Can't the puzzle of the accelerating universe be answered by multiple/infinite universes and their gravities?
Yes, it can. And probably the best source to get more details (since it's too lengthy to describe here) is one of the inventors of the theory - Prof. Linde of Stanford - see http://www.stanford.edu/~alinde/
He attempts to explain the accelerated expansion of the universe and inflation in the context of multiple universes and string theory.
All very interesting but it could be all very wrong. Or not. We just don't know! And we probably will NEVER know. Physics is based on developing theories (models) which can be tested by experiment or observation. The model makes certain predictions, which are then tested. If the predictions are close to observations, then it's a good model. If it isn't, then there's a problem with the model and a new one is sought.
Many cosmological models are not testable. They're not open to observation. And there's active debate among some experts of their basic principles. Is the universe expanding? The majority of physicists believe so, but not all! Is it accelerating? Even more debate! And what about string theory? There's considerable debate, since currently, string theory does not make testable predictions.
I urge you to keep an open mind on these questions. Science never provides definitive "answers" - just models that work under a given set of parameters.
For example, it is 'generally' assumed that the Big Bang occurred some 13.7 billion years ago. Although this idea is believed to be valid by the majority of cosmologists, it is by no means universally accepted. The "Big Bang", based on Hubble's velocity-distance relation and the microwave background radiation, is very much still a theory, and there are alternative theories. Some observations do not support an expanding universe or the Big Bang. There are several references concerning this, but perhaps the most authoritative person is Halton Arp, a leading astronomer and researcher on galaxies, who wrote "Seeing Red". That book is highly recommended to get an alternative view. Or read "A Different Approach to Cosmology" by Hoyle, Burbidge, and Narlikar. That's another great book which gives a scientific view on how the universe has always been in a steady state.
And what about string theory? A very good book on string theory and its inability to prove anything is "Not even Wrong" by Peter Woit. In it, he argues that any scientific theory should be testable and predict certain results, which string theory can't. It can't be proven right or wrong. It's simply a way of trying to make sense of the universe, but is not a testable scientific theory. See http://www.math.columbia.edu/~woit/
So unless a theory is tested by the scientific method (i.e., predicts certain outcomes and reproduces predicted results), it must be taken with a grain of salt.
Prof. James Gort