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Is it possible to estimate the Higgs Mass from the CMB Power Spectrum?

General Relativity and Standard Model are considered as a theory of dynamical scale symmetry with definite initial data compatible with the accepted Higgs mechanism. In this theory the Early Universe behaves like a factory of electroweak bosons and Higgs scalars, and it gives a possibility to identify three peaks in the Cosmic Microwave Background power spectrum with the contributions of photonic decays and annihilation processes of primordial Higgs, W, and Z bosons in agreement with the QED coupling constant, Weinberg's angle, and Higgs' particle mass of about 118 GeV.

concepts. Moreover, this ΛCDM explanation contradicts to the vacuum postulate. Since the CMB power spectrum is one of the highlights of the present-day Cosmology with farreaching implications and more precise observations are planned for near future [1], the detailed investigation of any possible flaw of the standard theory deserves an attention and a public discussion.
In this paper we try to describe the CMB power spectrum in accord with the wellestablished Wigner's theory of the relativistic state classification, where any relativistic particle in quantum field theory can be associated with a unitary irreducible representation of the Poincaré group given in a definite frame with a positive energy.
The cosmological scale factor, its local excitations used for description of the CMB power spectrum, and Poincaré group transformations can be naturally included in the Wigner classification, if General Relativity is considered as the theory of the joint non-linear realization of the affine and conformal symmetries with the Poincaré group of the vacuum stability [4], where the scale invariance of laws of Nature [5,6] is realized dynamically by means of the dilaton Goldstone field.
The dynamical scale symmetry plays a role of the principle of a choice of variables in the accepted General Relativity (GR) and the Standard Model (SM) [7]. The dilaton Goldstone field compensates all scale transformations of fields including the cosmological scale factor describing expansion of the Universe lengths in the Standard Cosmology [2]. Nevertheless, the cosmological dynamics can be introduced by help of Einstein's cosmological principle [8] that means averaging all scalar characteristics including the dilaton field over a constant Universe volume. This cosmological dynamics of the zeroth dilaton mode explains the redshift by a permanent increase of all masses in the Universe and leads to the Conformal Cosmology [9,10,11,12,13,14,15,16], where all measurable quantities are identified with the conformal ones (conformal time, coordinate distance, and constant conformal temperature).
General Relativity considered as the theory dynamical scale symmetry [4,6] changes the numerical analysis of supernovae type Ia data [17,18] and shows the dominance of the scalar field kinetic energy in all epochs of the Universe evolution including the chemical evolution, recombination, and SN explosions.
In the paper we try to describe the CMB power spectrum [19] in GR as the theory of dynamical scale symmetry in accord with the classification of relativistic states [3].

II. DILATONIC VARIABLES IN GENERAL RELATIVITY
Let us consider the accepted General Relativity supplemented by the Standard Model and an additional scalar field Q governing the Universe evolution where unitsh = c = M Planck 3/(8π) = 1 are used throughout the paper. This action depends on a set of scalar, spinor, vector, and tensor fields F (n) = φ, s, V µ , g µν with their conformal weights n = −1, −3/2, 0, 2, respectively.
Following the foundation of the GR as a dynamical scale symmetry [4,6] we define all observable fields F (n) as scale-invariants quantities using the following scale transformations of these fields F (n) in action (1) including the metric components g µν : where D is the dilaton compensating scale transformations of all these fields. Any concrete choice of the dilaton as a metric functional D[g] means a gauge fixing. In [12,20,21]  ij . Therefore, one can remove any scale factor from the spatial metric components in the Dirac-ADM parameterization [20] in terms of the simplex components ω (0) , ω (b) in the Minkowskian tangent space-time where e (b)i are the triads [21] with the unit spatial metric determinant |e (b)i e (b)j | = 1, N d is the Dirac lapse function, and N j are the shift vector components. In phenomenological applications, one can identify this choice with the CMB co-moving reference frame. In terms of the dilaton variables, the GR action takes the form where R (3) (e) is a curvature, △ = ∂ i [e i (a) e j (a) ∂ j ] is the Laplace operator, and v D = Simplex (3) as an object of frame transformations from the Earth frame to the CMB one moving to Leo with the measurable velocity 368 km/s separates the latter from the , is at heart of GR. One can see that variables (2) and interval (3) define a d-invariant finite coordinate volume V 0 d 3 x = V 0 < ∞, d-invariant evolution parameter in the field space of events, and a d-invariant time-interval N 0 dx 0 = dτ by Einstein's cosmological principle [8] as averaging of the dilaton D and the inverse Dirac lapse function N −1 d over this volume: The scale-invariant variables and d-invariant evolution parameter as the dilaton zeroth mode where is the zeroth mode action and the second term S U repeats actions (1) and (4) for nonzero harmonics associated with local excitations.

