You can refer to attached papers. They may answer your question.

Article Journey of the Universe from Birth to Rebirth with Insight i...

Article A Spiral Structure for Elementary Particles

Thanks Dr Mohamed El Naschie and Mr Surajkumar

I will definitely refer ur answers

Hi, I am not sure I understand what you have in mind by "relation". There are many ways in which you can connect DM/DE and the question of extra dimensions. One obvious example is the UED scheme which can provide a DM candidate. See Servant&Tait paper for instance. So I guess the answer to your question is yes, anyway.

See my publications an arxiv.

Permit me to offer some thoughts, based on theory I developed.  Within this framework, people might say that an answer to (a parallel to) your question is "no."

I developed a candidate catalog of elementary and composite particles.  (See sections 2.7 and 2.8 in the attachment.)  The catalog includes all known particles and suggests other ordinary-matter particles.  The catalog provides for ordinary-matter, dark-matter, and dark-energy particles.  (It turns out that 1 relative of photons and [yes, I know I should say 'hypothetical'] gravitons, "spans" all 3 categories [ordinary matter, …, dark-energy].)

People might say that the underlying math correlates with exactly 3 spatial dimensions.  (eqn. (1.1.4), eqn. (1.2.64), table 1.2.8, table 1.2.10 through table 1.2.12, etc., and sections 5.4, 5.5, and 7.2)  A key concept here is that all known particles (and all the candidate particles I suggest) have spins of S(S + DP - 2), with DP = 3.

People might say that the underlying math correlates with exactly 1 temporal dimension.  (sect. 5.4 and 5.5)

My having said such (including alluding to "no" above), I note that people might find interest in the notion that many of the math solutions (that I correlate with known and possible particles) correlate with solutions for math for which the number of (let's say space-like) dimensions is other than 3.  (See, for example, the D column in table 1.2.8 or 1.2.12.  And, note the DP columns in the same tables.)

I know that people might say that the attempted research to which I refer is not well-established.  But, perhaps people will find merit in the work and perhaps you will find something relevant to your question.

Book Theory of Particles plus the Cosmos: Small Things and Vast E...

Lightest Kaluza-Klein particle in an extra dimensional gauge model is a dark matter candidate. It is stable because KK parity does not allow it to decay to ordinary particles. For this reason it satisfies the requirement that the lifetime must be greater than the age of the universe. However this candidate particle must be electrically neutral, which will put some more constraints on the structure of the candidate model.

Ref: Servant and Tait: http://arxiv.org/abs/hep-ph/0206071

Dark energy and dark matter  are nothing, instead, they are merely a consequences to the curvature of the actual hyperbolic spactime of the universe

Article The Big Bang hyperbolic universe neither needs inflation nor...

Book The Hyperbolic Universe.

In this paper of mine, I showed that the unit of the mass of a virtual particle is \sqrt{-kg} and it means this unit is the complex number equivalent of the baryonic mass as we know it. Also as you know that complex numbers points to higher dimensions. Which means I found a relation between dark energy and the higher dimensions (at least 4th dimension).

Article Link between reduced Planck mass and dark energy