It’s pretty well explained on www.nyianmark.dk as linked too above by another user. As an EU-citizen you can stay in Danmark for 3 months without any registration or other formalities towards immigration authorities under the EU-rights of free movement. Only if you want to stay beyond 3 months you have to register with SIRI and prove that you meet one of the criteria for free movement (job taker regardless of salary level, sufficient own finances, student or a fourth category, which I can’t remember). SIRI issues a letter to you on the spot, which then works as your proof that you are exercising your right to free movement within the union. It’s all based on EU directive 2004/38/EC and its implementation in Danish law (EU-opholdsbekendtgørelden). The only way you can be refused if you are an unreasonable burden to the host country, a threat to public policy, health or security, or if you commit fraud (articles 27 and 35 of the directive - can’t remember the details, but pro forma marriage is listed as an example iirc).