Yes, definitely.

A whimsical (partial) answer to this question appears in an article by Daniel Asimov, Math Horizons, 1996:

https://www.maa.org/sites/default/files/pdf/horizonsarchive/february_1996.pdf

Asimov points to Archimedes who thought of the world saturated with numerical addresses that describe the location of every point in the physical world. 

If I have 0 and you give a "1" to me... I can build up the whole math .... if you see a phenomenon you can extract from it (all) the rules that drive the whole Universe : the rule maybe is simply just one :)

When we have only 1 logic , geometry , and total symmetry as in the pure crystal without defects ) all the mass of the universe are equal to zero and also all fields are equal to zero. But when we have 1 and 0 in the some time 1 type of logic but also 0 type of logic so we have many valued logic , many geometries that create , fuzzyness , breack of symmetry and defects as in the mater ( Crystal ).. In this 1 and 0 uncertainty we have stress as in a cystal where defects create internal force or stress. Now to avoid the stress the universe was generate with masses , field of forces and dynamic. In conclusion 1 and 0 together are the source of universe that try always  to move in a way to eliminate the stress generate by the uncertainty and restart the original situation with only 1  logic , geometry and so on

I think Victor's question was whether anything from the mathematics underlying number theory may be useful in cosmology problems. 

Yes, definitely.

A whimsical (partial) answer to this question appears in an article by Daniel Asimov, Math Horizons, 1996:

https://www.maa.org/sites/default/files/pdf/horizonsarchive/february_1996.pdf

Asimov points to Archimedes who thought of the world saturated with numerical addresses that describe the location of every point in the physical world. 

I would say that Math and in particular number theory are of course relevant to cosmology. However I do not think that the relation is as intimate as the one implied by Ptolemy and his mathematical model of the universe as a set of nested spheres

http://en.wikipedia.org/wiki/Ptolemy#Astronomy

I think that realistically, we should understand that all the cosmological models are simply models, and if by any chance we are able to solve them exactly or use number theoretical results and techniques to treat those models - these are still fundamentally approximate tools to explore the universe around us. 

@Eytan Katzav: I would say that Math and in particular number theory are of course relevant to cosmology.

We can carry forward the importance of cosmology in our view of numbers, if we consider the consequences of Pythagoras's dictim "All is number" and look more deeply into cosmology.   We can do this by taking a closer look at differential geometry, Riemann's view of space, and the notion that the universe is a manifold (a collection of coordinate charts, i.e., open sets in R^n)). 

This is the approach taken by M. Kim:

M. Kim, Why everyone should know number theory, 1998:

http://www.ucl.ac.uk/~ucahmki/numbers.pdf

Another way to ask is this question is here

https://www.researchgate.net/post/Assuming_the_premise_that_Nature_is_intrinsically_mathematical_what_evidence_is_there_supporting_this

where I let my answer there stand in this thread.  (What is RG netiquette for such cross posting?  Is there a policy?)

The reference URL supplied is a PDF of a 2006 conference about Physics and Math.  A much broader question than just "Cosmology", unless defined as 'all things", not just the universe creation myth(s), and predictions on where it is going, and the present state.

+1 to to the first two answers!  LOL

There is now a new branch of computer science that represents many physical phenomena in terms of 'digital life,' to more than a medium degree of accuracy. Where there is smoke, there is fire?  As computer science is a subset of number theory and cosmology was one of the modelled phenomena, thought I ought to mention it.  So, it's merits can be debated.

Dear Prof. James Peters, Sorin, Eytan: i am no expert in number theory, but i would agree with Prof. Peters that there could be deep connection between number theory and cosmology. For example, Hausdorff dimension of menger sponge is 2.73 which exactly corresponds to CMBR temperature. Another way is to consider the music of spheres. What do you think?

@Peter and Eytan: here is another paper on possible links between number theory and physics: http://www.math.fsu.edu/~marcolli/NTphysFinal.pdf. But i do not find yet any good paper for describing connection between cosmology and number theory. Best wishes

If one accepts number theoretical universality requiring construction of p-adic variants of physics and gluing all of them with real physics to a unified whole (p-adic physics would be physics of cognition and intention), one ends up with the view that the intersection of real and p-adic worlds correspond to rationals and their algebraic extensions.

One faces the challenge of constructing rational (and algebraically extended variants of various spaces involved: say imbedding space M^4xCP_2: these algebraic variants induce discretisation of space-time surfaces having also interpretation in terms of finite measurement resolutions.

