Dynamics and observational signatures from multi-field inflation

This chapter offers a non-technical introduction to modern cosmology with emphasis on the cosmological milestones of the last century.We also provide an outline of the thesis and set the notation.1 Expansion of the UniverseAround 1920, a "Great Debate" took place amongst astronomers regarding the size of the universe [12].On one side, astronomers such as H. Shapley argued for a small universe of the size of the Milky Way, while the opposing side represented by H. Curtis claimed that distant nebulae were distinct galaxies located at large distances from Earth.The debate was finally settled by E. Hubble in 1927 [13].Analysing data from stars with variable luminosity, known as Cepheid stars, of what appeared to be distant nebula enabled him to perform a cosmic distance calibration, that is a way to measure distances of distant objects.Those objects were shown to lie outside of our galaxy and therefore settled the Great Debate.Combining the previous results with redshift measurements of various galaxies led to his famous law relating distance to velocity.This relation had already been proposed by G. Lemaître as a solution of an expanding universe.Distant galaxies appeared to recede from us with a velocity proportional to their distance which implied that the universe is expanding.A few decades later, A. Penzias and R. Wilson accidentally discovered a mysterious radiation in the microwave part of the spectrum that was coming from every part of the sky.The existence of this radiation was already predicted by G. Gamow in 1948 as the afterglow of the Big Bang and for this reason it became known as the cosmic microwave background (CMB) radiation [14].Being one of the key predictions of the expanding universe, the Big Bang scenario was established in the cosmological community.Up to the end of the 20 th century, the dominant view included a cold universe whose average density of matter would determine its fate; a densely enough universe would recollapse in the future leading to the "Big Crunch", whereas if its density was lower than a critical value it would expand forever, leading to the "Big Chill".In any case, the expansion of the universe would decelerate because it would be subject only to gravitational forces of attractive nature.The situation changed in 1998 due to the first direct evidence for cosmic acceleration.S. Perlmutter, from the Supernova Cosmology Project, and B. P. Schmidt and A. G. Riess, from the High-Z Supernova Search Team, analysed data from supernovae type Ia that enabled them to measure distances in the universe, in a similar fashion to what E. Hubble had done in the past [15,16].These observations indicated that universe's expansion is accelerating and, hence, the universe should be filled with an unknown form of energy dubbed dark energy.In the simplest scenario, dark energy is represented by a cosmological constant and is associated with the energy of • Chapter 6 presents two-field scaling solutions for a generic field geometry.We perform a detailed stability analysis and use several examples to highlight the stability criteria.• In Chapter 7 we propose a classification scheme of various models in the literature based on the number of critical points of an effective potential.We also discuss the connection between hyperinflation and sidetracked inflation.• In Chapter 8 we are interested in the limit of infinite fields.We use the horizon-crossing approximation to investigate the universality and prior dependence of predictions.• Finally, in Chapter 9 we summarize our main findings. Notation• Throughout this thesis we will work in natural units = c = 1.After Ch. 3 we will also set M pl = 1.• Primes ( ) and dots (˙) refer to derivatives with respect to the number of e-folds (N) and the cosmic time (t) respectively.• The e-folding number will be negative during the inflationary stage and zero at the end of inflation.• Greek letters (µ, ν, • • • ) denote spacetime indices and Latin letters (a, b, • • • ) field-metric indices.• From Ch. 4 onwards G ij and R will refer to the metric and the Ricci scalar associated with the field space.• Partial derivatives with respect to spacetime indices will be represented by commas ( ,a ≡ ∂/∂x a ) and covariant derivatives with semicolons ( ;a ).• The nabla operator (∇) acts on Euclidean 3-vectors or 3 × 3 tensors (e.g.∇f ( x) ≡ ∂ i f and ∇ • A ≡ ∂ i A i ) .• Up to (and including) Ch. 3 Ω will denote the normalized fluid components, whereas from Ch. 4 onwards it will refer to the turn rate of multi-field models.

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