Syllabus

ASTRO/PHYS 545 Cosmology · AI-assisted scientific reasoning

Term: Fall 2026 | Meetings: Tue/Thu 10:35 – 11:50 am, 541 Davey
Instructor: Donghui Jeong, 518 Davey, djeong@psu.edu · Office hours Tue 3:00 – 4:00 pm, or by appointment
TA: Tristan Weaver, tsw5383@psu.edu · Office hours Thu 3:00 – 4:00 pm and Fri 10:00 – 11:00 am, 441 Davey

1. What this course is

This is not a lecture course with AI added to it. The premise is that AI systems now produce cosmology derivations, code, and literature summaries of high apparent quality, so producing such material is no longer the scarce thing. What is scarce is the ability to carry it the whole way: to choose what is worth asking, to tell whether what comes back is true, and to get from there to something nobody knew before.

The course trains one loop, repeatedly:

Think → Ask AI → Inspect → Challenge → Verify → Revise → Synthesize → Ask the next question.

The loop runs three times over, on material that is progressively less well defined. In weeks 2 through 6 you apply it to problems whose answers are known. In the middle of the term you use it to explore the knowledge space of cosmology and chart it: what is claimed, on what evidence, and where the settled part runs out. In the final project you take one small corner of that space, chosen by you, and map it in depth: far enough in to see exactly where the charted part ends, and then one step past it.

Use AI freely; it is encouraged and unrestricted (§12). Whatever route you take, you are expected to defend at a blackboard anything that appears in work you submit under your name.

What you check AI against changes through the term, by design. In the foundation weeks you have the course lecture notes: a document that is supposed to be correct, against which an AI derivation can be compared line by line. I wrote them and nobody has refereed them, so “supposed to be” is doing real work in that sentence. Finding an error in the notes is worth more to me than any solved problem, and I would far rather hear about it at the blackboard than not at all. In the map weeks you have papers instead, which are authoritative in a weaker sense and disagree with one another. In the final project you have your own map and nothing else. The written reference is withdrawn in stages, but the instructor is not: the standard in the room is the same in week 15 as in week 1, and the capstone is where you find out whether that standard has become yours.

The notes exist, so reproducing them is not the work. Reading them is, and then solving eight problems that the notes make possible without making easy.

One thing to settle at the outset. Cosmology has a short list of very well measured numbers and it is easy to mistake them for the subject. Consider what the precision is hiding.

We know the dark matter density to a percent and we do not know what dark matter is. We know the dark energy density better than that and have no account of it whatsoever. We knew the baryon density to a percent for twenty years while being unable to say where most of the baryons were, and that accounting closed only recently. And “the CMB is a blackbody” is a statement about a bound, measured in 1990, not improved since, and sitting three orders of magnitude above the distortion \(\Lambda\)CDM predicts. No mission since has gone looking.

Each of these numbers is a statement about what the universe contains or how it began. Measuring them this accurately has done nothing to say what dark matter or dark energy is, and those two questions remain among the hardest in modern physics. Precision and ignorance sit together here. A parameter carried without its physical content is not knowledge of anything, and it is the part of the work an AI already does better than you.

What I am here for

My greatest aim for the term is that you leave a productive scientific commander of the AI army.

The figure is exact, which is why I use it. An army is fast, tireless and obedient, and it has no opinion whatever about whether the objective is worth taking. Choosing the objective, reading the ground, and recognizing a confident report from the field as wrong are the commander’s work, and none of it gets easier as the army grows. It becomes the only part that matters.

On being wrong in this room

The format puts you at a blackboard in front of the whole class and me, on a problem you may not have finished thinking about. Bring your own solution up with you. What is being watched is whether you are reconstructing the argument or copying it. You will be stuck there, publicly, more than once. That is not a side effect of the design; it is the design.

What you can do at a blackboard is a trained capacity and not a fixed one. It improves with the specific practice of doing it badly first, and the discomfort of not yet being able to do something is largely what improving feels like from the inside. If you arrive with a settled picture of what you are and are not good at, this term will be unpleasant and you will learn less than the person beside you who arrived willing to be visibly wrong. Leave the fixed picture at the door. It was never accurate anyway.

Who evaluates you

Not me, as far as I can arrange it. Evaluating your performance is the last thing I do here.

Your written work is graded by the TA. The record I keep of the blackboard is a record and not a verdict, and it is handed over rather than applied.

So when I take a line you have written and ask what it costs, nothing is at stake for your grade. I ask because that is the only way to find out what the line costs. Answer it the way you would answer a colleague.

