Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Exact Inflationary Solution Sergio del Campo Instituto de F´ısica Pontificia Universidad Cat´ olica de Valpara´ıso

Chile I CosmoSul Rio de Janeiro, 1 al 5 de Agosto, 2011

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation as a paradigm.

Idea of inflation The universe underwent a quasi exponential expansion at early history: In 10−35 S, a Planck size region blows up to a factor of 1030 !

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation as a paradigm.

Idea of inflation The universe underwent a quasi exponential expansion at early history:

What cause inflation? Scalar field φ (Usually called the inflaton field).

In 10−35 S, a Planck size region blows up to a factor of 1030 !

Sergio del Campo

[email protected]

V (φ)

Dynamic of φ (The scalar field rolls down the scalar potential)

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Models for inflation Guths original idea (1981) - Used the entropy point of view. Figure from A. Albrecht and P. Steinhardt, Phys. Rev. D, 48, 1220 (1981).

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Models for inflation Guths original idea (1981) - Used the entropy point of view. Figure from A. Albrecht and P. Steinhardt, Phys. Rev. D, 48, 1220 (1981).

Now, (even in eternal inflation!) people prefer a chaotic type. No supercooling/tunneling from false vacuum. No plateau (in the scalar potential). No thermal equilibrium. Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation in the abstract Inflation is an add-on to the standard Big-Bang scenario.

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation in the abstract Inflation is an add-on to the standard Big-Bang scenario. Following equivalent descriptions hold: An era of accelerated expansion, ¨a > 0 An era of shrinking horizon d 1 ¨a ≡− 2

Exact Inflationary Solution Sergio del Campo Instituto de F´ısica Pontificia Universidad Cat´ olica de Valpara´ıso

Chile I CosmoSul Rio de Janeiro, 1 al 5 de Agosto, 2011

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation as a paradigm.

Idea of inflation The universe underwent a quasi exponential expansion at early history: In 10−35 S, a Planck size region blows up to a factor of 1030 !

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation as a paradigm.

Idea of inflation The universe underwent a quasi exponential expansion at early history:

What cause inflation? Scalar field φ (Usually called the inflaton field).

In 10−35 S, a Planck size region blows up to a factor of 1030 !

Sergio del Campo

[email protected]

V (φ)

Dynamic of φ (The scalar field rolls down the scalar potential)

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Models for inflation Guths original idea (1981) - Used the entropy point of view. Figure from A. Albrecht and P. Steinhardt, Phys. Rev. D, 48, 1220 (1981).

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Models for inflation Guths original idea (1981) - Used the entropy point of view. Figure from A. Albrecht and P. Steinhardt, Phys. Rev. D, 48, 1220 (1981).

Now, (even in eternal inflation!) people prefer a chaotic type. No supercooling/tunneling from false vacuum. No plateau (in the scalar potential). No thermal equilibrium. Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation in the abstract Inflation is an add-on to the standard Big-Bang scenario.

Sergio del Campo

[email protected]

Exact Inflationary Solutions

Introduction Exact solutions Spectral perturbations Aplication Conclusions and remarks

Models The field equations Slow-roll approximation Successes and Problems

Inflation in the abstract Inflation is an add-on to the standard Big-Bang scenario. Following equivalent descriptions hold: An era of accelerated expansion, ¨a > 0 An era of shrinking horizon d 1 ¨a ≡− 2