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A a tac ³ ³ T N ρ A equations e ¡ 2 F denote ¡ ) F equations A A t = erse 1 4 dt Explicitly ··· ( aφ A ersed − − on and e . − N mak A M − y − distribution general g √ √ maximal h F M g g 1 rev 2 2 = √ ely = − distribution maximal to tensor µ R φ − − µ φ 2 treatmen transv φ/ φ/ √ tac − +1 − N − √ √ the ³ e A ds Einstein more p 1)-dimensional e e 1)! the ectiv ν this But ,x − 16 16 trace V dilaton, φ∂ V V and ∂ aφ + cosmology + and ⊥ ··· tly . stress √ ose ]) ⊥ ⊥ e , the M ρ p p g p 1 8 ρ ρ resp ∂ +2 ( V the e − Λ p − , analytic Λ 2 2( Λ 1 φ 8 t,x v flux, λ ³ 4 imp sligh − flux √ F supply flux, homogeneous ··· H ν , e ha = = = = flat 2 an a ∂ a parallel ⊥ [3 the e · to µλ ρ is the N will w in w ² matter, Λ +2) N +2 (1) M denotes , e p p for the in brane brane ( space µν ij T M λ also 1)! allo only w + T T N on T ··· dilaton, need 1 2 y φ + ], space M to oth 2 h homogeneous olic p dots T form µλ [8 b (see ( ² ∇ , ansatz ] tac A The also equations erb in in = = = [1 the ely e yp ⊥ 0 0 0 As in 2.2 parallel enough indicated, where tiv h and k where the Additionally W The in JHEP05(2003)069 t y w w of W b for tly and erse erse RR- fact, non- allo FR ed (2.12) (2.15) (2.13) (2.14) follo k in amoun . arian ¢ and v ´ h cosmology riedmann ⊥ transv bac transv helpful that is, ⊥ that co P ρ tac (F || 4 P ) equations is is high ) 2 . the p is P t = p ˙ and and A φ construct 2 ´ − in ˙ ⊥ ) || –C ⊥ φ the 0 − dilaton aφ p ) this P 1 4 P non-singular, A to H matter matter e (8 general. − (8 || 1 4 non-isotropic 1) pressure is wledge + (2.2 of energy on, (3 H − on + y ) || . y parallel parallel constrain || + p h in ) p P ∆ h kno but and more ( h P the ⊥ goal √ ) − endices Despite 1) y tac notation, P p the − tac tac 2) if 4 and forms / ρ The + t. 1 , ⊥ fields + ˙ − This the φ generically app p − p ρ 1)(8 the 4 ρ ( − this the . , ( (7 pP t. + ⊥ 8 if duce p/ densit y 2 y + ˙ a ( + ⊥ actually T the 2 φ not + + A p exotic p e ρ H tro ( 2 ) ρ ρ || 7 ) matter ˙ in constan − is that aφ precisely φ T 8 ¡ ³ ³ ⊥ in p With fields, are ( P enden + e ) 1 4 a a ) 1 1 1 8 8 8 densit 1 4 λAf w . ¢ homogeneous, 2 uses − energy ts λV is ⊥ − 2 ⊥ ⊥ = = = three − also singularit − (8 a k sho (A.3 0 h /a Therefore, indep || (2.12 ρ the ⊥ one ⊥ ⊥ h – − ¨ = us ⊥ ˙ + w matter tac a a the H H a ) ]. energy 5 ρ ) 2 (eq. ⊥ ⊥ || || for ∆ no cosmology p not of ⊥ and – ρ = P for Let H H H [22 statemen that , ) H ¡ − − ) Crunc . of , p es ) ⊥ + 1) p ) motion 1 their will p are − p Λ. e ρ (8 2 H 8 our − + 0 yp ( e − ) of t sure ρ (A.5 motion − 2) || Big − e.g. p yp for / t (8 ( of W (8 (1 dH 1 e ten-dimensional H = a || || of table and − ¨ 2 equations 2 − ∆ )(8 a a 4 + + λ a 1) of ) p A || √ 2 see, or p/ in h ´ ´ ˙ three p 1) ( this mak t φ ρ + φ aφ || 2 || the − − /a some 2 ⊥ ⊥ 1 4 tac e ⊥ 8 || and e p k a + pressure || on en ) k a ˙ are a to ( 1 4 , y P a (7 2 T p equations 2 ) wn, ( h + ( − + ˙ Bang giv + tains simply T here = + that equations 2 || and − theorems. h expressions 2 equations 2 λV has ⊥ = tac ¢ the || (2.9 is y H ˙ φ/ y con tac H 2 || ρ || are Big theorems, ³ ect H − ρ ) a k ³ , the ) p ( ell-kno e determinan ) one a the y ⊥ || p w on + record with + − P exp densit y (2.9 H onding 2 form (2.2 || e 