For instance, proper time constant hyperboloid in future light-cone - essential in TGD and also in  based cosmology -  is replaced with any of its discrete variants defined as tessellations of hyperbolic by a discrete subgroup of Lorentz group.  This is like lattice in condensed matter theory but with lattice points replaced by quantized recession velocityes.  There is infinite number of this kind of lattice like structures and lattice cells correspond to hyperbolic spaces: this involves extremely refined number theory and also manifold topology (Thurston conjecture about the volume of 3-manifold as topological invariant in hyperbolic metric) .

The  prediction would be quantisation of  cosmic red shifts and this has been indeed reported. 

Cosmic temperature equal to Hausdorff dimension is certainly an accident since temperature is not dimensionless quantity and its value changes when you change units. 

@Prof. Matti Pitkanen: thanks for your answer, would you mind to give link to your paper discussing quantization of redshift? Thanks

Just a remark, as a followup to Pitkanen's impressive comments: the early attempt by A. Schild ["Discrete space-time and integral Lorentz transformations", Canadian J. Math.,  1(1949), 29-47] to build a discrete special relativity leads to quite a few problems of arithmetic (in $\mathbb Z$ or ${\mathbb Z} + \sqrt{-1} {\mathbb Z}$). 

@Peters JF: Great .... I just would  like to highlight the fact that although today's cosmology is a discipline of physics would be good to remember that "kosmos" stands for "order" and "logos" for "word", i.e. to extract the order from the things, from all things. but not an order, but the fundamental order, or the absolute truth, the "ARKE". Arkimedes, this ancient Italian from Siracusa, loved to look for beauty and elegance of the things, he knew that everything has a reason. So the whole universe reduced to an order. On the other side Im thinking back to a Diophantine equation. During the study of that I opened the doors for numerous speculations, wonderful thoughts about prime numbers and divisibility criteria, elliptic equations and so much more, up to the irrationality of PI: all in one, simply. The Diophantine equation says:

show that the integers couple [n,m] that satisfies the equation n^3 = m^2 + 2 -> (3,5) is the only one.

Fano and also Tifft has done work with redshift quantisation: http://en.wikipedia.org/wiki/William_G._Tifft .

The chapter http://tgdtheory.fi/public_html/tgdclass/tgdclass.html# cosmomore  contains some TGD inspired speculations about redshift quantisation.

There is a very well known result in number theory that (1+2+3+4+5+6.................= -1/12) a startling result (sum of all the +ve natural nos amounts to -1/12, its not sum up to infinity ... but all ,a single number not included you get a very large number. Its used in string theory to calculate Casimir Force in one direction.

http://empslocal.ex.ac.uk/people/staff/mrwatkin/index.htm

@Prof. M. Pitkanen, V. Fulcoli, K. Ryu, Bhaskar and Sorin: thank you for your answers. Best wishes

My two cents to complete M.Pitkanen's answer on usage of p-adic numbers in physics. The p-adic mathematical physics is now a rapidly developing area of research, numerous papers and several monographs are published, international conferences are held every couple of years, etc. etc. Concerning the p-adic cosmology especially, I'd like to mention works of Branko Dragovich on p-adic space-time. Branko Dragovich has an account here on ResearchGate.

@Vladimir: thank your for your answer. P-adic cosmology seems interesting. Best wishes

always......

https://www.researchgate.net/publication/315825530_Theory_of_Empty_Universe_Second_Draft

Article Theory of Empty Universe (Second Draft)

A number of famous scientist including Eddington and Dirac attempted to link cosmology and number theory. The major intent failed, but some important connections remain. Fine structure constant and the constant pi are thought to be fundamental components of cosmology.

Scaling factors and size ratios have some interesting orders of magnitude, but have not been fundamentally connected to cosmology until recently. Scale relativity does support a type of number theory both in algebras and in geometries. Squeezed quantum also connect a number system to a physical representation.

Much of the cause of failures in attempts to unite cosmology with number theories is in the lack of substantial definitions of what is being attempted and how the two concepts are connected. With out a systematic construction much effort has produced nothing.

In modern times symmetries and orthogonal groups have been used to built up cosmologies from fundamental principles and those programs produced useful results and a standard model in which the numbers are connected to physical quantities in a systematic and well defined way.

So I would say the answer is yes, with a condition that rules and principles apply.

thanks Jerry

Vic