I’m not a religious person, or someone who blindly believes everything written in religious texts. In fact, I am a very skeptical person. I’m answering this question because I find religious cosmology intriguing.

• Concept of Multiverse or MWI:

The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own. The existence of the other worlds makes it possible to remove randomness and action at a distance from quantum theory and thus from all physics.

The concept of multiverses is mentioned many times in Hindu Puranic literature, such as in the Bhagavata Purana.

Every universe is covered by seven layers — earth, water, fire, air, sky, the total energy and false ego — each ten times greater than the previous one. There are innumerable universes besides this one, and although they are unlimitedly large, they move about like atoms in You. Therefore You are called unlimited (Bhagavata Purana 6.16.37)

What am I, a small creature measuring seven spans of my own hand? I am enclosed in a potlike universe composed of material nature, the total material energy, false ego, ether, air, water and earth. And what is Your glory? Unlimited universes pass through the pores of Your body just as particles of dust pass through the openings of a screened window (Bhagavata Purana 10.14.11)

Source: Hindu cosmology

• Story of Revati and Time Dilation:

Revati was the only daughter of King Kakudmi. Feeling that no human could prove to be good enough to marry his lovely and talented daughter, Kakudmi took Revati with him to Brahmaloka (abode of Brahma) to ask the God's advice about finding a suitable husband for Revati. Then, Kakudmi bowed humbly, made his request and presented his shortlist of candidates. Brahma laughed loudly, and explained that time runs differently on different planes of existence, and that during the short time they had waited in Brahmaloka to see him, 27 chatur-yugas had passed on Earth and all the candidates had died long ago. Brahma added that Kakudmi was now alone as his friends, ministers, servants, wives, kinsmen, armies, and treasures had now vanished from Earth and he should soon bestow his daughter to a husband as Kali yuga was near.

Source: Revati

In the theory of relativity, time dilation is a difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses.

• Grandiose time scales:

Hindu cosmology involves some very large numbers. Just for example, the age of Earth predicted in Vishnu Purana (ancient Hindu scripture) is 4.32 billion years which is quite close to the current estimate of the age of the Earth - 4.5 billion years.
Carl Sagan was so impressed with such large numbers, the kind of which do not feature in creation myths of other civilizations, that he mentioned it in his Cosmos series:

“It is the only religion in which the time scales correspond, no doubt, by accident, to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma 8.64 billion years long. Longer than the age of the earth or the sun and about half of the time since the big bang. And there are much longer time scales still.”

But if you compare the numbers from Hindu cosmology with current estimates from science, it becomes clear how wrong they are. The estimated age of the Universe is 13.7 billion years, whereas according to Hindu cosmology it is 155 trillion years. Even if we ignore that number and take the start of a mahayuga to mean the start of the Universe or the birth of Earth, the age of current mahayuga - 120 million years is nowhere close to either the age of the Earth or the Universe. Of all the numbers listed in Vishnu Purana, just one number - 4.32 billion years - comes close to a number given by science.

• Big Bang, Big Crunch hypothesis and endless cycle of destruction and creation of universe in Hindu Cosmology:

Big Crunch: The Big Crunch is one possible scenario for the ultimate fate of the universe, in which the metric expansion of space eventually reverses and the universe re-collapses, ultimately ending as a black hole singularity or causing a reformation of the universe starting with another big bang.

Hinduism is the only religion that propounds the idea of life-cycles of the universe. It suggests that the universe undergoes an infinite number of deaths and rebirths.