Barnen somnar inte utan sin filt.

Barn means children in a general or indefinite sense, like children / kids.

Barnen is the definite plural form and means the children.

Swedish usually adds the definite ending to the noun instead of using an article like the.
So:

• barn = children / kids
• barnen = the children

In this sentence we’re talking about specific children (the ones we know about), so Swedish uses barnen.

Both relate to sleep, but they are used differently:

• somnar = fall asleep, the process of going from awake to asleep
• sover = sleep, the state of being asleep

So:

• Barnen somnar inte = The children do not fall asleep.
• Barnen sover inte = The children are not sleeping.

In this sentence, the focus is on them not managing to fall asleep without the blanket, so somnar is correct.

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

In a simple statement:

1. Subject: Barnen
2. Finite verb: somnar
3. Negation / other elements: inte utan sin filt

So Barnen somnar inte … is the normal order.

Barnen inte somnar … is wrong in standard Swedish.

Yes, here utan means without.

• utan sin filt = without their blanket

Be aware that utan can also mean but / but rather / instead in some constructions:

• Inte kaffe utan te. = Not coffee but tea.

In your sentence, it’s clearly the without meaning.

Swedish distinguishes between:

• sin/sitt/sina: reflexive possessive – refers back to the subject of the same clause
• deras: non‑reflexive – refers to someone else’s or is neutral about whose

Here, Barnen are the subject, and the blanket belongs to them. So Swedish uses the reflexive form:

• Barnen somnar inte utan sin filt.
  = The children don’t fall asleep without their (own) blanket.

If you said:

• Barnen somnar inte utan deras filt.

then it would usually mean:
The children don’t fall asleep without their blanket – where the blanket belongs to some other group of people, not the children themselves.

The form of the reflexive possessive pronoun (sin / sitt / sina) depends on the noun it modifies, not on the owner:

• sin
  • en-word, singular: sin filt, sin bok
• sitt
  • ett-word, singular: sitt hus, sitt barn
• sina
  • any plural noun: sina filtar, sina böcker, sina barn

Since filt is an en-word and singular (en filt, a blanket), we use sin:

• utan sin filt = without their (own) blanket

Yes, you can say:

• Barnen somnar inte utan filt.

That means roughly The children don’t fall asleep without a blanket / without any blanket – it’s more general.

With utan sin filt, you specify that it’s their own blanket, probably that particular blanket they’re attached to. It sounds more specific and personal:

• utan filt = without (any) blanket
• utan sin filt = without their own blanket

In your sentence, filt is singular: one blanket.

• Singular: en filt = a blanket
• Definite singular: filten = the blanket
• Plural: filtar = blankets
• Definite plural: filtarna = the blankets

If the children each needed their blankets (plural), you could say:

• Barnen somnar inte utan sina filtar.
  = The children don’t fall asleep without their blankets.

Here sina matches the plural filtar.

Yes, there’s a nuance:

• Barnen somnar inte utan sin filt.
  States a fact: they don’t (in practice) fall asleep without their blanket.

• Barnen kan inte somna utan sin filt.
  Adds kan (can), emphasizing ability: they cannot fall asleep without their blanket (it’s impossible / very hard for them).

Both are natural; the version with kan inte sounds a bit stronger.

The finite verb still wants to be in second position. Inte comes after that.

Example: move utan sin filt to the start:

• Utan sin filt somnar barnen inte.

Order:

1. Adverbial: Utan sin filt
2. Finite verb: somnar
3. Subject: barnen
4. Negation: inte

You can move elements for emphasis, but somnar stays in position 2, and inte follows it.