## 1 Introduction  
Microalgae have immense potential for a wide range of biotechnological applications, thanks to their high growth rate, biomass productivity, and capability to thrive in diverse environments [1]. These photosynthetic organisms are particularly valuable for producing proteins, essential fatty acids, and vitamins, making them ideal for use in nutraceuticalids, food supplements, and animal feed [2]. In the pharmaceutical industry, microalgae are being studied for the production of high-value compounds, such as antioxidants, pigments, and bioactive molecules with potential therapeutic applications [3]. Additionally, microalgae's high lipid content makes them suitable for biofuel production, including biodiesel and bioethanol [4; 5]. Beyond product generation, microalgae play a crucial role in environmental biotechnology. They can be utilized in wastewater (WW) treatment to remove contaminants like heavy metals and excess nutrients while simultaneously producing valuable biomass [6; 7]. Moreover, microalgae contribute to carbon capture and sequestration, aiding in climate change mitigation [8; 9]. Among the many microalgae species, _Haematococcus pluvialis_ is one of the most extensively studied [10]. This strain is of significant commercial interest due to its unparalleled ability to produce astaxanthin, a keto-carotenoid determining the reddish or pinkish color of some crustaceans, fishes, and birds. Astaxanthin is also present in marine bacteria, fungi, red yeasts (such as _Plaffia rhodozyma_), certain higher plants like the Adonis species, krill, and various microalgae, including Chlorococcus species, _Chlorella zofingiensis_, and _Dunaliella salina_. Among the latter ones, _Haematococcus pluvialis_ represents the richest natural source of astaxanthin commercially available [11]. These microalgae undergo four life cycles: vegetative cell growth, encystment, maturation, and germination. However, they typically consist of only two stages--vegetative (green) and maturation (red) [12]. Astaxanthin is produced during the maturation stage, while chlorophyll is produced during the vegetative stage. Astaxanthin is highly valued across various industries, including nutraceuticalals, cosmetics, aquaculture, and food, due to its potent anti-inflammatory, anti-aging, and immuno-boosting properties [13; 14]. The commercial exploitation of _H. pluvialis_ primarily hinges on its astaxanthin production, which can reach concentrations far higher than those found in other natural sources. Astaxanthin has been documented to be 54-times more powerful than \(\beta\)-carotene, 65-times for vitamin C, and 100-times for \(\alpha\)-tocopherol [15]. Under suitable stress conditions, such as high photon flux intensity, _Haematococcus_ can accumulate up to 3-5% of astaxanthin on a dry weight (DW) basis [16]. High light intensity is particularly critical in enhancing astaxanthin production, as it triggers a protective response that leads to the synthesis and accumulation of astaxanthin, acting as an antioxidant to protect the cells from damage [17]. To maximize astaxanthin production, various cultivation strategies have been developed, involving phototrophic, heterotrophic, and mixotrophic systems. Phototrophic cultivation, which relies solely on light and CO\({}_{2}\), is commonly used but is often limited by slow growth rates and lower biomass yields [18]. Heterotrophic cultivation, where organic carbon sources are used, can increase biomass but might compromise the astaxanthin content [19]. Mixotrophy, which combines both phototrophic and heterotrophic methods, offers a promising approach to simultaneously enhance biomass and astaxanthin production [20]. A successful two-stage culture model has been developed for _H. pluvialis_. The first stage, known as the green stage, is characterized by high cell yield and is crucial for subsequent astaxanthin biosynthesis. The second stage, referred to as the red stage, allows for the rapid accumulation of astaxanthin [21].