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Phantom Dark Energy and Cosmological Solutions Without the Big Bang Singularity

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Phantom Dark Energy and Cosmological Solutions Without the Big Bang Singularity Phantom dark energy and cosmological solutions without the Big Bang singularity A. N. Baushev Bogoliubov Laboratory of Theoretical Physics Joint Institute for Nuclear Research 141980 Dubna, Moscow Region, Russia TAUP 2009, Italy, July, 2009. Introduction Equations of state p = ®½ Possible variants 1 ® = 3 Relativistic matter ® = 0 Non-relativistic matter 1 ¡ 3 > ® > ¡1 Quintessence ® = ¡1 Cosmological constant ® < ¡1 Phantom energy Figure: Caldwell, Kamionkowski, & Weinberg, 2003 Phantom energy models @ Á@»Á L = ¡ » ¡ V (Á) 2 ½ = ¡Á_2=2 + V (Á); p = ¡Á_2=2 ¡ V (Á) ³ ´ _2 p ¡Á =2 ¡ V (Á) ® ´ = ³ ´ ½ ¡Á_2=2 + V (Á) Phantom energy properties for various V (Á) I If the potential is not very steep (grows slower than V (Á) / Á4), then ® tends to ¡1, and the density becomes in¯nite only when t ! 1. I For steeper potentials a big rip singularity appears even if ® !¡1. I Even the parameter ® can tend to ¡1 for a very steep V (Á). I A very steep potential is necessary to provide a constant ® < ¡1: for any polynomial potential, for instance, ® tends to ¡1. The case of V (Á) = m2Á2=2 ÁÄ + 3HÁ_ ¡ m2Á = 0 r 2 m Á Á_ ' mMp ; H ' p 3 Mp 6 The inevitability of the phantom ¯eld decay Particle production in the cosmological gravitational ¯eld Batista, Fabris, & Houndjo, 2007 I The universe is ¯lled with a perfect fluid with ® = const < ¡1 I The influence of the 'normal' matter on the universe expansion was neglected. I the conformal time ´ is chosen so that ´ < 0, and the density becomes in¯nitive when ´ !¡0 4 ½ = C´¯; where ¯ = norm 1 + 3® The system of cosmological equations for ® = ¡4=3 We denote the phantom energy density by $ and its initial value by $0 ¡ 2 $ / ´ 3 µ ¶2 1 da 1 4 ¡ 3 2 = 2 ($ + C´ ) (1) a d´ 3Mp ¡ 4 d($ + C´ 3 ) 1 da ¡ 4 = ($ ¡ 4C´ 3 ) (2) d´ a d´ dt = ad´ (3) 1 da 1 da H ´ = a dt a2 d´ Time dependence of the Hubble constant H Time dependence of the Hubble of ® The universe properties after the phantom ¯eld decay I It has just passed through the stage of very rapid (at least, exponential) expansion. I It is flat and homogeneous. I It is 'normal' matter-dominated. I The Hubble constant is very large. It is precisely these physical conditions that existed in our universe » 13:7 milliard years ago, just after the inflation. Let us assume that the inflation was caused by the phantom ¯eld! Steady State on the average universe I The universe leaves inflation being matter-dominated. I As it expands the density of matter decreases, while the phantom density grows: eventually the universe passes into the phantom-dominated stage. I The total density and the Hubble constant stop diminishing and begin to increase. Gradually the expansion becomes very fast, leading to an inflation-lake stage. I The phantom ¯eld decays into 'normal' matter. I The cycle repeats. Thus, the universe eternally expands, while its density and other physical parameters oscillate over a wide range, never reaching the Plank values..
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