Is it possible to detect if everyting in the Universe is changing size? This may be a trivial question, but I cannot find a good answer to it.
What would happen if the size of everything in the Universe is multiplied by some constant factor at the same time, let's say everything doubles its size for instance. People double their size, houses double their size, streets, towns, Earth... up to the whole known Universe.
The relative proportions and distance between objects would remain... If we measure our own size with a meter, the reading would be the usual one.
From current theories, it this something that can or cannot happen? that can or cannot be detected?
Would that change our perception of constants like c, gravity, or temperature?
Why? (in very simple terms...)
Is there any reference, any previous study of this problem?

(This part has been added/edited to improve the question)
From this question, I went to this book by Benjamin Crowell, following Ben Crowell advice. This section describe in better words my idea. Citation:

8.2.6 Observability of expansion
[...]
To organize our thoughts, let's consider the following hypotheses:

*

*The distance between one galaxy and another increases at the rate
given by a(t) (assuming the galaxies are sufficiently distant from one
another that they are not gravitationally bound within the same
galactic cluster, supercluster, etc.).

*The wavelength of a photon
increases according to a(t) as it travels cosmological distances.

*The size of the solar system increases at this rate as well (i.e.,
gravitationally bound systems get bigger, including the earth and the
Milky Way).

*The size of Brooklyn increases at this rate (i.e.,
electromagnetically bound systems get bigger).

*The size of a helium
nucleus increases at this rate (i.e., systems bound by the strong
nuclear force get bigger).

We can imagine that:

*

*All the above hypotheses are true.

*[...]


The author then propose to look at the first claim, all hypotheses are true...

If all five hypotheses were true, the expansion would be undetectable,
because all available meter-sticks would be expanding together.
Likewise if no sizes were increasing, there would be nothing to
detect. These two possibilities are really the same cosmology,
described in two different coordinate systems. But the Ricci and
Einstein tensors were carefully constructed so as to be intrinsic. The
fact that the expansion affects the Einstein tensor shows that it
cannot interpreted as a mere coordinate expansion. Specifically,
suppose someone tells you that the FRW metric can be made into a flat
metric by a change of coordinates. (I have come across this claim on
internet forums.) The linear structure of the tensor transformation
equations guarantees that a nonzero tensor can never be made into a
zero tensor by a change of coordinates. Since the Einstein tensor is
nonzero for an FRW metric, and zero for a flat metric, the claim is
false.

The author says this claim is impossible, the demonstration is not understandable for me as I'm not an expert in the domain, and don't know what are FRW or Ricci and Einstein tensors.
 A: Though I've not encountered any specific research into this, I ask how would you design such an experiment: Every form of measurement is calibrated against every other - our definition of spatial length, time, mass, inertia and energy in its various forms are all related to physical phenomena reproducible on this planet. If non arbitrary spatial distance were changed continuously, it would create no difficulty or even perceivable difference in the other measurements as they are all interdependent. A Plank length in any frame of reference would remain a Plank length.
That having been said, measurable change in spatial dimensions as derived from calculations of the Delta Doppler shift of far distant galaxies, I have not encountered any papers relating to such phenomena locally. And by locally I mean in our local cluster of galaxies. See here. It does not appear to be a phenomenon which will give you a noticeably bigger house or garden, as it is considered that local gravitational phenomena prevent expansion on this scale.
As to C, the gravitational constant and temperature should continue working just fine within whatever frame of reference you find yourself, see paragraph 1.
As to the "What if" question, that's for some alternate universe, perhaps you could yourself research what phenomena applied and write a Sci-Fi story based on it. (That's not meant to be as rude and insulting as it sounds -I only wish to assert that what ifs such as this, are not easy to answer in a Physics forum.)
A: It seems that you in some sense are referring to inflation, that is commonly described as "expansion of the Universe" and sometimes incorrectly understood as "expansion of everything in the Universe".
Indeed, when everything doubles its size, including wavelength of radiation and all other possible lengths and masses and time, we are not able to detect anything. This is just equivalent to redefinition of a meter.
However, if only space lengths are changed, like size of a chair, then we can detect this by measuring how long does it take for light to pass the distance of 1 chair. If time is not rescaled, then this gives different answer. (Here one may comment on size of a pendulum clock, but lets think about number of oscillations of radiation emitted by Caesium atom.)
So, you see to make this undetectable you should balance all possible ways to measure distances. This balance effectively gives rescaling of a meter.
Obviously, this is NOT what happens in the cosmological inflation, where only space expands. I am personally not aware of any theories exploring expansion of objects, may be because this is not very interesting.
