Swayambhu or स्वयम्भू (Sanskrit “self-manifested”, “self-existing”) means “that is created by its own accord”. In Sikh prayer, it is called Ajuni Saibham. In Tibetan, this word appears as “Rangjung”.
The word Swayambhu is used to describe a self-manifested image of a deity, otr ku (Tibetan) which was not made by human hands, but instead is naturally arisen, or generated by nature.
The word etymology of swayambhu is Svayam (स्वयम्) which means self or on its own and bhu (भू) which means to take birth or arising. The idol of Venkateshwara at Tirumala is one such example.
In Sikh prayer, the word ‘Ajuni’ makes God to be unborn. Saibham (saibhang) explains God as self-manifested, self-existent or self-effulgent.
Based on details in Bhagavata Purana and Matsya Purana, Narayana is said to be the self-manifested Swayambhu form of Brahman as the first cause of creation.
The Manu Smriti “In the beginning, all this existence was one undifferentiated, un-manifested, indefinable, unarguable and unknown in every way. From this condition arose the Universe of ‘name and form’ (namarupa), through the medium of the Self-existent Creator, Svayambhu.”
In terms of quantum physics, from the quantum field of unmanifest arose the quantum fluctuation, which led to the birth of Hirnagarbha or the golden egg leading to the birth of universe.
In Spiritual Vedic Science, consciousness, soul and the spirit are Swayambhu.
Soul never dies and is never born. It self-exists in the universe. The very basic nature of any living cell is multiplication and that can only happen in the presence of Swyambhu.
In quantum physics, a quantum fluctuation (or vacuum state fluctuation or vacuum fluctuation) is the temporary change in the amount of energy in a point in space as explained in Werner Heisenbergs uncertainty principle. This allows the creation of particle-antiparticle pairs of virtual particles.
Quantum fluctuations may have been necessary in the origin of the structure of the universe: according to the model of expansive inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure.
A quantum fluctuation is the temporary appearance of energetic particles out of empty space, as allowed by the uncertainty principle.
The uncertainty principle states that for a pair of conjugate variables such as position/momentum or energy/time, it is impossible to have a precisely determined value of each member of the pair at the same time. For example, a particle pair can pop out of the vacuum during a very short time interval.
The Puranas say that Hirnagarbha the golden egg remained floating for a year and did not divide till it was entered by a Swyambhu or in other words experienced a quantum fluctuation.
Based on this theory it is possible that the whole universe could have been created at the same time without going through the Darwinian principles.
In Bhagavad Gita chapter 10.3, Krishna says
यो मामजमनादिं च वेत्ति लोकमहेश्वरम् |असम्मूढ: स मर्त्येषु सर्वपापै: प्रमुच्यते || 3||
“Those who know me as unborn and beginningless, and as the Supreme Lord of the universe, they among mortals are free from illusion and released from all evils.”
बुद्धिर्ज्ञानमसम्मोह: क्षमा सत्यं दम: शम: |सुखं दु:खं भवोऽभावो भयं चाभयमेव च || 4||अहिंसा समता तुष्टिस्तपो दानं यशोऽयश: |भवन्ति भावा भूतानां मत्त एव पृथग्विधा: || 5||
“From me alone arise the varieties in the qualities amongst humans, such as intellect, knowledge, clarity of thought, forgiveness, truthfulness, control over the senses and mind, joy and sorrow, birth and death, fear and courage, non-violence, equanimity, contentment, austerity, charity, fame, and infamy.”
महर्षय: सप्त पूर्वे चत्वारो मनवस्तथा |मद्भावा मानसा जाता येषां लोक इमा: प्रजा: || 6||
“The seven great Sages, the four great Saints before them, and the fourteen Manus, are all born from my mind. From them, all the people in the world have descended.”
Then from 10.20 to 10.37 Krishna goes on to describe the list of his creations as self-manifest.