2. Learning objectives

By the end of the term you can:

1. Foundational knowledge. State and derive the core results of modern cosmology at the level required to judge whether an AI-generated derivation is correct.
2. AI-assisted scientific reasoning. Define a problem, form your own approach, delegate appropriately, verify the result, and locate and repair the errors.
3. Literature to knowledge map. Read a body of papers and extract the intellectual structure of a subject: what is claimed, what was measured, what is assumed, and what would overturn it.
4. Research initiation. Identify a genuine gap, convert it into a research question, and execute the smallest piece of evidence that moves it forward.

Fifteen weeks produce a student who can begin an independent scientific investigation, not a finished researcher.

A specific list of what you should be able to do, organized by topic, is on the Topics and Objectives page.

3. Semester structure

4. Class format

Every class from week 2 onward runs the same structure. It does not change between phases; only what goes on the blackboard does.

Before class

You read the assigned material and you solve problems. In the foundation weeks the material is the course lecture notes, which are the reference for the term; nothing is gained by writing them again. In the map weeks it is a bounded set of papers. No textbook is assigned, though you should own one (§14).

The instructor distributes, one week ahead: the topic and its reading, eight problems (four for Tuesday and four for Thursday), and any additional references.

Two submissions a week. Solutions to all eight problems are due Monday at noon, and the final version, carrying its repair history, is due Friday. Both are timestamped, and the instructor reads the opening lines before Tuesday.

Monday’s deadline is for the written solution. Being able to stand at a blackboard and produce it is separate work, and it happens in the days before each class: solved once, digested twice.

In the map weeks the cadence changes. One subject per session rather than one topic per week, so there are two of everything: two paper sets, two maps, two deadlines.

Two lines are written without AI, one at each end of the submission. In the map weeks they attach to each map rather than to the week.

Opening: the point in your solutions you were least able to verify. A class’s worth of these takes a couple of minutes to read and shows the instructor, before anyone reaches the board, where the class is collectively unsteady; that is where the stress test is aimed.

Closing: where AI was wrong, incomplete, or confidently vague this week, and how you found out. If it was not, say so; that claim is testable at the board. If you worked some problems without AI, note which.

With the problem-set reflection (§6), these two lines are the whole written record of how you work.

Preparing for the board. Everything you present is written on the blackboard by hand, in eight minutes. Deciding what earns a place there is the central act of understanding in this course, and it is the one step AI cannot do for you: a solution you did not compress yourself does not fit on a board. Nothing about this preparation is collected. The board is the assessment.

In class (75 min)

The four problems of a session are not independent. They are one argument cut into four segments, so each takes the previous one’s result as input and the blackboard fills left to right into a single complete structure. Thursday’s first segment takes Tuesday’s last result.

Orientation. Five things, a minute each:

• Submissions checked in. This happens before the draw, and the draw does not exclude anyone who failed to submit.
• Problems drawn, roles confirmed.
• How today continues from the last session. On Thursdays this is not narrative: the first segment takes Tuesday’s blackboard result as its input.
• The result today’s chain arrives at.
• Where next week goes.

Nothing about where the difficulties lie. Naming a trap in the first five minutes retires the segment built around it.

Synthesis. Three things, briefly: which of today’s statements are physical and which are choices; where the class was collectively wrong, which the instructor can see from a set of opening lines and one blackboard and nobody else can; and where this appears in research.

Synthesis is about the reasoning that happened in the room, not about the physics. If the physics was wrong, that belongs in the repair. A synthesis block that turns into a corrective lecture defeats the format. Ten minutes is the guard.

Class time is the only resource that cannot be reproduced at a desk: all of us and a blackboard in one room. Nothing that works equally well alone is scheduled into it.

Roles

Four names are drawn at the start of every class, one to each segment. Everyone else enhances what goes on the board: all of you are challenger and alternate at once, on duty every class. If you see something, say it.

The draw is random and it is made in the room. Each draw is independent: taking the board on Tuesday does not remove you from Thursday’s draw, and it is possible to be drawn twice in a week or not at all for three. Four names out of a class this size is not long odds, and you do not know which of the four problems you get. So you prepare all four, every time.

Presenter. You reproduce the argument at the blackboard, state where each assumption enters, and mark what remains unresolved in your own understanding.

Everyone else. Three kinds of enhancement count.

