The Starobinsky model predicts a primordial inflation period without the presence of an inflaton field. The modified version of this model predicts a simple time dependence for the Hubble parameter H(t), which decreases slowly between the Planck epoch and the end of the inflation, H(t) = M Pl -betaM²Pl t, where beta is a dimensionless constant to be adjusted from observations. We investigate an inflaton model which has the same time dependence for H(t). A reverse engineered inflaton potential for the time dependence of H is derived. Normalization of the derived inflaton potential is determined by the condition that the observed density fluctuations, <FONT FACE=Symbol>dr</FONT>/<FONT FACE=Symbol>r »</FONT> 10-5, are created at ~ 60 e-folds before the end of inflation. The derived potential indicates an energy (mass) scale, Mend ~ 10(13) GeV, at the end of inflation. Using the slow roll parameters, which are obtained from this potential, we calculate the spectral index for the scalar modes nS and the relative amplitude of the tensor to scalar modes r. A tensor contribution, r ~ 0.13, and an approximately Harrison-Zeldovich density perturbation spectrum, nS ~ 0.95, are predicted.

We investigate models that suggest that the vacuum energy could decay into cold dark matter (CDM) or into a homogeneous distribution of thermalized cosmic microwave background (CMB) photons. We show that the agreement of the density fluctuation spectra obtained from the CMB and galaxy distribution data puts strong limits on the rate of vacuum energy decay. A vacuum energy decaying into CDM increases the density of the CDM rho, diluting the CDM density fluctuations (<FONT FACE=Symbol>dr</FONT>/rho)². The temperature fluctuations of the CMB photons (deltaT/T)² are approximately proportional to (<FONT FACE=Symbol>dr</FONT>/rho)², at the recombination epoch. We define F as the predicted increase of (<FONT FACE=Symbol>dr</FONT>/rho)² (or (deltaT/T)²) at the recombination epoch. Since the present observed (<FONT FACE=Symbol>dr</FONT>/rho)² derived from the CMB and galaxy distribution data agree to ~ 10%, the maximum value for F is Fmax <FONT FACE=Symbol>@</FONT> 1.1. Our results indicate that the rate of decay of the vacuum energy into CDM or CMB photons is extremely small.

Large scale magnetic fields in galaxies are thought to be generated, by a mean field dynamo. In order to have generated the fields observed, the dynamo would have had to have operated for a sufficiently long period of time. However, magnetic fields of similar intensities to the one in our galaxy, are observed in high redshift galaxies, where a mean field dynamo would not have had time to produce the observed fields. MHD turbulence produces small scale magnetic fields at a faster rate than it does mean fields, which can diffuse toward larger scales. If the turbulence is helical, magnetic fields generated at small scales can become correlated over large scales. We study the evolution of magnetic field correlations in the first objects formed in the universe, due to the action of a turbulent, helical, stochastic dynamo, for redshifts 5 < z < 10. Ambipolar diffusion can play a significant role in this process due to the low level of ionization of the gas in the first objects. We show that for reasonable values of the parameters that characterize the turbulent plasma in the time interval considered, fields can grow to high intensities (~ muG), with large coherence lengths (~ 2 - 6 kpc).

We treat here the problem of dark matter in galaxies. Recent articles seem to imply that we are entering into the precision era of cosmology, implying that all of the basic physics of cosmology is known. However, we show here that recent observations question the pillar of the standard model: the presence of nonbaryonic "dark matter" in galaxies. Using Newton's law of gravitation, observations indicate that most of the matter in galaxies is invisible or dark. From the observed abundances of light elements, dark matter in galaxies must be primarily nonbaryonic. The standard model and its problems in explaining nonbaryonic dark matter will first be discussed. This will be followed by a discussion of a modification of Newton's law of gravitation to explain dark matter in galaxies.