Q: In the three cultures we have so far studied - Roman, Mediæval and Muslim, how did /does the garden play a role in their respective religions?

In the Roman, Medieval, and Islamic culture, religion played a main role in the design and function of the garden. In the three cultures the garden facilitated mans connection with the God/Gods. 

In the Roman culture, religion permitted all aspects of their life and the garden was no exception. The religion in Ancient Rome was centered around Gods and explanations for events usually involved one of the Gods. The Romans believed that the Gods controlled their lives, so consequently, they spent much of their time worshipping them. Since gardens were so intrinsic in the Roman household, with almost every house having some sort of garden, it would make sense for religion to be expressed in the garden. Religion in the roman garden was expressed in three different ways: statuary (which can be seen below), aediculas, and herms. 

(https://forum.disabroad.org/bbcswebdav/pid-197065-dt-content-rid-600207_1/courses/garden_1502213/03%20SP%2015%20The%20Roman%20Garden.pdf)

The garden was seen as a paradise: somewhere to escape to. The religious statues in the garden could serve a couple of purposes. First, statues of Gods like Liber, the God of fertility and vine growing, would be thought to bring life to the flowers. The statues could also serve as a figure to pray to.

Religion in the medieval period was just as prevalent, argumentatively more so, as in the Roman gardens. Religious aspects in the medieval garden can be seen below.

(http://www.motherearthliving.com/~/media/Images/MEL/Editorial/Blogs/In%20the%20Garden/Herbal%20Travels%20The%20Cloisters/DSCN8144)

Above a cloister is shown which means there are four pathways, symbolising the four rivers of Eden, that meet at a center water feature. The medieval garden, similar to the Roman garden, would be used as an escape or paradise. Prayer in the garden would be common since it gave an escape from the main house. In a medieval monastery, the garden would have a functional purpose, but usually have a statue of Mary present. The garden was a way to express religion outdoors. 

Similar to the Romans and in the Medieval period, the daily life of a typical Muslim revolved around religion. However, the main difference between the Muslim religion was they believed in the after life. The garden was particularly important in this idea of afterlife because the Muslim garden represented the afterlife a devoted Muslim hoped to enter. For this reason, Muslim gardens were a peaceful escape 

(http://3.bp.blogspot.com/-aLAmgz7XeP8/U2pWRbzSj0I/AAAAAAAAAMY/ejTOypMCLz8/s1600/100905_603.jpg)

Like Roman and medieval gardens, Islamic gardens also often had 4 gardens or flowerbeds , called Chahar Bagh, with a central water source that fed into 4 rills. These rills  also symbolised the 4 rivers of life.



Useful Links:
http://catnaps.org/islamic/islagard.html
http://www.historylearningsite.co.uk/ancient_rome_and_religion.htm
http://www.tcnj.edu/~anchouse/garden.html
http://www.nationaltrust.org.uk/article-1356400618277/