Dirac suspected it, and made the Large Numbers Hypothesis: http://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis But is has not been validated by experiment.

One would not expect the speed of light a few seconds after the big bang to have been 300 Mm/s as it is today; neither would one expect the earth's gravity to be 10 N/kg throughout the atmosphere. However, we usually meet and apply these quantities within time and length intervals relatively too small for them to register any significant changes. Our problem is our indiscriminate use of 'extrapolation'.

As Claude has already said, the Dirac large numbers hypothesis was one idea in this direction. Some experimental results suggest the contrary: http://www.sciencemag.org/content/339/6115/46 . But I personally suspect universal constans have not had the same value over time.

My personal take is that they encode the fundamental properties of the piece of something (we may call it energy) that started as our universe. So I suspect that that they are changing in time but they are interconnected. These constants that describe large superstructure are reciprocal to that describing the microlevel. While the universe expand and the macrolevel changes so the constants should change. For instance, the speed of light encodes interconnection between the space dimensions (kinematic aspect of movement) to the energy (dynamic aspect of movement). I suspect that the speed of light actually is changing with the changing size of our universe.

@Boguslaw Stec.

Thank you for raising this interesting question about the Fundamental Physical Constants (FPCs). Thank you also for your above comment.

The variation in time of FPCs could be a nice way to go around cosmological singularities as suggested in the following paper by Dabrowski and Marosek:

"Regularizing cosmological singularities by varying physical constants".

arxiv.org/pdf/1207.4038.pdf

The following paper by Damour discusses another issue:

"The Equivalence Principle and the Constants of Nature".

arxiv.org/pdf/0906.3174.pdf

Concerning your comment, I do agree that the Fundamental Physical Constants (FPCs), such as the celerity of light, may encode some sort of class equivalences between dimensions.

Concerning your question, I do not have a decided opinion:

On one hand, if the FPCs are not varying in time, we will be left with the problem of explaining their observed values (and if they did not have their current values, we probably would not even be here to observe them).

On the other hand, should the FPCs be varying in time, could we still call them "fundamental"? How about their rate of change, would they become new "more" fundamental values, which would remain yet to be explained?

Thanks again.

Feynman on Initial Conditions, Evolving Laws, and What We Consider Physics

http://www.preposterousuniverse.com/blog/2012/10/18/feynman-on-initial-conditions-evolving-laws-and-what-we-consider-physics/

There is an interesting video clip where introduces the idea as a kind of meta-issue in physics:

“What, today, do we not consider part of physics, which we may ultimately be part of physics?”

His answer (which should be cued up here at the 7:10 mark) is the initial conditions of the universe, as well as the possibility that the physical laws themselves evolve with time.