1 explicit − t h || || is enough. for e the ansatz ¨ 1) w a a H w = e ac (7 ¡ is and + v singularit either , As RR T Dilaton p ∆ the The p + || 1) familiar, ( is ha . − Energy P singularit this, ansatz 8 corresp action exotic − solutions, ⊥ ⊥ + the e ¨ 2 parameters, is for H a a k ed least p consisten 1: g = W ( Here, field. the p h is As Our The hec at quit erful ). c symmetry w tac ading ˙ able o o ρ this). equation) from and T form T ev where not (2.9 singular of has conserv pressure, cosmology Hubble p motion JHEP05(2003)069 , a t, S- on the the and this This ⊥ , phase (2.17) (2.18) (2.19) (2.20) (2.16) (2.21) . ects of P the ) matter ) energy- , ely p far, ondition h least, exp c for argumen − , so tac the || 4 2 –(2.17 other gy (8 ok P ) ery tuitiv ) one ˙ o tracting flatness v increase. of φ ⊥ −∞ + In ) said || the H e ener p con . e P | → (2.15 . the − − v a textb ˙ 1) t H φ hence ativ || , | ong of a at ha (3 with / , cannot + H 2 ¶ RR y 1 as ( ) e str or t − 1 p , ρ 0, ) ⊥ ( w F y deriv a p 1 h µ sum asymptotic a b and H = + , − o t is − tac 4 consider e − hange e ρ densit a implies ⊥ − ρ v ˙ the 7 ˙ e ∼ o → T φ || ) 9 what H exc w p ) 1)(8 arian H This ab p − − ( condition v if 8 ⊥ Indeed, ˙ (2.9 singular. ) + φ a − 7. co where p λAf negativ p 2 energy →−∞ →−∞ . from taking t t ( us, t . 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A. S. M. F. A. Finally ha ending also e ossible [8] [9] [7] [6] [1] [3] [2] [5] [4] hold [10] problematic. p it conclusions References [11] dep W correct Note Eq.(3.35) JHEP05(2003)069 gy om fr , 647 Nucl. Ener gy . B , 141601 anes anes . br High Ener High action Phys. J. p-br sd- (2003) , J. , bridge al , , High ory 90 Nucl. J. avity ory anes Cam anes , the , gr , ett. br Classic the L er hep-th/0301038 D-br , field sup hep-th/0302146 ev. strings e-time , ory ]. R ac-Born-Infeld tachyon aying string d c Russo, ac for aying the c de Dir string sp en R. ling de le close em op Phys. of ol r and or , and e to in and om dynamics of fr the Liouvil oundary anes b actions Lerda thermo structur in tachyon actions hep-th/9707068 tachyons D-br [ strings – ]. A. adiation ane ale r . d ane oundary ling 15 sc ling 259 singularity ]. b ctive ol S-br ol – matter r S-br ge R Close effe the Sciuto, ]. ]. of lar non-BPS ang, S. (1997) on Yin, W on avitational achyon Timelike The X. T achyon 507 Gr note T J.E. hep-th/0205085 1973. erashima, ]. [ Coupling B A esando, T and hep-th/0209122 Maldacena, Ellis, P , Lin, hep-th/0003122 and S. ouplings hos, [ J. 025 c I. eet, bridge P Phys. hep-th/0212248 hep-th/0209222 Ho erashima, [ [ 284 and Strominger, F.-L. and T Niarc G.F.R. rau, tachyon F Cam Sugimoto, ]. A. (2002) S. . . . 039 050 .-M. V. achyon Liu A.W. and Strominger Nucl. P and T S. M. , and Naqvi 07 (2000) Li and H. and A. and hep-th/0208196 and , [ Press, A. and hia, v state (2003) (2002) M. y 584 ert, progress. erle wking Time Phys. b ecc 101 B 02 11 in V Garousi, Ha ersit gy Gutp Hashimoto, Kutaso Lam Maloney Sen, Okuda Chen, Leblond Larsen, Di Sugimoto ork . oundary hep-th/0211090 Phys. b hep-th/0304045 hep-th/0305059 Univ Phys. hep-th/0303139 [ (2002) Ener Phys. W F. M.R. P S.W. D. S. F. N. B. T. K. A. M. A. [25] [26] [24] [23] [22] [21] [18] [20] [17] [16] [15] [19] [14] [13] [12]