a. The Steady State theory, which says the universe is never born, never dies, and is always like what it is.
b. The Big bang theory, which says the universe began with a point of energy exploding in a "big-bang".
Since the universe is expanding and evolving, 1st theory is not 100% correct automatically. Big Bang theory says that the current age of universe is 11-20 billion years. But according to new observations, i.e. clusters of galaxies, super-clusters, Great Wall (Tully's complexes), it is quite evident that our universe is much much older than that. Lots of cosmologist believe that big-bang theory is not correct although it is most widely accepted. In short, modern man is not aware of forces and science which are needed to expain the creation of universe.
Lets look at vedic science and what it says. Right now I am quoting only what it says:
a. Total age of universe is 311.04 trillion years (human years).
b. Current age is around 155.521972944 trillion years.
How it is calculated:
-> There are 4 ages on earth which keeps circulating:
Satya Yuga - 1.728 million years
Treta Yuga - 1.296 million years
Dwapara Yuga - 0.864 million years
Kali Yuga - 0.432 million years
Total: 4.32 million human years.
-> This yuga cycle is called maha (in english, it means great/big) or divya (divine) yuga. One thousand such cycles forms one day of Brahma (a demigod in hindu religion which governs the universe). So one day of Brahma is 4.32 million * 1000 = 4.32 billion human years. Each such day of Brahma is called a "kalpa". His night also constitutes 4.32 billion human years. During his day, life exists in universe. In nighttime, no form of life exists. So one complete day and night has 8.64 billion human years.
-> Age of Brahma is 100 years. Each year of Brahma has 360 days and same number of nights. Thus, total age of Brahma is 360 * 100 * 8.64 billion = 311,040 billion human years. i.e. 311.04 trillion years. This period is called "maha kalpa".
-> The life span of the universe is one "maha kalpa". i.e. 311.04 trillion human years. This time span is also the duration of one breath of "Vishnu" (the ultimate god in hindu religion). When he exhales, thousands of universes emerges and one "Brahma" is born in each universe. When "Vishnu" inhales, all universes get sucked and Brahma dies.
-> This cycle is non-ending and eternal. Thats why "Vishnu" is considered eternal in Vedic Science (or religion).
How much old is our universe:
-> Note that the period of Satya Yuga is 0.4x, Treta Yuga is 0.3x, Dwapara Yuga is 0.2x and Kali Yuga is 0.1x where x is the time-span of one maha-yuga cycle. I will use 'x' as 1 maha-yuga cycle subsequently.
-> In 1 day of Brahma, there are 14 "manvantara". Each "manvantara" is divided into 71 "maha-yuga" cycles. So total make 14*71 = 994x (mahayuga cycles).
-> Remaining cycles (1 day of Brahma contains 1000 maha-yuga cycles) are used to fill gaps between manvantara. Before and after each manvantara (called as "sandhya" and "sandhyamsa" respectively), there is a junction of 1.728 million (age of Satya Yuga, or 0.4x) human years. Total number of junctions are 15 (since there are 14 manvantaras). So total gap period is = 0.4 * 15 = 6x. Hence total makes 1000 maha-yuga cycles or 1 brahma day.
-> According to the Vedic texts, current age of Brahma is 50 Brahma years and 1 brahma day (we are in the 1st day of 2nd half of brahma)and we are in the seventh "manvantara", in the 28th turnover of its 71 yuga cycles. In this cycle, we are in the start Kali Yuga. Age of kali yuga is not known perfectly but it is around 5000-10000 years. For calculation, lets assume 8000 human years.
-> So current age of our universe (in terms of maha-yuga cycles) =
(50 * 720 * 1000) -- 50 years * (360 days + 360 nights) * total no. of cycles in one day/night
+ (6 * 71) -- 6 manvantara each of 71 maha-yuga cycle
+ (7 * 0.4) -- 7 junctions or gaps for 6 manvantara
+ (27 * 1) -- we are in 28th cycle of 71
+ (0.4+0.3+0.2) -- In this cycle, we are in Kali Yuga. Satya Yuga, Treat Yuga and Dwapara yuga are 0.4x, 0.3x and 0.2x respectively.
+ around 8000 human years -- very small, so ignoring it.
Thus total age = (36,000,000 + 456.7)x = 36,000,456.7 * 4.32 million = 155,521,972.944 million years = 155.521972944 trillion human years. Now add the age of kaliyuga. i.e. around 8000 human years. One we calculate the exact age of kaliyuga, we can know the exact age of universe.
How ancient Indians (or Vedic people, more precisely) come up with these numbers, I dont have a clue.