We introduce DAS (Domain Adaptation with Synthetic data), a novel domain adaptation framework for pre-trained ASR model, designed to efficiently adapt to various language-defined domains without requiring any real data. In particular, DAS first prompts large language models (LLMs) to generate domain-specific texts before converting these texts to speech via text-to-speech technology. The synthetic data is used to fine-tune Whisper with Low-Rank Adapters (LoRAs) for targeted domains such as music, weather, and sports. We introduce a novel one-pass decoding strategy that merges predictions from multiple LoRA adapters efficiently during the auto-regressive text generation process. Experimental results show significant improvements, reducing the Word Error Rate (WER) by 10% to 17% across all target domains compared to the original model, with minimal performance regression in out-of-domain settings (e.g., -1% on Librispeech test sets). We also demonstrate that DAS operates efficiently during inference, introducing an additional 9% increase in Real Time Factor (RTF) compared to the original model when inferring with three LoRA adapters.