• Securing it. Naming an assumption that was used and not stated, a step that does not follow, a result quoted outside the range where it holds.
• Continuing it. Picking up the derivation where the presenter stopped.
• Widening it. A different route to the same place, a connection to something from another week, a physical reading of a step that had been only algebra.

The third is worth as much as the first. In a class this size there are usually two or three ways through a problem, and a segment that surfaces them is worth more than one that does not.

Nobody at this blackboard is defending anything. The room is working out together whether the argument holds, and the presenter is the one who happens to be holding the chalk. A question that asks for repetition enhances nothing.

The record. Presenting and enhancing are recorded class by class: a circle for taking the board, a check for any of the three above. Participation is 30% of the grade (§10), and this is what it consists of. Nobody is asked to speak on a schedule. The accounting is simply not hidden from you.

Instructor. The instructor takes an apparently harmless line and asks what it costs: Is this true, or true under an assumption you did not state? Is this a physical statement or a coordinate statement? Does it survive outside matter domination? Where exactly did general relativity enter?

Getting stuck is course material, not failure. When a presenter stalls: 30 seconds alone, then the floor, then the instructor. Picking up someone else’s stalled derivation is among the most valuable things anyone does in this room, and it is marked as one. The point at which the argument broke is recorded and becomes the starting point of that week’s repair.

After class

Final version due Friday. Across the week your solutions pass through three states: what you submitted Monday, what Tuesday exposed, and what Thursday exposed. You repair them after each class and submit once at the end.

The final version carries its own history: changes marked or shown as a diff, with two or three sentences on what was wrong and why you had not caught it. That history is the graded part.

5. Week 1: orientation

I take both meetings this week. It is the only week I do.

Reading: Ch. 1. Physics review, natural and Planck and astronomical units, index notation.

Conventions fixed here are used for fifteen weeks: \(\hbar=c=k_B=1\) and how to restore them, the relation between \(m_{\rm pl}\) and the reduced \(M_{\rm Pl}\), the signature, and the sign conventions for the curvature tensors. Sign errors later in the term are traced back to this list.

Tuesday. Lecture. A practice problem is distributed:

Estimate the temperature at which the universe became neutral. Two numbers are available to you: the binding energy of hydrogen, 13.6 eV, and the ratio of photons to baryons, roughly \(10^9\). Use both, and say what each one does and where it comes from. Then say what you would need in order to do better than an estimate.

Submit it by noon on Wednesday. Not graded, and the point is not the answer: it is a rehearsal for the submission format, including the two lines, and for what happens at the board. Reading them beforehand also tells me where the estimate breaks down, which is where Thursday goes.

Thursday. The instructor works the problem at the blackboard under the rules of §4, and is challenged. Nothing about the format is explained that can be shown instead.

6. Weeks 2–6: Foundation

One topic per week across both meetings. Tuesday establishes the setup and the core derivation; Thursday extends and interprets it.

Two sets of topics are deliberately absent.

The classical cosmological tests (redshift drift, number counts, Olbers’ paradox, Alcock-Paczynski, optical depth) are applications of the week 4 machinery rather than foundations of it, and are set as a problem set instead of taking class time.

Everything downstream of equilibrium thermodynamics (freeze-out, dark matter relic abundance, nucleosynthesis, recombination, linear perturbation theory) enters in the map phase as literature rather than as derivation. This is the largest single choice in the syllabus, and it is not a cut for time. The standard curriculum marches through cosmic history deriving everything and arrives at the CMB power spectrum having spent a term on derivations most of you will never perform again.

Note what this is not. Linear perturbation theory is not omitted. It appears in the evidence for dark matter, in how the initial conditions are measured, in every survey session, and in most of the papers you read, and you need to understand it well enough to tell whether a claim resting on it is sound. What you will not do here is work the derivation by hand.

That distinction is the bet this course makes. Producing a result and being able to judge one are different skills, and the second is the one that has become scarce. If you are going into that area, work through Dodelson and Schmidt (§14); a term spent deciding whether what you read is correct puts you in a better position to do it.

Computation. At least one problem a week requires a numerical or symbolic calculation, verified against something you derived independently. The question is never whether the code runs. It is whether you can establish that a result you did not compute by hand is trustworthy, which is what the final project asks with the answer unknown.

Problem sets

Three, in weeks 2, 4 and 6, with the due date announced when each is assigned. These are separate from the weekly eight and they exist because of a limit in the class format.

A board segment is eight minutes, so a weekly problem has to be reproducible and defensible in that time, and the weekly set never asks you to sustain a calculation across an afternoon. A problem set does. The criterion is simply that it does not fit on a blackboard.

