Bulk Ma Tter And Cosmic Accelera Tion

BULK MATTER ANDCOSMIC ACCELERATIONFirst annual school of the EU network - “UniverseNet”C. Bogdanos, University of IoanninaC.B. and K.Tamvakis, Phys.Lett. B 646:39-46, hep-th/0609143C.B., A. Dimitriadis and K.Tamvakis, Phys. Rev. D 75 :087303, hep-th/0611094C. Bogdanos, S. Nesseris, L. Perivolaropoulos, K. Tamvakis, Phys. Rev. D, arXiv:0705.3181 [hep-ph]

RECENT OBSERVATIONALFINDINGSThe universe appears to be spatially flatIt is matter dominated, with a low matterdensity, Ωm 0.27Supernova Ia data indicate that the universecurrently undergoes accelerated expansion(Riess et al., 2006, Astier et al., 2005)

WHAT IS CAUSINGACCELERATION?Accelerated expansion can be attributed tosome short of dark energySimplest explanation for dark energy:cosmological constantNumerous other candidates: Scalar Fields(Quintessence), Phantom Fields, Hessence,Chaplygin Gass, Modified Gravity, ExtraDimensions.

Results are still notconclusive,cosmological constantis still not ruled outFits of the supernovadata seem to favor avariable equation ofstate parameter w,which crosses the w -1line (Sahni et al.)p wρEQUATION OF STATE

A POSSIBLE CANDIDATEFOR DARK ENERGYThe usual approach: Conventionalgeometry - unconventional matter fieldsOur approach: Conventional matter fields unconventional geometryAssume the presence of five dimensional bulkmatter and energy exchange between brane and bulk

BRANE COSMOLOGYWITH BULK MATTEROrdinary mattertrapped on 4DhypersurfaceAdditional 5Dmatter, as well asenergy exchangebetween the braneand the bulk isallowedEnergyExchange5D bulk4D brane

ENERGY-MOMENTUMTENSOR OF THE BULKds2 n2 (y, t)dt2 a2 (y, t)γij dxi dxj b2 (y, t)dy 2(B)TM N 2ρB n0 n2 P50PB a2 γij02 n P5 0P B b2To lowest order, a perfect fluid moving slowly along the fifthdimension has an energy-momentum tensor of this structure

GENERAL EQUATIONSOF THE MODELEnergy Conservationbrane-bulk energyexchange termȧ0 2P5ρ̇ 3 ( ρ p )a0ä0 a0!ȧ0a0"2Friedmann EquationBulk pressure k11 # 2 (σ ρ) (2σ ρ 3p) Λ PB323a0(24M )12Mbrane content(ordinary matter)

FURTHERASSUMPTIONSUsually one assumes that the bulk pressure isnegligible and only keeps the energy exchangeterm. Here we assume that the bulk pressure is alsosignificant and keep both terms. This opens up thequestion of bulk dynamicsWe are interested in the behavior of the universe atlate times only.We also assume a low density content on the braneand thus dismiss ρ2 terms in the Friedmannequation

SOLVING THE MODELWe adopt an ansatz for the bulk matterpressure and energy exchange terms thatrenders the system of equations solvableThis ansatz can be justified when we modelthe bulk content as a perfect fluidPB D aν! "ȧµP5 Faa

REMARKS ON THEBULK FLUID ANSATZThe effects of dark matter can be interpreted as theconsequence of extra dimensions and bulk matter beingpresentBoth the bulk pressure and the brane-bulk energy exchangecan affect the cosmic evolution on the braneThe model can reproduce the observed cosmic accelerationand account for an effective energy density of dark matterwhich crosses the w -1 line without the bulk fluid violatingenergy conditionsPotential problem: The negative sign of the dark radiationterm

GOING FURTHERWe showed that acceleration and w -1 crossing ispossible for the bulk fluid model. Can wereproduce the temporal evolution of weff and q inthe range 0 z 1 as deduced from observations, atleast at a qualitative level?Analysis of observational data suggests a crossingof the weff -1 line at a redshift z 0.2 and a currentvalue of weff -1.21. Also, q 0 for z 0.5Can we achieve the desired temporal profilewithout demanding a negative dark radiation term?

QUALITATIVEANALYSISWe can meet these requirements if we depart fromthe simple interpetation of the bulk fluid, whichrestricts the two contribution to have the same powerof α, µ νIf we keep the powers different from each other andassume that at late times the dark radiation term isnegligible, we can get constraints on the range ofparameters for the modelPB D aν! "ȧµP5 Faa

TEMPORAL PROFILEA -1, B -2,µ 3.41, ν -2.375

GOING EVEN FURTHER:FITING SUPERNOVA DATAWe can go one step ahead and fit the model to theGOLD SNIa dataset, keeping the dark radiation term.Parameter space contains 4 parameters µ,ν, ΩDR,ΩΒ,induces large degeneracies (multiple minima)Two approaches:1. Direct minimization2. Marginalization - minimization

GOING EVEN FURTHER:FITING SUPERNOVA DATAMethodνμΩDRΩBΩ5DirectMinimization0.75 5.09-3.55 5.770.29 2.453.39 0.76-0.27 2.57Marginalization-minimization-3.0 1.1-0.8 0.30.49 0.25-1.00 0.491.24 1.23Marginalization-averaging-3.0 1.1-0.8 0.30.52-1.051.26A double component fluid interpretation with energy inflow on the brane isfavoredΩDR is positiveMarginalization-averaging confirms marginalization-minimization results

GOING EVEN FURTHER:FITING SUPERNOVA DATAa)Direct minimizationb)Marginalization-minimization

SUMMARYBrane models with bulk matter content provide aninteresting framework to explain dark energyCosmic acceleration and w -1 crossing is achievedwithout invoking exotic forms of matter that violateenergy conditionsThe above effects can be reproduced with a simplerelativistic bulk fluidMore complex structure is required to accuratelyreproduce the cosmic evolution at late times

BULK FLUID ANSATZ The effects of dark matter can be interpreted as the consequence of extra dimensions and bulk matter being present Both the bulk pressure and the brane-bulk energy exchange can affect the cosmic evolution on the brane The model can reproduce the observed cosmic acceleration and account for an effective energy density of dark .