How would be the effects on India, Central Asia and Asia in general if Indo-European speakers did not migrate into the Indian subcontinent?
The Harrapan civilisation flourishes and after that the world as we know it is butterflied away.
It's really dibuous Harrapean civilisation decline was due to invasions or migrations, would it be only because there's no much traces of violent destruction.
That they could have been a factor is possible, but mostly unprooved, but it is more currently believed that the same set of climatic changes that provoked migrations provoked similar effects in the Indus Valley (becoming more arid) and having populations (or at least cultural features, but these don't exactly walk on themselves) East and South.
This. It appears that the end of the Indus-Sarasvati civilization was mainly due to the Sarasvati River drying up, due to a combination of monsoon rainfall patterns changing and geological uplift changing the course of its tributaries.
It appears that the Sarasvati River was the main focus of the Harappan civilization, with larger cities, and more of them, on its banks than on the banks of the Indus. It was only by accident that the earliest (and most well-known) discoveries of ancient Harappan cities were in the Indus watershed, giving the false impression that the civilization was focused on the Indus.
It was only after the Sarasvati had dried up that the Vedic culture moved to the Ganges as its central river. The shift can be seen in the Vedic scriptures. The earliest texts are all about the Sarasvati (and hence must have been composed before ~1900 BC when it had almost totally dried up, and probably much earlier going by astronomical indications), and it's only in later texts that the Ganges becomes the primary focus.
Note that this date is before the Aryan Invasion is supposed to have happened, which is currently dated to c. 1800 BC, so a possible scenario is that the Sarasvati dried up, the Vedics shifted their focus and the bulk of their population to the Ganges, and THEN the Aryans migrated into the nearly-abandoned Sarasvati and Indus watersheds, combining their early IE religious beliefs with those of the non-IE (possibly Dravidian) Vedics to form the archaic Hinduism of the early Upanishads.
The theory of Aryan invasion is based on the theory that the Dravidian civilization on the banks of Saraswati and Indus has no connection with the Vedic culture of Aryans. If the Vedas were compiled by the settlers of Saraswati-Indus river banks, ie. the Dravidians, why should another group replace them? The Vedas were all compiled by the same group of people.
The Hinduism can be traced to the IVC. The statues of Pasupati(The Lord of the beasts) and the Mother Goddess found in IVC resemble the idols of Lord Shiva and Durga in Hinduism. Hinduism, though the name is of much later origin, can be traced to the IVC. This shows that the present Indian Civilization is a continuation of the IVC.