Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Muslim scholars view that swallowing unavoidable things such as one’s saliva doesn’t break the fast.
In his response to your question, Dr. Wael Shihab, PhD in Islamic Studies from Al-Azhar University. He is currently the Imam of the Downtown Toronto Masjid in Canada states:
Fasting in Ramadan is one of five pillars of Islam. This fact is well-established by the Qur’an, the authentic Sunnah, and consensus (ijma`) of Muslim scholars.
On the authority of Abu `Abdur-Rahman `Abdullah, the son of `Umar ibn al-Kattab (may Allah be pleased with them) who said: I heard the Messenger of Allah (peace and blessings be upon him) saying, “Islam is built upon five [pillars]: testifying that there is none worthy of worship except Allah and that Muhammad is the Messenger of Allah, establishing the prayers, giving zakah, making pilgrimage (hajj) to the House and fasting the month of Ramadan.” (Al-Bukhari and Muslim)
Allah Almighty says, “O you who believe! Fasting is prescribed to you as it was prescribed to those before you, that you may (learn) self-restraint; (Fasting) for a fixed number of days; but if any of you is ill, or on a journey, the prescribed number (should be made up for) from days later. For those who can do it (with hardship), is a ransom, the feeding of one that is indigent. But he that will give more, of his own free will, it is better for him. And it is better for you that you fast, if you only knew. Ramadan is the (month) in which was sent down the Qur’an, as a guide to mankind, also clear (Signs) for guidance and judgment (between right and wrong). So every one of you who is present (at his home) during that month should spend it in fasting, but if anyone is ill, or on a journey, the prescribed period (should be made up for) by days later. God intends every facility for you; He does not want to put to difficulties. (He wants you) to complete the prescribed period, and to glorify Him in that He has guided you , and perchance you shall be grateful.” (Al-Baqarah 2: 183-185)
Regarding your question about swallowing one’s saliva while fasting, this doesn’t invalidate the fast as it is unavoidable. Scholars say that the following acts do not break the fast:
b) Wearing Kuhl,
c) Kissing one’s wife or husband if he/she is able to control himself/herself,
d) Rinsing: rinsing the mouth or nostrils with water provided that it is not overdone,
e) Swallowing unavoidable things such as one’s saliva,
f) Tasting food,
g) Taking injections,
h) Smelling flowers or wearing perfumes, etc.
i) Experiencing a wet dream,
j) Eating or drinking due to forgetfulness,
k) Involuntarily vomiting.
Allah Almighty knows best.