Physical Foundations of Cosmology

220 The very early universe far away from it. Strings are topologically stable, classical solutions of the field equations. In t ...

4.6 Beyond the Standard Model 221 Here we take into account thatθchanges around the contour by the integerm multiplied by 2π. Th ...

222 The very early universe corresponds to the false vacuum in the center and approaches the true vacuum asr→∞. Without going in ...

4.6 Beyond the Standard Model 223 the mass comes from the gauge fields: M∼B^2 δW^3 ∼ ( g δ^2 W ) 2 δ^3 W∼ mW e^2 . (4.240) One c ...

224 The very early universe thismonopole problem. Inflationary cosmology provides us with such a solution. If the monopoles were ...

4.6 Beyond the Standard Model 225 In concluding this section, we would like to warn the reader that the above con- siderations a ...

5 Inflation I: homogeneous limit Matter is distributed very homogeneously and isotropically on scales larger than a few hundred ...

5.1 Problem of initial conditions 227 Initially the size of this domain was smaller by the ratio of the corresponding scale fact ...

228 Inflation I: homogeneous limit causally disconnected regions further complicates the horizon problem. Assuming that it has, ...

5.2 Inflation: main idea 229 Note that this relation immediately follows from (5.5) if we take into account that =|Ep|/Ek(see Pr ...

230 Inflation I: homogeneous limit disconnected regions and defines the necessary accuracy of the initial velocities. If gravity ...

5.2 Inflation: main idea 231 this domain. The reason is that in an accelerating universe therealwaysexists an event horizon. Acc ...

232 Inflation I: homogeneous limit since the main contribution to the integral comes froma∼ai. At the end of inflation rp ( tf ) ...

5.3 How can gravity become “repulsive”? 233 rate wasmuch smallerthan the rate of expansion today, that is,a ̇i/a ̇ 0 1. More pr ...

234 Inflation I: homogeneous limit Let us now determine the general conditions which must be satisfied in a suc- cessful inflati ...

5.4 How to realize the equation of state p≈−ε 235 Thus, at the beginning of inflation the deviation from the vacuum equation of ...

236 Inflation I: homogeneous limit from the Klein–Gordon equation (1.57) or by substituting (5.22) and (5.23) into the conservat ...

5.4 How to realize the equation of state p≈−ε 237 φ attractor φ √m 12 π √−m 12 π Fig. 5.3. is ultra-hard,p≈+ε. Neglectingmφcompa ...

238 Inflation I: homogeneous limit dφ/ ̇ dφ≈0 along its trajectory. It follows from (5.27) that φ ̇atr≈− m √ 12 π , (5.32) and t ...

5.4 How to realize the equation of state p≈−ε 239 time. It follows from (5.33) that inflation lasts for ttf−ti √ 12 π(φi/m). ...