13.1 Inflationary Theory and Models

Inflation theory explains the rapid expansion of the early universe, solving key problems in Big Bang cosmology. It provides a mechanism for generating primordial density fluctuations and explains the observed large-scale structure of the universe.

Various inflationary models exist, including slow-roll and chaotic inflation. These models describe how a scalar field drove the expansion, with quantum fluctuations seeding cosmic structure. The end of inflation led to reheating, marking the beginning of the radiation-dominated era.

Early Universe Inflation

Inflation and Its Necessity

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• Inflation describes rapid exponential expansion of the early universe
• Occurred approximately 10^-36 seconds after the Big Bang
• Expanded universe by a factor of at least 10^26 in a fraction of a second
• Solves several problems in standard Big Bang cosmology (horizon problem, flatness problem)
• Provides mechanism for generating primordial density fluctuations
• Explains observed large-scale structure of the universe

Horizon and Flatness Problems

• Horizon problem addresses uniformity of cosmic microwave background (CMB)
• Regions of CMB should not have been in causal contact without inflation
• Inflation allows previously disconnected regions to have been in contact earlier
• Flatness problem questions why universe appears nearly flat
• Observable universe contains about 10^62 Planck volumes
• Inflation expands a small, curved region to appear flat on large scales
• Without inflation, initial conditions would need to be fine-tuned to one part in 10^62

Scalar Field and Inflationary Dynamics

• Scalar field (inflaton) drives inflation
• Possesses potential energy that dominates over kinetic energy during inflation
• Scalar field slowly rolls down its potential energy curve
• Energy density of scalar field remains nearly constant during inflation
• Negative pressure of scalar field causes exponential expansion
• Quantum fluctuations in scalar field seed structure formation
• End of inflation occurs when scalar field reaches minimum of potential

Inflationary Models

Slow-Roll Inflation

• Most widely accepted model of inflation
• Scalar field evolves slowly compared to Hubble expansion rate
• Potential energy dominates over kinetic energy of the field
• Characterized by slow-roll parameters epsilon and eta
• Epsilon measures how quickly the field is rolling
• Eta measures the curvature of the potential
• Both parameters must be much less than 1 for slow-roll inflation to occur
• Predicts nearly scale-invariant spectrum of primordial fluctuations

Chaotic and Eternal Inflation

• Chaotic inflation proposed by Andrei Linde in 1983
• Initial conditions for inflation can be arbitrary or "chaotic"
• Inflation occurs when scalar field has large initial value
• Field rolls down potential, inflation ends when slow-roll conditions violated
• Eternal inflation suggests inflation continues indefinitely in some regions
• Quantum fluctuations can drive scalar field uphill in its potential
• Results in creation of infinite number of pocket universes
• Leads to concept of multiverse with varying physical properties

Post-Inflationary Effects

Reheating and Energy Transfer

• Reheating occurs at the end of inflation
• Energy stored in inflaton field converted to particles and radiation
• Process can occur through coherent oscillations of inflaton field
• Particle production through parametric resonance (preheating)
• Reheating temperature typically between 10^9 and 10^10 GeV
• Marks beginning of radiation-dominated era in standard Big Bang cosmology
• Crucial for understanding baryogenesis and subsequent evolution of universe

Cosmic Strings and Topological Defects

• Cosmic strings hypothetical 1-dimensional topological defects
• May form during symmetry-breaking phase transitions in early universe
• Predicted by some grand unified theories and string theory models
• Could contribute to structure formation and gravitational wave background
• Characterized by tension (energy per unit length) typically of order 10^-6 c^4/G
• Network of cosmic strings evolves through interconnection and loop formation
• Observational constraints from CMB and gravitational wave experiments
• Other topological defects include domain walls and magnetic monopoles