ASTR 420 · Lecture 06

Lecture 06: The Cosmic Microwave Background

Cosmology

The near-perfect blackbody spectrum tests thermal history; anisotropies carry information about geometry, baryons, matter, and initial perturbations.

Objectives and route

Interpret the CMB spectrum and anisotropy amplitude as evidence for a hot early universe.
Define and distinguish blackbody spectrum, acoustic peaks, and parameter inference.
Derive or audit one quantitative relation with units and assumptions.
Connect the calculation to an observational test and a limitation.

Terms for This Lecture

Blackbody spectrum

Definition: The thermal radiation distribution fixed by temperature when matter and radiation have reached equilibrium.

Why it matters here: In The Cosmic Microwave Background, Blackbody spectrum is needed to reason about blackbody spectrum, acoustic peaks, and parameter inference rather than merely label the phenomenon.

Relationship: It is interpreted alongside Temperature anisotropy and the lecture relation below; identify which quantities are observed, calibrated, or model-derived.

Limitation or common confusion: The frequency of the intensity peak depends on the spectral variable; wavelength and frequency peaks are not reciprocal labels.

\(I_nu(T)=2h nu^3 / c^2 [e^(h nu/kT)-1]^-1\)

Motivating evidence

The near-perfect blackbody spectrum tests thermal history; anisotropies carry information about geometry, baryons, matter, and initial perturbations.

Cosmological claims are indirect: an observable is calibrated, placed in a model, and compared against alternatives. Keep those layers separate throughout the lecture.

blackbody spectrum, acoustic peaks, and parameter inference. The axes, labels, and geometry carry the physical inference rather than serving as decoration.

Physical framework

Start from the governing relation and define its domain:

\(I_nu(T)=2h nu^3 / c^2 [e^(h nu/kT)-1]^-1\)

State the coordinate choice, units, boundary conditions, and approximation before substituting numbers. The same symbol can mean a different quantity in Newtonian, special-relativistic, and expanding-space contexts.

Read the visual

Use the figure introduced on the evidence slide as an argument: identify the measured axis, the inferred axis, the comparison model, and the parameter that controls the conclusion.

The paired lab asks you to reproduce the visual from a supplied data extract and test one modeling choice.

Worked calculation

Wien's law gives nu_peak approximately 281.97 GHz for T=2.7255 K.

The frequency of the intensity peak depends on the spectral variable; wavelength and frequency peaks are not reciprocal labels.

Estimate the scale first, then check dimensions and comparative direction. The displayed value is generated from shared ASTR420 constants and data.

Evidence versus inference

Raw data are not the same as calibrated observables.
A fitted parameter is conditional on the likelihood, prior, and selection function.
Independent probes can agree because the model is useful, or disagree because an assumption is hidden.

Boundary condition

Limit of the model: The frequency of the intensity peak depends on the spectral variable; wavelength and frequency peaks are not reciprocal labels.

Ask what happens if the dominant assumption fails. In cosmology, approximation honesty matters because distances, times, and abundances accumulate model dependence.

Active reasoning

Prompt: Use Wien's law to estimate the frequency of the CMB intensity peak.

Predict the direction before calculating. Then name one observation that could discriminate between two explanations.

Connection to the seven-unit arc

Earlier tools: ASTR310 radiation, dynamics, and statistical mechanics.
Paired data activity: use the corresponding CSV and reproduce the calculation with a perturbation test.
Next step: combine this probe with an independent epoch or distance measure.

Takeaways

Interpret the CMB spectrum and anisotropy amplitude as evidence for a hot early universe.
A cosmological parameter is meaningful only with its model and uncertainty context.
State whether a number is live-verified, a published value awaiting spot-check, or an instructor-provided model value.
Carry the limitation forward into the lab and problem set.

Reading and provenance

OpenStax Astronomy 2e, section 29.4; embedded Figures 29.16-29.22.

OpenStax Astronomy 2e Chapter 29 embedded figure numbers were checked against the extracted text; the source index has chapter-label offsets near the Chapter 29 boundary, so the adopted PDF remains the final exercise-number authority.

Additional sources and dataset status are recorded in reference-log.md. Standard published values not re-fetched this session are level 2 and require human spot-checking.