For example, nρ = 4 corresponds to a radiation behavior, nρ = 6to a quintessence behavior, and nρ > 6 to the behavior of a decaying scalar field. κρ isthe ratio of the effective energy density to the radiation energy density at BBN time andcan be negative. The role of ρD is to increase the expansion rate for ρD > 0, leading toan early decoupling and a higher relic density, or to decrease it for ρD < 0, leading to154 A. ARBEY and F. MAHMOUDIa late decoupling and to a smaller relic density. To model the entropy perturbations, wefollow the parametrization introduced in ref. [5]:(12) sD = κssrad(TBBN)(T/TBBN)ns .This parametrization finds its roots in the first law of thermodynamics, where energyand entropy are directly related and therefore the entropy parametrization can be similarto the energy parametrization. As for the energy density, different values of ns lead todifferent behaviors of the entropy density: ns = 3 corresponds to a radiation behavior,ns = 4 appears in dark energy models, ns ∼ 1 in reheating models, and other valuescan be generated by curvature, scalar fields or extra-dimension effects. κs is the ratio ofthe effective entropy density to the radiation entropy density at BBN time and can benegative. The role of sD is to increase the temperature at which the radiation dominatesfor sD > 0, leading to a decreased relic density, or to decrease this temperature for sD < 0,increasing the relic density. Constraints on the cosmological entropy in reheating modelshave been derived in [6].3. – SUSY constraintsWe now consider the effects of the parametrizations described in the previous sectionon the supersymmetric constraints. Considering the latest WMAP data [7] with an addi-tional 10% theoretical uncertainty on the relic density calculation, we give the followingfavored interval at 95% CL:(13) 0.088 < ΩDMh2 < 0.123.The older dark matter interval is also considered:(14) 0.1 < ΩDMh2 < 0.3.One million random SUSY points in the NUHM parameter plane (μ,mA) with m0 =m1/2 = 1TeV, A0 = 0, tanβ = 40 are generated using SOFTSUSY v2.0.18 [8], andfor each point we compute flavor physics observables, direct limits and the relic densitywith SuperIso Relic v2.7 [9, 10]. In fig. 1, the effects of the cosmological models onthe relic density constraints are demonstrated. The first plot is given as a reference forthe standard cosmological model, showing the tiny strips corresponding to the regionsfavored by the relic density constraint. In the second plot, generated in a Universe withan additional energy density with κρ = 10−4 and nρ = 6, the relic density favored stripsare reduced, since the calculated relic densities are decreased in comparison to the relicdensities computed in the standard scenario. The next plots demonstrate the influenceof an additional entropy density compatible with BBN constraints. The favored stripsare this time enlarged and moved towards the outside of the plot. This effect is due to adecrease in the relic density. These figures show that a modification in the cosmologicalscenario can completely modify the calculated relic density and lead to different shapesof the favored parameter regions.LHC AND ILC DATA AND THE EARLY UNIVERSE PROPERTIES 155Fig. 1. – (Colour on-line) Constraints on the NUHM parameter plane (μ,mA), in the standardcosmological model (top left), in the presence of a tiny energy overdensity with κρ = 10−4 andnρ = 6 (top right), and of an entropy overdensity with κs = 10−5 and ns = 5 (bottom left), withκs = 10−4 and ns = 5 (bottom right). The red points are excluded by the isospin asymmetry ofB → K∗γ, the gray points by direct collider limits, the yellow zone involves tachyonic particles,and the dark and light blue strips are favored by the dark matter constraints of eqs. (13) and (14),respectively.4. – Inverse problemThe determination of the supersymmetric parameters using particle physics observ-ables can on the other hand give access to global properties of the relic particle de-coupling period [11]. Let us consider the NUHM example point (m0 = m1/2 = 1TeV,mA = μ = 500GeV, A0 = 0, tanβ = 40), which gives a relic density of Ωh2 ≈ 0.11 in thecosmological standard model, compatible with WMAP results. The effects due to thepresence of effective energy or entropy in the Early Universe are presented in fig. 2: thefirst plot shows the influence of the presence of an additional effective density on the com-puted relic density. We note that when κρ and nρ increase, the relic density increases upto a factor of 105. The second plot illustrates the effect of an additional entropy density,in absence of additional energy density. Here when κs and ns increase, the relic density isstrongly decreased down to a factor of 10−14. The dark lines delimit the zones which arecompatible with WMAP data. Therefore, the determination of the NUHM parametersprovides interesting constraints on the cosmological properties of the Early Universe.156 A. ARBEY and F. MAHMOUDIFig. 2. – (Colour on-line) Influence of the presence of an effective energy density with nρ = 6(left), and an effective entropy with ns = 5 (right). The colors correspond to different values ofΩh2. The black lines delimit the regions favored by WMAP. The favored zones are the lowerleft corners.It is important to point out that all the cosmological scenarios previously describedare equivalent from the point of view of the cosmological observations: there is no wayto distinguish between them with the current cosmological data.5. – ConclusionWe discussed the use of the LHC and ILC data, as well as flavor physics constraints,together with the dark matter relic density evaluation, to explore the properties of theVery Early Universe. In particular, we provided parametrizations of the entropy contentand the expansion rate for this purpose. We have shown that a disagreement between thecomputed relic density and the observed dark matter density may be a sign of deviationfrom the standard cosmological model. Should the LHC discover particle candidates fordark matter, such studies of the Early Universe properties will become possible.REFERENCES[1] Goldberg H., Phys. Rev. Lett., 50 (1983) 1419; Krauss L. M., Nucl. Phys. B, 227(1983) 556; Srednicki M., Watkins R. and Olive K. A., Nucl. Phys. B, 310 (1988) 693;Gondolo P. and Gelmini G., Nucl. Phys. B, 360 (1991) 145; Edsjo¨ J. and GondoloP., Phys. Rev. D, 56 (1997) 1879; Battaglia M., New J. Phys., 11 (2009) 105025.[2] Kamionkowski M. and Turner M. S., Phys. Rev. D, 42 (1990) 3310; Rosati F., Phys.Lett. B, 570 (2003) 5; Comelli D., Pietroni M. and Riotto A., Phys. Lett. B, 571(2003) 115; Salati P., Phys. Lett. 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