One problem, not a set of exercises. The workflow is fixed:

Step 1. Before AI, roughly ten minutes, written. The structure of the problem, your expected strategy, the equations you think you need, and what you do not know. Submitted as written, uncorrected.

Step 2. Work with AI. No restrictions.

Step 3. Solution. AI may draft it. You verify and correct it, and you submit it under your name.

Step 4. Interaction reflection, written without AI. What you first thought the strategy was; what you asked AI to do; what it contributed that you had not considered; where it was wrong, incomplete, or confidently vague; what you changed and how you knew to change it.

Step 4 is where this is assessed. Step 3 is not. Step 1 exists so that Step 4 has something to compare against.

7. Weeks 7–9 and 12–13: Knowledge maps

Ten sessions, ten subjects, one per session and two a week. The instructor supplies a bounded paper set, two or three papers, for each. The map replaces the problem set as that session’s deliverable.

Two subjects a week reads heavier than the foundation weeks and writes lighter.

Three paper summaries are not a map. What you want is the structure of the subject: paper-centric → idea-centric.

The subjects

Weeks 7–9. Constituents of the universe, in order of how well we know them.

Weeks 12–13. Current and future probes.

The first block is ordered by decreasing knowledge, so the sessions open progressively: by week 9 you are in territory nobody has settled. Each subject there is mapped by the questions still open about it. The second block is the instruments built to answer them, and it closes where the first block ended, on the initial conditions.

Approving a question takes a round trip, and I leave at the end of week 9, so the exchange happens inside it. You submit the corner you are working in by noon on the Friday of week 8, I reply to each of you in writing before the Tuesday of week 9, and the revised question is due that Thursday at noon. I approve it in writing before I leave. None of this uses class time.

Your project topic need not come from this list, and the four subjects of weeks 12–13 are not offered as candidates. The list exists to give you a field to practice on, not to constrain what you work on.

The four segments

The board accumulates into a map, and I photograph it at the end and post it to Canvas; that photograph is the map, and there is no other copy of it. What the four segments are depends on the block. A constituent is something the universe contains, and the map asks what we still want to know about it. A probe is an instrument for finding out, and the map asks what it can settle.

Weeks 7–9: constituents

Each subject is mapped by four things we still want to know about it. For baryons: why lithium disagrees when deuterium agrees, how cold the gas became, and how and when it was ionized again. For neutrinos: how many there are, and what their masses are, pursued three ways that are close to disagreeing. The four for each subject are on that week’s sheet, and the project you choose in week 9 can start from any of them.

Within any segment, four questions keep the board honest: what is claimed, what was measured, what has to be assumed, and what would overturn it. They are not the headings. They are what the floor asks.

The first is the one most often answered with a number. Reporting \(\Omega_{\rm dm}h^2 = 0.120 \pm 0.001\) is reporting a number, and any AI will do it faster than you. The claim is that the universe contains something that clusters and does not otherwise interact, that it was already non-relativistic when the modes we observe entered the horizon, and that nothing in the standard model does this. The number says how firmly.

Weeks 12–13: probes

An instrument makes no claim about the universe, so its map runs differently, forward: from what the detector records, through the modeling, to the number, and out to everything the same data turns out to be good for.

1. The purpose. What was it built to measure. What the instrument physically records, what quantity that is a proxy for, and the distance between the two.

   DESI records the redshifts and angular positions of galaxies. The target is the matter density field. Galaxies are not the matter field; they are a biased, discrete, selection-dependent sample of it, and every parameter DESI reports comes through that gap.

2. The chain. Every step from the recorded quantity to the reported number. Mark where a simulation enters, where a calibration enters, and where a prior enters. Say which steps are shared with the other instruments on the list.

3. The systematics. What corrupts the chain. Separate what more data fixes from what it does not, and state where the systematic floor sits relative to the statistical error at the end of the survey.

4. The rest of the data. What the same data supports that was not the reason for building it, and what this design cannot see in principle. The two lists usually come from the same choice.

Segment 4 is where the block earns its place after weeks 7–9. Design documents carry the headline science; the byproducts are scattered across papers written years later, by people who did not build the thing.

Every row on the list pairs instruments that are taking data with instruments that are not yet built, so much of the literature is design documents and forecasts. A forecast is not a measurement; it is a statement about what an instrument would achieve if the systematics behaved. Segment 3 is where that gets tested, and it is the segment AI is least able to supply, because the honest version of it is rarely written down.

