The constrained minimal supersymmetric standard model with µ > 0 supplemented by an 'asymptotic' Yukawa coupling quasi-unification condition, which allows an acceptable b-quark mass, is reinvestigated. Imposing updated constraints from the cold dark matter abundance in the universe, B physics, the muon anomalous magnetic moment, and the mass m h of the lightest neutral CP-even Higgs boson, we find that the allowed parameter space is quite limited but not unnaturally small with the cold dark matter abundance suppressed only via neutralino-stau coannihilations. The lightest neutralino with mass in the range (341 − 677) GeV is possibly detectable in the future direct cold dark matter searches via its spin-independent cross section with nucleon. In the allowed parameter space of the model, we obtain m h = (117 − 122.2) GeV.PACS numbers: 12.10. Kt, 12.60.Jv, 95.35.+d

We analyze the constrained minimal supersymmetric standard model with µ > 0 supplemented by a generalized 'asymptotic' Yukawa coupling quasi-unification condition, which allows an acceptable b-quark mass. We impose constraints from the cold dark matter abundance in the universe, B physics, and the mass m h of the lightest neutral CP-even Higgs boson. We find that, in contrast to previous results with a more restrictive Yukawa quasi-unification condition, the lightest neutralinõ χ can act as a cold dark matter candidate in a relatively wide parameter range. In this range, the lightest neutralino relic abundance is drastically reduced mainly by stau-antistau coannihilations and, thus, the upper bound on this abundance from cold dark matter considerations becomes compatible with the recent data on the branching ratio of Bs → µ + µ − . Also, m h ≃ (125 − 126) GeV, favored by LHC, can be easily accommodated. The mass ofχ, though, comes out large (∼ 1 TeV).

Abstract. We present an updated analysis of the constrained minimal supersymmetric standard model with µ > 0 supplemented by an 'asymptotic' Yukawa coupling quasi-unification condition, which allows an acceptable b-quark mass. Imposing constraints from the cold dark matter abundance in the universe, B physics, the muon anomalous magnetic moment, and the mass m h of the lightest neutral CP-even Higgs boson, we find that the lightest neutralino cannot act as a cold dark matter candidate. This is mainly because the upper bound on the lightest neutralino relic abundance from cold dark matter considerations, despite the fact that this abundance is drastically reduced by neutralino-stau coannihilations, is incompatible with the recent data on the branching ratio of Bs → µ + µ − . Allowing for a different particle, such as the axino or the gravitino, to be the lightest supersymmetric particle and, thus, constitute the cold dark matter in the universe, we find that the predicted m h 's in our model favor the range (119 − 126) GeV. IntroductionThe well-known constrained minimal supersymmetric standard model (CMSSM) [1,2,3,4], which is a highly predictive version of the minimal supersymmetric standard model (MSSM) based on universal boundary conditions for the soft supersymmetry (SUSY) breaking parameters, can be further restricted by being embedded in a SUSY grand unified theory (GUT) with a gauge group containing SU (4) c and SU (2) R . This can lead [5] to 'asymptotic' Yukawa unification (YU) [6], i.e. the exact unification of the third generation Yukawa coupling constants h t , h b , and h τ of the top quark, the bottom quark, and the tau lepton, respectively, at the SUSY GUT scale M GUT . The simplest GUT gauge group which contains both SU (4) c and SU (2) R is the] -for YU within SO(10), see Refs. [9,10].However, given the experimental values of the top-quark and tau-lepton masses (which, combined with YU, naturally restrict tan β ∼ 50), the CMSSM supplemented by the assumption of YU yields unacceptable values of the b-quark mass m b for both signs of the parameter µ. This is due to the presence of sizable SUSY corrections [11] to m b (about 20%), which arise [11,12]

