Learn Hardcore Swedish: Efter att barnen har somnat är tystnaden i huset viktig för oss. - After the children have fallen asleep, the silence in the house is important for us.

Har somnat is the present perfect (literally: have fallen asleep) and is used to show a completed action that is relevant to a later time. The structure is:

har (have) + somnat (past participle of somna, to fall asleep)

You could also say:

Efter att barnen somnat … – dropping har is possible in formal/written style and still means after the children have fallen asleep.
Efter att barnen somnade … is unusual and sounds more like a specific event in a story, not a general routine. For habits and general statements, har somnat (or somnat without har) is preferred.

What is the function of att here? Is it the same att as in the infinitive marker (to)?

It’s the same word att, but used a bit differently.

As an infinitive marker (like English to):
- att sova – to sleep
- att läsa – to read
As a subordinator introducing a clause (like English that in some cases):
- efter att barnen har somnat – literally after that the children have fallen asleep
- jag vet att hon kommer – I know (that) she is coming

In this sentence, att is the subordinator that connects efter with the whole clause barnen har somnat.

Why does the main clause start with är after the comma? Why not Tystnaden i huset är …?

Swedish has a verb-second (V2) rule in main clauses: the finite verb (here är) normally comes in second position.

The sentence order is:

Whole subordinate clause: Efter att barnen har somnat
Finite verb of the main clause: är
Subject of the main clause: tystnaden i huset
Rest: viktig för oss

So: Efter att barnen har somnat är tystnaden i huset viktig för oss.

You could also say:

Tystnaden i huset är viktig för oss efter att barnen har somnat.
Here the main clause starts with its subject, so är is still in second position: Tystnaden – är – viktig …

Why is it barnen and not just barn?

Barn is irregular:

singular: ett barn – a child
plural: barn – children
definite plural: barnen – the children

In this sentence we are talking about specific children (presumably the family’s own children), so Swedish uses the definite plural barnen:
Efter att barnen har somnat … – After the children have fallen asleep …

Why is it tystnaden i huset and not just tystnad i huset?

Tystnad means silence (an en‑word).

tystnad – (a) silence (indefinite)
tystnaden – the silence (definite)

Here we are talking about a particular silence – the specific silence in the house after the kids are asleep – so Swedish prefers the definite form tystnaden.

If you said tystnad i huset är viktig, it would sound more like you’re talking about silence as an abstract concept, not the silence that appears at that time.

Why is viktig not viktiga or viktigt here?

Adjectives in Swedish agree with the noun in certain ways:

en‑word, indefinite: en viktig bok – an important book
ett‑word, indefinite: ett viktigt hus – an important house
definite with a determiner: den viktiga boken, det viktiga huset

But when the noun is definite with a suffix (like tystnaden) and there is no separate determiner (den, det, de), the adjective appears in its base form:

Tystnaden är viktig. – The silence is important.
Huset är stort. – The house is big.

So tystnaden (definite) + är + viktig (base form) is the normal pattern.

Why is it i huset and not hemma here?

Both are possible but they have slightly different focuses:

i huset – literally in the house, focusing on the physical building/inside space.
hemma – at home, focusing on the idea of being at home rather than the building itself.

Tystnaden i huset paints a picture of the quiet inside the house after the children sleep.
Tystnaden hemma är viktig för oss would be understandable but sounds a bit more general and less tied to the specific image of the silent house.

Why is the preposition för used in viktig för oss, and not till oss?

With viktig (important), Swedish normally uses för:

Det här är viktigt för mig. – This is important to/for me.
Tystnaden i huset är viktig för oss. – The silence in the house is important to us.

Till is used more for movement or giving:

Ge det till mig. – Give it to me.
Vi åker till huset. – We are going to the house.

So viktig för någon (important for someone) is the standard pattern.

Can I say När barnen har somnat instead of Efter att barnen har somnat? Is there a difference?

Yes, you can say:

När barnen har somnat är tystnaden i huset viktig för oss.

The nuance:

När (when) – focuses on the time something happens; it can mean whenever in general statements.
Efter att (after (that)) – emphasizes that one event happens after another is finished.

In everyday speech, när is extremely common and often feels more natural; efter att makes the sequence (first the kids sleep, then the silence is important) a bit more explicit.