Inflation, Primordial Perturbations, and Reheating

Manual: General · Subject: Cosmology

Analyze the origin of structure from quantum fluctuations during a possible inflationary epoch.

Quantum Origins of Cosmic Structure

Inflationary Paradigm

Inflation is a phase of accelerated expansion, often modeled by a scalar inflaton field with potential $V(\phi)$ . It offers a mechanism for generating near scale-invariant primordial perturbations, explaining the horizon and flatness puzzles and providing a causal origin for structure through stretched quantum fluctuations.

Slow-Roll Quantities

Quantity	Definition	Interpretation
$\epsilon$	$\epsilon= -\dot H/H^2$	Measures departure from exact de Sitter
$\eta$	$\eta=\dot\epsilon/(H\epsilon)$ or potential form	Controls spectral tilt and termination
$n_s$	$n_s-1\approx -6\epsilon+2\eta$	Scalar spectral index
$r$	$r\approx 16\epsilon$	Tensor-to-scalar ratio

⚠️

Model-Building Challenge

No single inflationary model is universally accepted; viable scenarios must fit CMB constraints, UV-completion concerns, reheating, and the absence or presence of primordial non-Gaussianity and primordial $B$ -modes.

Which observable is most directly sensitive to primordial tensor modes?

CMB

B

-mode polarization Galaxy peculiar velocities Baryon acoustic oscillation scale Type Ia supernova stretch parameter

Reheating and Preheating

After inflation ends, the inflaton energy must be transferred to the standard-model and dark-sector degrees of freedom. Perturbative reheating, nonperturbative preheating, and thermalization determine the reheating temperature and can leave imprints on the primordial power spectrum and relic abundances.

Why is reheating important for connecting inflation to the hot Big Bang?

Single-Field vs Multi-Field Inflation

Single-field

Simpler dynamics and predictions.
Often yields mostly adiabatic perturbations.
Tensor-to-scalar ratio and tilt tightly linked.

Multi-field

Allows isocurvature modes and richer non-Gaussianity.
Reheating and field-space geometry matter.
Can evade or complicate single-field consistency relations.

What does the spectral index $n_s<1$ indicate in inflationary cosmology?

A blue primordial spectrum A scale-invariant spectrum exactly A red-tilted spectrum No primordial perturbations

Deriving the Primordial Power Spectrum

1

Quantize scalar fluctuations about the inflationary background.
2

Solve the Mukhanov-Sasaki equation with Bunch-Davies initial conditions.
3

Evaluate the mode amplitude at horizon exit.
4

Relate the resulting field perturbations to the curvature perturbation $\mathcal{R}$ .

Neuroanatomy Explorer

Memory Deck

Match the Pairs

Concept Constellation