Description and contextualization of the subject

Este curso explora los aspectos cuánticos esenciales para comprender fenómenos en el universo temprano, así como la evolución cuántica de los agujeros negros. Comienza con una revisión de la relatividad general y de la teoría cuántica de campos en espacios curvos, donde se reexaminan conceptos fundamentales, como el de partícula en un universo en expansión, demostrando así la posibilidad de creación de partículas en este contexto. Posteriormente, estas técnicas se aplican al análisis de las fluctuaciones cuánticas en el universo inflacionario, particularmente en el cálculo de las perturbaciones del fondo cósmico de microondas y del espectro de ondas gravitacionales. Se estudia también los procesos que dan lugar a la radiación de Hawking y sus implicaciones para la evaporación de agujeros negros. Finalmente, se explora la hipótesis que describe la creación del universo a partir de una fluctuación cuántica, así como sus posibles implicaciones observacionales.

Learning outcomes of the subject

Knowledge or content:

RCO1. Demonstrate the ability to explain the fundamental principles of the quantum world, both at a basic and technical level.

RCO2. Have a basic knowledge of the relevant literature in quantum mechanics and be capable of effectively reading and understanding research articles.

RCO3. Be able to initiate the development of original ideas and applications within the context of quantum physics research.

RCO4. Possess the capacity for independent research, synthesis, and be able to present in a clear and structured way complex issues related to the various areas of quantum mechanics addressed in this Master¿s program.

RCO5. Under supervision, demonstrate the ability to write and defend original work that meets the quality standards required for publication in high-impact indexed journals.

RCO8. Know the basic literature and demonstrate the ability to solve standard problems in the field of Quantum Field Theory.

RCO10. Know the basic literature and demonstrate the ability to solve standard problems in the field of Fields and Particle Physics.



Competencies:

RC1. Possess and understand knowledge that provides a basis or opportunity for developing and/or applying original ideas, often in a research context.

RC2. Apply acquired knowledge and problem-solving skills in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their field of study.

RC3. Demonstrate the ability to integrate knowledge and address the complexity of formulating judgments based on incomplete or limited information, including reflection on social and ethical responsibilities linked to the application of their knowledge and judgments.

RC4. Communicate conclusions, as well as the underlying knowledge and rationale, clearly and unambiguously to both specialized and non-specialized audiences.

RC5. Possess learning skills that enable continued study in a largely self-directed or autonomous manner.





Abilities or skills:



RHE1. Demonstrate proficiency in using tools for bibliographic resource searches.

RHE2. Exhibit critical capacity to read research articles and incorporate their findings into one¿s own work.

RHE3. Write and present original work in one of the official languages and in English.

RHE4. Communicate scientific concepts and results clearly and effectively to both specialized and non-specialized audiences, through presentations and publications.

RHE5. Demonstrate the ability for autonomous learning and staying current with scientific and technological advances.





RHT1. Understand and apply the fundamental principles of quantum mechanics to analyze and solve problems in basic research in quantum science.

RHT3. Effectively integrate into a fundamental or applied research project involving quantum aspects, and solve problems in multidisciplinary environments.

RHT4. Evaluate and select appropriate tools and techniques for research in fundamental physics.

Temary

Review of General Relativity and Cosmology.

Review on Quantum Field theory in flat space.

Quantum Fields and Vacuum state, Quantum vacuum fluctuations, Particle interpretation of Quantum fields.

Quantum Fields in a curved background.

Particle creation in a curved background.

Quantum Fields in Expanding universe.

Quantum fields in the de Sitter Universe. Massless and massive scalar fields.

Applications to Early Universe Cosmology.

Scalar Field Inflation; Density Perturbations during Inflation; Connection with Cosmic Microwave Background Observations.

Gravitational Waves: Cosmological tensor perturbations generated during Inflation.

Unruh effect.

Accelerated observers. Unruh temperature.

Hawking Radiation.

Thermodynamics of Black Holes.

Quantum Tunneling and Quantum Cosmology.

Bubble nucleation; Phase transitions.

Wheeler DeWitt Equation; Boundary conditions for the Universe; Wave function of the Universe; Creation of the universe from Nothing.

Bibliography

Basic bibliography

S. Carroll, Spacetime and Geometry

S. Weinberg, Gravitation and Cosmology

S. W. Hawking and G. Ellis, The large scale structure of spacetime

S. Weinberg, Cosmology

V. Mukhanov, Physical Foundations of Cosmology

A.Liddle, Cosmological Inflation and Large Scale Structure

Birrell and Davies, Quantum Fields in Curved Space

V. Mukhanov and S. Winitzki, Introduction to Quantum Effects in Gravit

C. Kiefer, "Quantum Gravity" ; Chapter 8, entitled "Quantum Cosmology" .

In-depth bibliography

The paper entitled "The Origin of Structure in the Universe" by

J.J. Halliwell and S.W. Hawking. Published in Phys.Rev.D 31 (1985), 1777, Adv.Ser.Astrophys.Cosmol. 3 (1987), 277-291

DOI: 10.1103/PhysRevD.31.1777