It is very likely that this year's ICC World Cup matches will be hampered by rain and many matches are likely to be played in DLS mode. However, due to rain, some top teams are likely to lose points. Sub-Indian countries receive a lot of rain during this season and the cricket venues are always humid due to rain so any conditions can be faced during the matches.
Both matches for today are abandoned due to rain. I guess the other match (in which Australia is playing) is delayed due to a wet outfield and even if it is started, it will be a T20 I guess.
By the way, since you said that we are likely to see rain in the coming days in India, does it mean that this world will be ruined by rain? Please don't tell me that. We had the Asia Cup recently and it was badly affected by rainy weather. We cannot afford a tournament as big as the World Cup to be disturbed by the rains. 50 Overs matches should remain 50 overs. Using DLS may not justify many results.