One place where the age of the universe is discussed is in Mahabharata Santi Parva. The relevant lines in the Mahabharata are:
'A year (of human beings) is equal to a day and night of the gods. The
division (as regards the god) consists in this: the half year for
which the sun travels from the vernal to the autumnal equinox is the
day of the deities, and the half year for which the sun travels from
the later to the former is their night. ....................The
learned say that these twelve thousand years (of the deities)
constitute what is called yuga. A thousand such yugas compose a
single day of Brahman. The same is the duration of Brahman's night.
With the commencement of Brahman's day the universe begins to start
into life. During the period of universal dissolution the Creator
sleeps, having recourse to yoga-meditation.'
Mahabharata, Santi Parva. Section CCXXXI
If you take the Mahabharat information then the life of a universe is given by (1x365 human years)x(12000)x(1000) =4.38 billion human years.
Please notice how carefully Mahabharata says that this is thought by the 'learned'. Any divine revelation will talk of scientific topics like the age of the universe in terms that will be understood by the learned of that time. Otherwise nobody will understand what is being said. Thus Gita should be understood as saying that the time scale of Brahma and the universe is enormous.
The Vedas say that Brahma lives in the Sun. Some commentators have said that Brahma is for this solar system only as he resides in the Sun. If there is life on other systems outside our own, they would have their own Brahmas. If you accept this, then the age of 1 day of Brahma maps pretty good to the lifetime of the Sun.
Sankaracharya has also said that these stories do not have to be taken literally as true. They can be taken as parables. They were done in this manner to make a complex situation understandable to ignorant people.
Reagrdless as to which story you think is better, all point to Brahman as the sole cause of this universe. All point to Brahman being the only true Reality. Realize God and ask Him directly what is true. Arguing over which story is true is pointless, it is the same as arguing over the husk and letting the rice be gone. As Ramakrishna Paramahamsa said, we are here to enjoy mangoes, not to count how many leaves are on each mange tree....
You should be a little less hesitant to accept science as absolute. What science was saying 200 years ago is different from what science was saying 100 years ago is different from what science says today and will be different from what science will be saying in 100 years. Less that 100 years ago it was still generally accepted that there was only 1 galaxy. I saw on the internet last week a new paper by some astrophysicists that says there was no big bang; the universe is expanding in both directions (past and future)...
The existence of the Universe consists of 3 equal parts, namely, Pradhama Parardha (First period of activity), Kshaya Kalpa (Great delusion) and Dviteeya Parardha (Second period of activity). It is 2 days and one night --- all three are of equal duration of 4.32 billion years. Kshaya kalpa and Dviteeya Parardha is called Sveta Varaha Kalpa. Thu, the existence of the Universe is 12.96 billion years and the science starting with a modest figure of 4.5 billion ears went up to 15 billion years and finally came down to about 13 billion years, a figure very close to the value of 12.96 bn years of Hindu cosmology.
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