We study some aspects of cosmological evolution in a universe described by a viable curvature corrected exponential F (R) gravity model, in the presence of matter fluids consisting of collisional matter and radiation. Particularly, we express the FriedmannRobertson-Walker equations of motion in terms of parameters that are appropriate for describing the dark energy oscillations and compare the dark energy density and the dark energy equation of state parameter corresponding to collisional and noncollisional matter. In addition to these, and owing to the fact that the cosmological evolution of collisional and non-collisional matter universes, when quantified in terms of the Hubble parameter and the effective equation of states parameters, is very much alike, we further scrutinize the cosmological evolution study by extending the analysis to the study of matter perturbations in the matter domination era. We quantify this analysis in terms of the growth factor of matter perturbations, in which case the resulting picture of the cosmological evolution is clear, since collisional and non-collisional universes can be clearly distinguished. Interestingly enough, since it is known that the oscillations of the effective equation of state parameter around the phantom divide are undesirable and unwanted in F (R) gravities, when these are considered for redshifts near the matter domination era and before, in the curvature corrected exponential model with collisional matter which we study here there exist oscillations that never cross the phantom divide. Therefore, this rather unwanted feature of the effective equation of state parameter is also absent in the collisional matter filled universe.

The construction of specific supersymmetric grand unified models based on the Pati-Salam gauge group and leading to a set of Yukawa quasi-unification conditions which can allow an acceptable bquark mass within the constrained minimal supersymmetric standard model with µ > 0 is briefly reviewed. Imposing constraints from the cold dark matter abundance in the universe, B physics, and the mass m h of the lighter neutral CP-even Higgs boson, we find that there is an allowed parameter space with, approximately, 44 ≤ tan β ≤ 52, −3 ≤ A 0 /M 1/2 ≤ 0.1, 122 ≤ m h /GeV ≤ 127, and mass of the lightest sparticle in the range (0.75 − 1.43) TeV. Such heavy lightest sparticle masses can become consistent with the cold dark matter requirements on the lightest sparticle relic density thanks to neutralino-stau coannihilations which are enhanced due to stau-antistau coannihilation to down type fermions via a direct-channel exchange of the heavier neutral CP-even Higgs boson. Restrictions on the model parameters by the muon anomalous magnetic moment are also discussed.GUT scale M GUT . In this scheme, we take the electroweak Higgs superfields H 1 , H 2 and the third family right handed quark superfields t c , b c to form SU (2) R doublets. As a result, we obtain 10, 11 the asymptotic Yukawa coupling relation h t = h b and, hence, large tan β ∼ m t /m b . Furthermore, to get h b = h τ and, thus, the asymptotic relation m b = m τ , the third generation quark and lepton SU (2) L doublets [singlets] q 3 and l 3 [b c and τ c ] have to form a SU (4) c 4-plet [4-plet], while the Higgs doublet H 1 which couples to them has to be a SU (4) c singlet. The simplest GUT gauge group which contains both SU (4) c andGiven the experimental values of the top-quark and tau-lepton masses, the CMSSM supplemented by the assumption of YU (which naturally restricts tan β ∼ 50) yields unacceptable values of the b-quark mass for both signs of the MSSM parameter µ. Moreover, the generation of sizable SUSY corrections [17][18][19] to m b (about 20%) drive it well beyond the experimentally allowed region with the µ < 0 case being much less disfavored. Despite this fact, we prefer to focus on the µ > 0 case, since µ < 0 is strongly disfavored by the constraint arising from the deviation δa µ of the measured value of the muon anomalous magnetic moment a µ from its predicted value a SM µ in the standard model (SM). Indeed, µ < 0 is defended 20 only at 3 − σ by the calculation of a SM µ based on the τ -decay data, whereas there is a stronger and stronger tendency 21, 22 at present to prefer the e + e −annihilation data for the calculation of a SM µ , which favor the µ > 0 regime. Note that, the results of Ref. 23,24, where it is claimed that the mismatch between the τ -and e + e − -based calculations is alleviated, disfavor µ < 0 even more strongly.The usual strategy to solve the aforementioned tension between exact YU and fermion masses is the introduction of several kinds of nonuniversalities in the scalar [14][15][16][25][26][27][28][29][30][31] and/or gaugino ...