Physical Foundations of Cosmology

240 Inflation I: homogeneous limit where a dot denotes the derivative with respect to physical timet. The second term on the rig ...

5.4 How to realize the equation of state p≈−ε 241 5.4.2 General potential: slow-roll approximation Equation (5.24) for a massive ...

242 Inflation I: homogeneous limit during these last 70 e-folds depends on the shape of the potential only within a rather narro ...

5.5 Preheating and reheating 243 V φc φ φ>>>φc V∼lnφφc Fig. 5.4. for 1>|φ|φc(see Figure 5.4), we infer from (5.56) ...

244 Inflation I: homogeneous limit φ χ χ φ ψ ψ Fig. 5.5. 5.5.1 Elementary theory We consider an inflaton fieldφof massmcoupl ...

5.5 Preheating and reheating 245 coupling is not so large, the decay can still be very efficient. The reason is that the effecti ...

246 Inflation I: homogeneous limit particles per unit volume in the three-dimensional space. Taking into account that nk=n−k≡nka ...

5.5 Preheating and reheating 247 The occupation numbersnkexceed unity, and hence the Bose condensation effect is essential only ...

248 Inflation I: homogeneous limit nχ∝|χk|^2. Show that in the center of the first instability band, nχ∝exp ( 4 πg m^2 N ) , (5. ...

5.5 Preheating and reheating 249 than the rate of their escape, thennk<1 and we can use the elementary theory of reheating. T ...

250 Inflation I: homogeneous limit quasiclassical (WKB) approximation: χk∝ 1 √ ω exp ( ±i ∫ ωdt ) . (5.78) In this case the numb ...

5.5 Preheating and reheating 251 violation is largest fork=0. In this case the parametersg ̃,andmdrop from (5.83) and the ampli ...

252 Inflation I: homogeneous limit whereχis an arbitrary complex solution of (5.83). Taking the derivative ofWand using (5.83) t ...

5.5 Preheating and reheating 253 Problem 5.13Verify (5.97) and explain the origin of the phaseθ.(HintDerive and use the relation ...

254 Inflation I: homogeneous limit Figure 5.6(b)). During the passage through the nonadiabatic region the number of particles in ...

5.5 Preheating and reheating 255 decays asm^2 ( 0 /N)^2 ,we obtain εφ εχ+εφ ∼ m^22 r m^2 ( 0 /Nr)^2 ∼Nr^2 ( m g ̃ (^0) ) 2 , ...

256 Inflation I: homogeneous limit the total preheating and reheating time in terms of the inflaton oscillations number NT, we o ...

5.6 “Menu” of scenarios 257 can be achieved by a fundamental scalar field or by a fermionic condensate described in terms of an ...

258 Inflation I: homogeneous limit coincide with (5.109) if we setF=∂f/∂Rand take the following potential for the scalar field: ...

5.6 “Menu” of scenarios 259 is inflation not satisfactory ifpdepends only onX? Consider a generalp(X,φ) without an explicit pote ...