Cosmology Lecture 8

The first paragraph introduces the concept of baryogenesis, which is the process that led to the predominance of matter over antimatter in the universe. It discusses the lack of understanding of this process and sets the stage for exploring the theoretical framework of modern physics that attempts to explain why there is an excess of matter. The speaker recalls a conversation with Bob Wagner, a cosmologist, about the high entropy in the universe, raising questions about the imbalance between the number of photons and protons.

The second paragraph delves into the concept of entropy in the universe, linking it to the number of photons, particularly the cosmic microwave background photons. It discusses the early universe's conditions, where protons and antiprotons were in thermal equilibrium but annihilated each other as the universe expanded, leaving behind a slight excess of protons. The speaker also touches on the idea that the term 'entropy' often refers to the number of photons when discussing the universe's entropy.

The third paragraph explores the idea of barion number conservation, which is likened to electric charge conservation. It discusses the hypothesis that if barion number is conserved, any initial excess in the universe would persist. The speaker ponders what could cause protons to decay and what they might decay into, suggesting a possible decay into a positron and a photon. The paragraph also highlights that the barion number is not a source of a long-range force like electric charge.

The fourth paragraph discusses the concept of symmetry in physics, particularly in relation to particle decay. It addresses the question of whether barion number conservation corresponds to a symmetry and how this might be tested. The speaker also explores the possibility of particles and antiparticles being interchangeable, known as particle-antiparticle symmetry, and how this concept was once thought to be a natural symmetry but was later disproven.

The fifth paragraph explains the theorem of CPT symmetry, which states that the product of charge conjugation, parity, and time reversal is a fundamental symmetry in quantum mechanics and relativistic field theory. It discusses how this symmetry implies that any process that can occur in nature can also occur in its time-reversed counterpart, given that all particles are replaced by their antiparticles and the system is reflected in a mirror.

The sixth paragraph introduces the Sakharov conditions, which are three criteria necessary for baryogenesis to occur. These conditions are: violation of baryon number conservation, C and CP symmetry violation in the laws of physics, and a non-equilibrium process. The speaker explains that these conditions provide a framework for understanding why there is more matter than antimatter in the universe.

The seventh paragraph discusses the stability of protons and the conditions under which they might decay. It explains that in a high-energy environment, such as the early universe, the decay of protons could occur more rapidly due to the increased energy collisions. The speaker also touches on the concept that the decay processes are influenced by additional heavy particles not accounted for in the standard model of particle physics.

The eighth paragraph explores the concept of particle-antiparticle symmetry and its violation, known as CP violation. It discusses how the processes that violate baryon number conservation must also violate CP symmetry to create a net excess of protons over antiprotons. The speaker explains that the violation of CP symmetry is necessary to give directionality to the baryogenesis process.

The ninth paragraph shifts the focus to the concept of cosmic inflation, which was proposed to explain the observed homogeneity and isotropy of the universe. It discusses how the universe's uniformity suggests it must have been even more homogeneous in the past, challenging the idea of how lumpiness or inhomogeneities could have originated and grown due to gravitational forces.

The tenth paragraph continues the discussion on the universe's large-scale properties, addressing the question of why the universe appears so smooth and flat over vast distances. It suggests that the small inhomogeneities or 'ripples' in the universe are uniformly distributed, indicating a lack of large-scale lumpiness and supporting the idea that the universe underwent a period of rapid expansion, or inflation.

The eleventh paragraph introduces the concept of friction in the context of field theory, drawing an analogy between the motion of a scalar field and a stone falling through a viscous fluid. It discusses the equations of motion for the field, highlighting the role of the Hubble expansion rate as a friction term that can slow down the evolution of the field, which is crucial for understanding the dynamics of cosmic inflation.

The twelfth paragraph focuses on the role of the scalar field, known as the inflaton, in driving the inflationary expansion of the universe. It discusses how the energy density of this field, comprised of kinetic and potential energy terms, influences the expansion of the universe. The speaker outlines the equations that describe the dynamics of the inflaton field and its potential energy, setting the stage for understanding the phenomenon of inflation.

The thirteenth paragraph derives the equation of motion for the scalar field, which includes a term accounting for the expansion of the universe, analogous to a frictional force. It emphasizes the role of the Hubble constant as a factor in this 'cosmic friction,' which slows the motion of the field and thus the rate of expansion of the universe. This paragraph provides the mathematical foundation for understanding how inflation can occur in the early universe.

The final paragraph of the script uses the falling stone analogy to describe how the cosmic friction term affects the evolution of the universe. It suggests that if the friction is strong and the potential energy hill is relatively flat, the field's evolution can slow down significantly, allowing for the vast expansion characteristic of cosmic inflation. The speaker concludes by indicating that this framework will be used to study the expansion and evolution of the universe in subsequent discussions.