Attribution

The failure mode of this phase is not error but fabrication. AI produces fluent literature summaries containing citations that do not exist, claims attributed to papers that concluded otherwise, and positions abandoned a decade ago presented as current. In the foundation weeks the notes catch this. Here only the room does, so two requirements follow.

Every claim attributed to a paper must be locatable in it. The standing question at the board is “where in the paper,” and the answer is a section or figure number.

The presenter reproduces one figure from one of the papers on the blackboard by hand, with axes, labels, and the approximate position of the data. Drawing a figure requires having looked at it.

Challenger. In the foundation weeks the task is to find the weakest step. Here it is to find a claim that the cited source does not support.

Synthesis. Which assumption on today’s board appeared more than once. Usually one assumption holds up half the subject, and it is visible only after all four segments are up.

Literature budget. Each map has a paper budget, stated rather than suggested, and you are not required to follow reference chains beyond it. You are training here to know when to stop reading and start thinking, as much as anything else.

8. Weeks 10–11: Project clinic and prototype

The instructor is away. Class meetings continue on the normal schedule, run by the students with the TA moderating. You arrive with the research question approved at the end of week 9 and you leave with a prototype.

Clinic sessions (4 meetings). The class divides across each pair of meetings, so everyone is on the board twice. In week 10 you put up your question and the papers you found, and the room builds the plan with you: which part of this can be finished in two weeks. In week 11 you show what the plan turned into, what the prototype does, and what it does not yet do. The format is the one practiced for nine weeks and it runs without the instructor.

Weekly progress report to the TA, who uses AI to triage completeness, conceptual problems, unstated assumptions, questionable claims, and next steps, and returns written feedback.

Nobody is expected to write a paper (although it will be great!). The report due in week 14 is not one; it is an account of what you asked, what you built, and what it showed. If a project turns into one later, so much the better, and it has happened. But fifteen weeks is not long enough for that to be the target, and aiming at it reliably produces less than aiming at one small result you can actually stand behind.

The prototype is small by design. Reproducing one published figure; a background or simple Boltzmann calculation; a toy parameter scan; reproducing an existing constraint; a simple likelihood; a numerical check of an analytic approximation; a small subset of public data.

The assessment question is not “did you write the code yourself.” It is:

Can you use AI to construct a scientific calculation and establish that its result is trustworthy?

You have been answering this all term: in week 3 against the Friedmann equations, in week 4 against three distance measures, in week 5 against the thermal history, in week 6 against slow roll. The difference is that here nobody knows the answer.

Due at the end of week 11:

1. Your revised research question, with an account of what changed since week 9 and why
2. The smallest piece of evidence that would move it forward, and whether your prototype produced it
3. The prototype, with the checks you ran on it

Item 2 is load-bearing. Two weeks with a research topic and an AI reliably produces a six-month programme, which is why the week 10 board is spent cutting one down.

9. Weeks 14–15: Capstone symposium

Four sessions, three talks in each. Fifteen minutes and ten of questions, adjusted to the final enrolment.

The talk is not judged on how much you produced. It is judged on whether it is a research talk:

• Here is the field.
• Here is what we know.
• Here is what we do not know.
• Here is the question I identified.
• Here is why it matters and why it is still open.
• Here is what I tried.
• Here is what I learned, including what failed.
• Here is what I would do next.

The last item is why the survey sessions of weeks 12–13 come where they do. “What I would do next” answered with reference to data that will exist within a few years is a plan; answered otherwise it is a wish.

A failed prototype, correctly diagnosed, is a result. A successful one you cannot explain is not.

The report is due at midnight on the Monday of week 14, from everyone, whether you talk that week or the next. The work stops for the whole room at the same moment, and the two weeks of talks are given on finished projects rather than on projects still moving. It covers the same ground as the talk, at the length that ground takes.

10. Assessment

Weekly work. The TA grades the Friday version, which you write having watched the material worked twice at a blackboard. It is expected to be correct, and correctness is marked. What separates one from another is the repair record and the two lines written without AI: a solution that was wrong and correctly diagnosed scores above one that was right and unexamined.

Participation. This is the record from §4 and nothing else: a circle for each segment you take, a check for each enhancement. The draw sets the circles, so they even out; the checks are where the variation is. What earns one is any of the three things in §4, judged by whether it moved the argument and not by how often you spoke. Errors made and worked through at the board cost nothing. Reciting a memorised solution earns a circle and no more. Attendance credit (§11) enters here.

Problem sets. The interaction reflection carries the majority of the weight.

