http://sci.esa.int/planck/51559-hemispheric-asymmetry-and-cold-spot-in-the-cosmic-microwave-background/

Two Cosmic Microwave Background anomalous features (...) are confirmed (...). One is an asymmetry in the average temperatures on opposite hemispheres of the sky (...).

(end of quote)

and on March 21,

*Nature News*reported on this issue [6] :

http://www.nature.com/news/planck-telescope-peers-into-primordial-universe-1.12658

The asymmetry "defines a preferred direction in space, which is an extremely strange result", says Efstathiou.

(end of quote)

Planck was thus confirming with more precision a previous observation by WMAP.

But is such a resullt really "extremely strange" ? It is actually quite normal, and almost trivial, considering the space-time pattern I have been dealing with since 1996.

For a description of the spinorial space-time, see also my previous articles in this blog. The cosmic time

*t*(age of the Universe) is just the modulus of the space-time position spinor ξ .

In September 2011, a year and half before the Planck announcement, I explicitly wrote :

http://arxiv.org/abs/1011.4889

http://arxiv.org/pdf/1011.4889v4.pdf

*6.2.c A privileged space direction ?*

A specific property of the spinorial space-time considered here is that, to each point ξ , a (complex)

one-dimensional spinorial subspace can be associated such that for any point ξ′ of this subspace

one has :

ξ† ξ′ = | ξ′ | | ξ | exp (iφ) (11)

where exp (iφ), with φ real, stands for a complex phase.

If | ξ′ | = | ξ | so that ξ and ξ′ belong to the same constant-time hypersphere, the complex phase exp (iφ) is associated to the SU(2) matrix transforming ξ into ξ′. This transformation, U = exp (i/2 t

^{−1}

**σ**.

**z**) where t is the cosmic time t = | ξ | and

**z**a real space vector, is generated by a sigma-like matrix

**σ**.

**z**| z |

^{−1}associated to a unique space direction

**z**| z |

^{−1}on the constant time hypersphere.

ξ and ξ′ are both eigenspinors of

**σ**.

**z**. For each point ξ of the spinorial space-time, other than ξ = 0, there exists a unique space direction for which ξ is an eigenspinor of the associated sigmalike matrix. Exponentiating this matrix with an imaginary coefficient generates the directions of the relevant (complex one-dimensional) spinorial subspace associated to ξ .

With | ξ′ | = | ξ | and a positive phase φ, one actually has :

ξ′ = exp (i/2 t

^{−1}| z |) ξ (12)

and similarly, with − | z | instead of | z |, if φ is negative.

The set of points of the spinorial space-time thus generated obviously corresponds to a (spinorial)

circle of radius | ξ′ | = t (t = cosmic time) on the constant-time hypersphere, including the

point ξ itself and its SU(2) antipodal - ξ .

Thus, ”looking at” the initial point of our Universe ξ = 0 from a point ξ of the present time spatial hypersphere naturally leads, in the spinorial coordinates considered here, to the definition of a privileged space direction on the space hypersphere itself.

The direct memory of the geometry leading to such a privileged space direction is basically lost

if standard space coordinates on the constant-time hypersphere are used and standard matter is dealt with without incorporating its deepest structure as well as the most primordial origin of the Universe. However, several possible tracks from this spinorial effect in Cosmology and Particle Physics can still be considered.

In particular :

- The internal structure of standard spin-1/2 particles, as well as their interaction properties at very small distance scales, may contain the expression of a similar phenomenon.

- Signatures from a pre-Big Bang era can yield relevant information on this privileged space direction and on effects of the same origin through WMAP, Planck and other experiments.

- Similarly, ultra-high energy cosmic rays may be sensitive to both cosmological and ”beyond Planck” phenomena containing effects related to the privileged space direction.

Further work on this subject is clearly required.

(end of quote)

This was reminded, in particular, in my contribution to Proceedings of the ICFP 2012 conference (OAC Kolymbari, Crete, June 2012) were I wrote last February :

http://hal.archives-ouvertes.fr/docs/00/79/55/88/PDF/PreBBCreteNew.pdf

A specific cosmological property of such a spinorial space-time is [17] that to each point ξ, a privileged space direction can be associated at cosmic scale through the subspace where for any point ξ' one has:

ξ† ξ' = | ξ' | |ξ | exp (iφ) (8)

and exp (iφ), with φ real, stands for a complex phase. This subspace is generated using a σ matrix of which ξ is an eigenstate. Then, the privileged space direction is obtained by multiplying ξ by an arbitrary complex phase.

(end of quote)

The transparencies I presented in June 2012 can be found at the address :

http://indico.cern.ch/getFile.py/access?contribId=215&sessionId=56&resId=0&materialId=slides&confId=176361

Combined with parity violation, a cosmology based on the spinorial space-time can readily lead to phenomena like that reported by WMAP and Planck. More detailed mechanisms will be discussed in the next article.

[1] L. Gonzalez-Mestres,

*Physical and Cosmological Implications of a Possible Class of Particles Able to Travel Faster than Light*, contribution to the 28th International Conference on High Energy Physics, Warsaw 1996, arXiv:hep-ph/9610474, and references therein.

