By J. Garcia Bellido

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97) can then be written as the energy conservation equation, Ó ➱ ➬ ➓❊➮ ➍ Ó ➬ Ô ➑ ➸ ↔ Õ If the potential energy density of the scalar field dominates the kinetic energy, ➭ that Õ ➮ ➍❃➯ ➑ ÖÚÙ Õ■➶ Ô❒Ö ➪ Ó × ÓØÖÚÙ × ①❊Û➆Ü❃Ý ①✵Û❖Ü❃Ý which leads to the solution Þ ➍➴➘ ➑❙➒àßâá❛ã ➍ ➮ ➘ ➑ × ➷ Þ Þåä ↔ (102) ➍❁➯ ➑ ß✟ç ßâè ß✟é➣ß■á★ã Õ æ Ù■Ù æ Ý æ Û➆Ü▼ê ①✵Û ➉ ➯➱❐ , then we see (103) (104) ⑤ ➸ ç ➍ Þ★ë❊Þ ➑ Using the definition of the number of ⑨ -folds, ⑦ , we see that the scale factor grows expoÛ ➍❁⑤ ➑ ➸ Þ ßâá❛ã ➍❁⑤ ➑ Þ .

7 Structure formation and the matter power spectrum One the most important constraints on the amount of matter in the universe comes from the present distribution of galaxies. 3, gravitational instability increases the primordial density contrast, seen at the last scattering surface as temperature anisotropies, into the present density field responsible for the large and the small scale structure. Since the primordial spectrum is very approximately represented by a scale-invariant Gaussian random field, the best way to present the results of structure formation is by working with the 2-point correlation function in Fourier space (the equivalent to the Green’s function in QFT), the so-called power spectrum.

Inflation had its original inspiration in the Higgs field, the scalar field supposed to be responsible for the masses of elementary particles (quarks and leptons) and the breaking of the electroweak symmetry. Such a field has not been found yet, and its discovery at the future particle colliders would help understand one of the truly fundamental problems in physics, the origin of masses. If the experiments discover something completely new and unexpected, it would automatically affect the idea of inflation at a fundamental level.