III. COSMOLOGICAL DYNAMICS OF THE ZEROTH DILATON MODE
Let us consider the Early Universe when one can neglect all these local excitations S U ≃ 0 (complete expressions of action (6) see in Appendix A). In this case, the cosmological evolution of the Empty Universe arises in the form of a conformal mechanics of zeroth harmonics of all scalar fields F = D, φ, Q with equations ∂ 2 τ F = 0 and the initial data defined so that the mechanism of spontaneous electroweak symmetry breaking does not differ from the accepted one in SM. Recall, that the accepted spontaneous symmetry breaking mechanism is based on the Coleman-Weinberg potential equation dV( φ I )/d φ I = 0 in the perturbation theory restricted by the constraint ∂ τ φ = 0. In our perturbation theory (8), loop diagrams also lead to the effective potential with the same equation treated as a constraint that keeps the vacuum equation ∂ 2 τ φ = 0. Using as example this potential free model of the Empty Universe, one can see that the Standard Cosmology observable quantities are connected with the conformal ones by relation (2): This relation determines the scale factor conformal masses and time and the horizon H = H 0 a −2 . In this case, the dilaton solution of the motion equation In terms of the effective cosmological factor (10) and conformal time (11) this solution becomes  (11), and the constant CMB conformal temperature T CC = T SC a(z) = 2.725 K during the cosmological evolution process. The dilaton variables (2) and (3) explain redshift by the permanent increase of all masses in the Universe [9,10,11,12,13,14,16]. The corresponding does not contradict the recent SN data [17] analyzed in the framework of the Conformal Cosmology [9,11], where the redshift is explained by running masses (11), in the case of the conformal mechanics (8) leading to the rigid state dominance H 0 ≫ √ T d .
Calculation of the primordial helium abundance [10,28] takes into account weak interactions, the Boltzmann factor, (n/p) e △m/T ∼ 1/6, where △m is the neutron-proton mass difference, which is the same for both SC and CC, △m SC /T SC = △m CC /T CC = (1+z) −1 m 0 /T 0 , and the square root dependence of the z-factor on the measurable time-interval defined in Eqs. (11) and (13)  Quantization of the theory constructs a vacuum state with minimal energy defined as

IV. THE EARLY UNIVERSE AS FACTORY OF HIGGS PARTICLES
It was shown in Ref. [12] that the Empty Universe acts as a factory of longitudinal vector bosons and Higgs particles (h) distinguished by their direct interaction with the dilaton. In particular, the field equations for creation and annihilation operators take the form The third term leads to collisions and the Boltzmann-type distribution [22] Here the conformal boson temperature T F ∼ T 0 is determined by the collision integral Creation of these primordial particles started at the moment a W I when their wavelengths coincided with the horizon length M −1 as it follows from the uncertainty principle. This gives the instance of creation of primordial particles, in particular, W -bosons The conformal photon temperature value T γ = T γ (z)a(z) = T γ (0) can be estimated from the kinetic equation (15). If n( T F ) ∼ T 3 γ , one can see that this temperature value 3K is astonishingly close to the observed temperature T 0 = 2.725 K of the cosmic microwave background radiation. The latter can be treated as the final decay product of the primordial bosons that inherits their temperature.
The problem is to obtain parameters of the diffusion reaction system arising in this case from the Standard Model computing the relevant cross sections and decay rates.
The present-day data of photon density inherits the primordial vector boson density, Ω rad ≃ M 2 W 0 · a −2 W I = 10 −34 10 29 ∼ 10 −5 [12]. In the same way intensive creation of vector bosons in the Early Universe leads to CP nonconservation [12] due to the ABJ anomaly and the CKM-mixing in the fermion-W -boson interaction. So that the cosmological evolution and this non-conservation freezes the fermion number. This leads to the baryon-number density n b = n γ X CP , where the factor X CP ∼ 10 −9 is determined by the superweak interaction of d and s quarks, which is responsible for CP violation experimentally observed in K-meson decays [24] (see Appendix C).
The present-day baryon density Ω b ≃ 2α W ≃ 0.06 is calculated by the evolution of the baryon density from the early stage, when it was directly related to the photon density.