Final project. Weighted across the week 11 brief, the prototype, and the capstone talk.

Who grades. The TA does. Written work is marked against the criteria above, and the instructor’s record of the board is handed over rather than applied. The instructor’s role in the room is to press the argument, not to score the person giving it (§1).

Official solutions. The TA posts them after the Friday deadline, never before. Releasing them earlier would turn Monday’s submission into a draft and the week’s repair into copying.

11. Attendance

This course is student presentation and challenge. Attendance is not encouraged; it is required. If you are not in the room you are not in the draw and you are enhancing nothing, and neither shows up in the record. Both halves of the participation grade are earned here and nowhere else.

Attendance credit. Every student begins the term with full attendance credit. If you are absent and the draw assigns you a problem, you lose one credit. Absence on a day you were not drawn carries no deduction, because the class absorbed it.

Covering a missing presenter. The segment goes to whoever picks it up, and they get the circle. Nobody in this room is ever unprepared for a problem: everyone prepares all four, so stepping in costs you an expectation, not a night of work.

Arranged absence. Notify the instructor before the Monday deadline and you are removed from the draw. No credit is lost, and you owe one additional presenter slot later in the term. Illness, research travel and comparable obligations are arranged absences: the distinction is notice, not justification.

Threshold. Three lost credits make participation unrecoverable at a passing level and require a meeting with the instructor before you continue in the course.

12. AI policy

AI is allowed here without restriction, and I encourage you to use it. Solutions, derivations, code and literature analysis may be AI-generated in whole or in part.

If you would rather work a problem out on your own, do that. It is a good way to spend an afternoon and nothing is lost by it. The course is not interested in which route you took; it is interested in whether you can defend where you arrived. Say in your closing line which problems you did which way.

A few problems name AI use as part of the task, because what is being examined there is the verification of something you did not derive yourself. Those say so.

Every submission carries your name and your responsibility.

AI is not used for two things: the opening and closing lines of each weekly submission, and the interaction reflection in each problem set. Those are the places where your judgment rather than your output is visible, and delegating them removes the only written evidence the course collects about how you work. Everything else is checked at the board, where AI is not available to you.

On defending your work. Anything submitted under your name may be put to you at the board without warning. The only workable strategy is to understand what you submit.

13. Deliverable summary

14. Books

The reading for each week is the course lecture notes. No textbook is required and none is assigned.

You should nevertheless own one. This is a course about deciding whether a claim is correct, and that is difficult with a single source. When an AI derivation and the lecture notes disagree, what settles it is a third authority that was written by someone else, for a different audience, with different conventions. Having one on your desk, in a subject you will keep working in, is worth more than which one it is.

Choose by your background and your taste. The following are all credible.

Recent

A Course in Cosmology: From Theory to Practice (D. Huterer) · PSU Libraries. Broad and current, and closest to the order this course takes.

Modern Cosmology (S. Dodelson and F. Schmidt) · PSU Libraries. Linear perturbation theory in detail and done well. The closing sections on statistics are good too.

Cosmology (D. Baumann) · PSU Libraries. Described to me as a modernised Kolb and Turner. If you prefer theoretical clarity, this may suit you.

Particle Cosmology and Astrophysics (D. Hooper) · PSU Libraries. Better suited to students coming from particle physics.

From the 2010s

Cosmology (S. Weinberg) · PSU Libraries. A great book: insightful, accurate, clear. One caveat, that the notation differs from most others. Contains an analytic approximation for the CMB power spectrum.

Physical Foundations of Cosmology (V. Mukhanov) · PSU Libraries. The chapters on nucleosynthesis, inflationary perturbations and the CMB power spectrum are excellent. Everything is done as analytically as it can be.

The Primordial Density Perturbation (D. Lyth and A. Liddle) · PSU Libraries. Focused on how density perturbations are generated and how they become observables, including primordial non-Gaussianity.

Galaxy Formation and Evolution (H. Mo, F. van den Bosch, S. White) · PSU Libraries. Essentially everything from inflation to galaxy formation. The galaxy formation chapters are particularly useful.

Classics

Principles of Physical Cosmology (P. J. E. Peebles) · PSU Libraries. The classic. The classical cosmological tests are explored particularly well, and the later sections are organized by subject so you can move between them.

Cosmological Physics (J. Peacock) · PSU Libraries. A good reference for the wider subject, including AGN and galaxy formation.

The Early Universe (E. W. Kolb and M. S. Turner) · PSU Libraries. The classic text on early universe theory and the thermal history.