The morphology and strength of the primordial magnetic field which is generated spontaneously in the early universe are studied for three models: (1) inflation (2) primordial magnetized bubble and (3) primordial turbulence models, We calculate the power spectra of magnetic field that are scale-free and proportional to k1.5,k3~4 and k2/3, respectively. The configurations of magnetic field having these power spectra are visualized. To constrain the present strength of the primordial magnetic field we calculate the anisotropy of the microwave background radiation in Bianchi type I universe with globally homogeneous magnetic field. From the COBE limit of the quadrupole moment of (δT/T)l=2 the present strength of horizen-scale magnetic fields Bp is constrained to be less than 9 × 10-8G.

The power spectrum of the galaxy distribution is accurately measured up to wavelengths over 100h−1 100h−1 Mpc from the CfA 1 and 2 catalogs. We find that our results agree with power spectra calculated by others from smaller samples of optical, radio and infrared galaxies. The power spectrum of an open CDM model (Ωh Ωh = 0.2 and δ8 δ8 = 1; see below for definitions) best approximates the observed power spectrum. The power spectrum of the standard COM model (Ωh Ωh = 0.5 and δ8 δ8 = 1) is inconsistent with the observed one at the 99% confidence level. Our best estimation of the corresponding correlation function in real space is ξ(r)=(r/6.2h−1Mpc)−1.8 ξ(r)=(r/6.2h−1Mpc)−1.8 for r < 20h−1 20h−1 Mpc.