This question is an exact duplicate of:
Thanks for those of you who took their time answering my problem but it seems that there is a misunderstanding between us. Most answers are based on the assumption of Electroweak symmetry breaking which was not my intent. My question belongs to an era even before this breaking took place. So, here is the edited version that it reflects my thought processes better than previous version of the question in the hope that new responses will be modified accordingly.
Let's assume that the singularity from which our Universe was created about 13.8 billion years ago (according to the Big Bang Standard cosmological model,) proceeded such that there was no need of any sort of spontaneous symmetry breaking (for any reason) to produce massive particles in early epochs. This would have created numerous massless fundamental particles. How do you think the history of our Universe would have been changed in terms of the underlying physics in large scales? In other words, if building blocks of our Universe (at least baryonic matter) were in fact all massless due to the absence of some sort of Mechanism, what would have happened to gravity? Here I truly mean before the epoch where EW and Strong interactions got separated. So, I am not talking about EW symmetry breaking but EW-Strong symmetry breaking (which happened even earlier than EW symmetry breaking such that even hadrons could not form into massive particles.) After all, we believe gravity is intertwined with spacetime fabric. What would have been the story if all the baryonic matter had started out being massless?
Somehow I thought knowing the answer for this question can guide us towards establishing a better understanding of Dark Matter and Dark Energy sectors. Maybe all the mystery lies in the fact that we have all three components interacting with each other and that's why it's too hard to make sense of everything. So, removing at least one component right from the beginning of the Universe (namely baryonic matter) should be a nice thought experiment.
Thank you for your time,