The degree scale feature in the CMB spectrum in the fractal universe

The position of the degree scale feature in the CMB spectrum is determined within the framework of the fractal universe with a power index of 2. The presence of any feature in the cosmic microwave background (CMB) anisotropy spectrum whose physical scale is known provides us with the ability to perform the angular diameter distance test [1]. Any feature progects as an anisotropy onto an angular scale associated with multipole leff = kd (1) where k is the size of the feature in k-space, d is the angular diameter distance to the feature. Anisotropy measurements on degree scales pin down the feature in the CMB spectrum. The position of the feature is leff = 263 [2], leff = 260 [3]. In the Friedmann universe, the degree scale feature is considered to arise due to acoustic oscillations in the photon-baryon fluid at last scattering. The feature represents the sound horizon when the universe recombines. The potential fluctuation ∆M/M is a relation of the scales. The mass M defines the scale of homogeneity. The mass ∆M defines the scale of fluctuations. The scale of homogeneity can be specified with the distance r covered by the CMB photon. The distance r gives the mass of radiation M restricted within r. Then the size of the potential fluctuation ∆r is defined via the value ∆M/M . The size of the potential fluctuation ∆r represents the feature in the CMB spectrum, with the value r being the distance to the feature. Determine the above feature in the CMB spectrum within the framework of the universe with the linear evolution law [4]. The model is based on the premise that the evolution of the universe is not defined by the matter but is a priori specified. The scale factor of the universe is a linear function of time a = ct. (2) The scale of mass is a linear function of the scale factor