V. THE CMB TEMPERATURE ANISOTROPY
The collision integral equation (15) generalized to anisotropic decays T 0 → T 0 + △T , σ → σ + σ γγ gives us the formula |△T /T 0 | ≃ (2/3)|σ γγ /σ| and a possibility to estimate the magnitude of the CMB anisotropy. Its observational value about 10 −5 ∼ α 2 [19] testifies to the dominance of the two photon processes. Therefore, the CMB anisotropy revealed in the region of the three peaks ℓ 1 ≃ 220, ℓ 2 ≃ 546, and ℓ 3 ≃ 800 can reflect parameters of the primordial bosons and their decay processes, in particular h → γγ, W + W − → γγ, and ZZ → γγ. The values of multipole momenta at the peaks can be obtained by a simple dimensional analysis using the accepted formula [25] where d P d = a 2 P d H −1 0 = a −1 P d d P d is the conformal horizon (15) at the instances of the processes (P ) h → γγ, W + W − → γγ, and ZZ → γγ marked by the corresponding cosmological scale factor a P d , and M P d = M P 0 a P d is the conformal mass of emitters in the given process.
One can see that the more horizon-length the more number of emitters covered by the horizon, and the more values of multipole momenta. The substitutions of d P d = a 2 P d H −1 0 and M P d = M P 0 a P d into the Eq. (19) give us the multipole momenta where the initial data M P 0 /H 0 = 1/a 3 P I given by Eq. (16) is taken into account, and ℓ hd = ℓ 1 , ℓ W d = ℓ 2 , ℓ Zd = ℓ 3 .
Identifying all photon energies in these processes with the mean photon one k eff in the CMB, multiplied by the corresponding z-factor a P d /a P I , we can obtain the Gamov-type relation for the spectrum of photon energy E P γ = M P 0 = m h0 /2, M W 0 , M Z0 in the processes h → γγ, W + W − → γγ, and ZZ → γγ, respectively, with the peaks in the CMB spectrum where k eff ≃ 9.8GeV is defined by the boson masses: ℓ The value of Higgs particle mass is estimated as if one takes into account that in the process h → 2γ the photon energy is the half of the Higgs boson mass. This value of the Higgs boson mass is close to the present fit of the LEP experimental data supporting rather low values just above the experimental limit m h > 114.4 GeV [29]. The variation of action (6) with respect to the lapse function N d leads to the energy is the local energy density as the sum of energy densities T J = T J + T J in terms of conformal fields (2) and determines the diffeo-invariant lapse function and the diffeo-invariant interval dτ = N 0 dx 0 through the energy density (A. 2) The dilaton field D = D + D is defined by equation where The Hamiltonian approach to the theory (6) was considered in [13] in the Dirac gauge [20] P D = 0, ∂ k e k (b) = 0.

Appendix B: The Newton law status in cosmological perturbation theory
The investigation of the large-scale structure in the Early Universe is one of the highlights of the present-day Cosmology with far-reaching implications. In particular, the comparison of the cosmological perturbation theory in the ΛCDM model with the Hamiltonian approach to the same cosmological perturbation theory [13] reveals essential differences of these approaches and their physical consequences.
In order to demonstrate these consequences, we consider the case of integrable diffeoinvariant spacial coordinates, when the simplex components in interval (b) = dx (b) are total differentials. The latter means that the coefficients of the spin-connection = 0 together with the three-dimensional curvature R (3) = 0 in accord with observational data [19]. In this case, the transverse components of the shift vector can be defined by constant, take forms [13,14] e −D/2 = 1 + 1 2 where D (±) (x, y) are the Green functions satisfying the equations are the local currents.
In the case of point mass distribution in a finite volume V 0 with the zeroth pressure and the density whereF µν = −iF a µν g W τ a /2 is the strength of the vector fields, F a µν = ∂ µ A a ν −∂ ν A a µ +gǫ abc A b µ A c ν . Taking the integral of the equality in (C.1) with respect to conformal time and the threedimensional variable x, we can find a relation between the change of the fermion number F (i) = d 3 xj Specifically, we have where η L is the W-boson lifetime, and N W is the contribution of the primordial W boson. The integral over the conformal spacetime bounded by three-dimensional hypersurfaces η = 0 and η = η L is given by ) sin(2θ(η L )) is the Bogoliubov condensate [12] that is specified by relevant solutions to the Bogoliubov equations. Upon a numerical calculation of this integral, we can estimate the expectation value of the Chern-Simons functional in the state of primordial bosons.
At the vector-boson-lifetime value in (18), this yields the following result at n γ = 2, 402 × T 3 /π 2 where n γ is the number density of photons forming Cosmic Microwave Background radiation.
On this basis, the violation of the fermion-number density in the cosmological model being considered can be estimated as [9,12] ∆F (i) /V 0 = N CS /V 0 = 0.8n γ .
According to SM, there is the CKM-mixing that leads to CP nonconservation, so that the cosmological evolution and this nonconservation freeze the fermion number at η = η L .
This leads to the baryon-number density [24,26] where the factor X CP is determined by the superweak interaction of d and s quarks, which is responsible for CP violation experimentally observed in K-meson decays [27].
From the ratio of the number of baryons to the number of photons, one can deduce an estimate of the superweak-interaction coupling constant: X CP ∼ 10 −9 . Thus, the evolution of the Universe, primary vector bosons, and the aforementioned superweak interaction [27] lead to baryon-antibaryon asymmetry of the Universe n b (η L ) n γ (η L ) ≃ X CP = 10 −9 . (C.6) Thus, the primordial bosons before their decays polarize the Dirac fermion vacuum and give the baryon asymmetry frozen by the CP -violation so that for billion photons there is only one baryon.
The problem is to show that the Universe matter content considered as the final decay product of primordial bosons is in agreement with observational data [12].