[2] L. Gonzalez-Mestres,

*Space, Time and Superluminal Particles*, arXiv:physics/9702026

[3] L. Gonzalez-Mestres,

*Cosmic rays and tests of fundamental principles*, CRIS 2010 Proceedings,

*Nucl. Phys. B, Proc. Suppl.*

**212-213**(2011), 26, and references therein. The

*arXiv.org*version arXiv:1011.4889 includes a relevant Post Scriptum.

[4] L. Gonzalez-Mestres,

*Pre-Big Bang, fundamental Physics and noncyclic cosmologies*, presented at the International Conference on New Frontiers in Physics, ICFP 2012, Kolymbari, Crete, June 10-16 2012, mp_arc 13-18, and references therein.

[5] Planck March 21 statement

*Hemispheric asymmetry and cold spot in the Cosmic Microwave Background.*

[6] Mark Peplow,

*Planck telescope peers into primordial Universe*,

*Nature News*31 March 2013.

Pre-Big Bang, vacuum and noncyclic cosmologiesto the HEP 2011 Conference (Grenoble, July 2011), I wrote :http://pos.sissa.it/archive/conferences/134/479/EPS-HEP2011_479.pdf

Pre-Big Bang, vacuum and noncyclic cosmologies(...) an even more primordial question seems to be that of the origin of half-integer spins, that cannot be generated through orbital angular momentum in the usual real space-time. It turns out that the use of a spinorial space-time [7, 8] with two complex coordinates instead of the conventional four real ones presents several attractive features. Taking the cosmic time to be the modulus of a SU(2) spinor leads by purely geometric means to a naturally expanding universe [8, 9], with a ratio between cosmic relative velocities and distances equal to the inverse of the age of the Universe. No reference to standard matter, hidden fields, gravitation or relativity is required to get such a result that looks quite reasonable from an observational point of view.

(...)

2. A spinorial space-timeAs spin-1/2 particles exist in our Universe, the most natural description of space-time would be a spinorial one [7, 8] with, at least, a SU(2) symmetry group [14]. With these minimal hypotheses, taking a preferred reference frame as suggested by cosmological data and required if superbradyons exist, a cosmic time can be defined. Given a spinor ξ , and considering the positive SU(2) scalar | ξ |

^{2}= ξ^{†}ξ where the dagger stands for hermitic conjugate, the cosmic time would bet= | ξ | and the associated space given by the S^{3}hypersphere | ξ | =t. Then, if ξ_{0}is the observer position on the | ξ | =t_{0}hypersphere, space translations correspond to SU(2) transformations acting on the spinor space, i.e. ξ = U ξ_{0}where U = exp (i/2t_{0}^{−1}σ.x) ≡ U(x), andσis the vector formed by the Pauli matrices. The vectorxis the spatial position of ξ with respect to ξ_{0}at constant timet_{0}, and is different from the spinorial position ξ − ξ_{0}. Space rotations are obtained as SU(2) transformations acting on the spatial position vector with respect to a fixed point ξ_{0}. The origin of our time can be associated to the point ξ = 0. This leads to a naturally expanding Universe where cosmological comoving frames would correspond to straight lines crossing the origin ξ = 0.Such a geometry automatically yields the well-known relation between relative velocities and distances at cosmic scale for comoving frames, usually called Hubble’s law but actually first formulated by Georges Lemaître [15, 16]. In our spinorial approach to space-time, if θ is a constant angular distance between two cosmological comoving frames, the S

^{3}spatial distancedbetween the two corresponding points on the | ξ | =thypersphere will bed= θt. The ratio between relative velocities and distances is then given by the inverse of the age of the Universe. This value is in reasonable agreement with present observations while matter, standard relativity, gravitation and specific space units have not yet been introduced in our description of space-time. It is therefore tempting to conjecture that the usually postulated dark energy is not required to explain the observed acceleration of the expansion of the Universe. Instead, gravitational and other standard effects can possibly account for past fluctuations of the velocity/distance ratio [8, 9].Although the spinorial relative position ξ − ξ

_{0}defined above corresponds to a path through past times violating standard causality, and the production of half-integer orbital angular momenta in experiments has never been reported, it may happen that such a position spinor makes sense at very small distance scales. It would then be possible to generate the spin 1/2 as an actual internal orbital momentum in an underlying composite picture of quarks and leptons possibly linked to a pre-Big Bang cosmology. Then, the spinorial space-time would also be crucial for our understanding of the ultimate structure of matter beyond conventional quantum field theory.Contrary to the conventional mathematical structure of the Poincaré group, the spinorial spacetime discussed here incorporates space translations and rotations in a single compact group. This is radically different from the assumptions that led to the Coleman-Madula theorem in 1967 [17]. Therefore, the present SU(2) approach to space-time and its natural SL(2,C) extension can open the way to a new unification between space-time and internal symmetries [8]. Such a new unified symmetry may in turn provide indirect checks of the spinorial space-time pattern suggested.

This SU(2) description of space-time considered here is also close to a SO(4) approach where, instead of being imaginary, the cosmic time would be given by the modulus of a four-vector [8]. To date, cosmological data have not excluded a S^{3}hyperspherical Universe.(...)

(end of quote, Copyright owned by the author under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ ) PoS (EPS-HEP2011) 479

Luis Gonzalez-Mestres