According to Hinduism,
- What happens between death and rebirth?
- Does the soul go to heaven/hell in between?
- If so, does rebirth occur irrespective of whether the soul went to heaven or hell?
For minor good or bad deeds people do not go to either heaven or hell and are reborn in the earthly plane. For those people who do go to either lower heaven or hell are reborn in the earth plane after their punya (merit) due to extraordinary good deed (reason for going to lower heaven) or paapa (demerit) due to extraordinary evil deed (reason for going to hell) are exhausted.
The physical body dies but the mind and the senses leave the physical body. Persons who have not attained moksha are part of the life-death-life.... cycle. They may also have to stay in heaven or hell for some time if they have done a particularly good thing or a heinous crime, respectively. After the merit of their particular good karma or the demerit of their particular bad karma is exhausted, they will again be born into the Earth plane. The process is linked to the concept of residual karma. This residual karma idea and what happens to evil-doers is explained in Brahma Sutra.
But of others (i.e. those who have not performed sacrifices etc.) the ascent is to the abode of Yama, and after having experienced (the results of their evil works) the descent (to the earth again takes place). On account of such a passage (for the evil-doer) being declared by the Sruti.
(Brahma Sutra Sankara Bhasya 3.1.13)
The Sruti passage referred to in the above shloka is:
The Hereafter never reveals itself to a person devoid of discrimination, heedless, and perplexed by the delusion of wealth. "This world alone exists," he thinks," and there is no other." Again and again he comes under my sway.
(Yama speaks in Katha Upanishad I.2.6)
It is clear that if you do bad deeds that you end up in Yama Loka. However, there are two perplexing questions here. Does the person who descends to earth from Yama loka return with any Karma (i.e. is the Karma of the evil-doer after serving his term in Yama loka zero?)? What decides that a person will after death be immediately reborn in earth or return to earth after serving a time in Yama loka? These two questions are actually linked. The answer to this question is given in Brahma Sutra:
On the exhaustion of (good) work (the soul) with residual Karma (descends to this earth), as is known from the Sruti amd Smriti, along the path (it) went by (from here) and differently too.
(Brahma Sutra Sankara Bhasya 3.1.8)
The above Sutra says that what is exhausted in heaven is only that specific Karma which gave the soul a birth in lower heaven, but on the exhaustion of this Karma the remaining Karma, good and bad, brings it back to earth. While this Sutra talks of heaven and good deed, it also applies to Yama Loka and bad deeds. Let me explain the idea by a concrete example. Let us suppose that a dead person has a list of 10 karmas with goodness values (1, -3, 4, 5, -100, 4, 3, 2, 5, 8) where the minus sign stands for evil deeds. What Brahma Sutra Sankara Bhasya 3.1.8 is saying is that this person will go to Yama Loka only for that extremely evil deed of goodness value -100. After he has exhausted the bad effect due to the -100 Karma, he can then go back to earth with the residual karma (1, -3, 4,5,4,3,2,5,8). The idea is that only extremely evil or good deeds lead a man to Yama loka or to lower heavens. All minor good and bad karmas are served on the earth plane.The person who has attained moksha is free forever from the endless cycle of Samsara. The cycle of birth and death will only end after the attainment of moksha or liberation. The length of the process will depend on how quickly or slowly the person will attain moksha.
According to Garuda Purana (especially) and the Bhagavata Purana (in general):
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Is there heaven/hell in between death and rebirth?
According to Gita, it seems that Purusha may have an afterlife which is heavenly or hellish depending on one's Karma.
BG 9.20 - Those who are versed in the Vedas, who are drinkers of Soma and are purified of sin, pray for the heavenly goal by worshipping Me through sacrifices. Having reached the place (world) of the king of gods, which is the result of righteousness, they enjoy in heaven the divine pleasure of gods.
BG 16.16 - Bewildered by numerous thoughts, caught in the net of delusion, (and) engrossed in the enjoyment of desirable objects, they fall into a foul hell.
However, it doesn't imply that the realms such as "heaven" & "hell" exists. They are the layers of 3 modes of material nature.
When a consciousness is under influence of Sattva, it travels upwards to deva-s which are heavenly regions; under Rajas, it stays at wherever it is; under Tamas, it falls downwards to Asura-s, which are hellish regions. See this answer.
Does the soul go to heaven/hell in between?
A consciousness which holds mind & senses would navigate to the regions of Prakruti which are imprinted inside the mind during the death. And the mind may imprint things, which it has accumulated by learning throughout the life.
BG 8.6 — Also [when] the body is left remembering this or that "Nature" at the end, O son of Kunti, [it] always approaches towards establishing those nature(s) only.
BG 13.22 - Purusha being seated(situated) in Prakruti, experiences the [sattva, rajas, tamas] modes born of Prakruti. Contact with these modes, is the cause of its births in good and evil wombs
If so, does rebirth occur irrespective of whether the soul went to heaven or hell?
Only in the case of Moksha, the rebirth doesn't occur. In all the other cases, the rebirth keeps occurring.
BG 9.21 - After having enjoyed that vast heavenly world, they enter into the human world on the exhaustion of their merit. Thus, those who follow the rites and duties prescribed in the three Vedas, and are desirous of pleasures, attain the state of going and returning.
BG 16.20 — Those fools being born among the demoniacal species in births after births, without ever reaching Me, O son of Kunti, attain conditions lower than that.