The possibility to avoid the cosmic initial singularity as a consequence of nonlinear effects on the Maxwell eletromagnetic theory is discussed. For a flat FRW geometry we derive the general nonsingular solution supported by a magnetic field plus a cosmic fluid and a nonvanishing vacuum energy density.The nonsingular behavior of solutions with a time-dependent Λ(t)-term are also examined. As a general result, it is found that the functional dependence of Λ(t) can uniquely be determined only if the magnetic field remains constant.All these models are examples of bouncing universes which may exhibit an inflationary dynamics driven by the nonlinear corrections of the magnetic field.

Graviton production in flat three-space Robertson-Walker universes is studied. An arbitrary sequence of stages governed by scale factors exhibiting exponential or power-law behavior is considered. By the derivation of exact expressions for the Bogolubov coefficients associated with the several transitions between different cosmic eras, a general method to obtain the power spectrum and energy density of the relic gravitational waves is described. The results are applied for a simple three-stage model involving both an inflationary and noninflationary initial phase. Exact and explicit formulas for the spectrum and time evolution of the energy density parameter 0, are found. From considerations involving the production of primordial 'He it is shown how the maximum allowed value for 0, relates to the baryon to photon ratio, the neutron mean life, and the number of light neutrinos. It is found that the energy density associated with the relic gravitons cannot exceed 6% of that associated with photons at the time of nucleosynthesis. From this limit, constraints on some parameters of the early Universe are derived. Independent constraints are obtained by assuming that gravitons do not dominate the cosmic dynamics today.PACS number(s1: 04.30. +x, 98.80.Cq 0556-282

The gravitational wave equation for a spatially flat Friedmann-Robertson-Walker universe is derived in the context of scalar-tensor theories of gravity, which have the Brans-Dicke theory as a particular case. This equation is solved for several cosmological scenarios, including the expansions governed by the Nariai as well as the Gurevich-Finkelstein-Ruban solutions of Brans-Dicke theory and for a new set of exact solutions of other scalar-tensor theories. The amplification of gravitational waves is studied in comparison to what happens in the general relativistic case. It is shown how the coupling with the scalar field changes the scales defining very large and very small wave numbers, and consequently the value of the amplification coefficient. It is found that very small values for the coupling parameter could lead to amplification of subhorizon waves. The creation of the corresponding high-frequency gravitons is explained as a response to the rapid time variation of the gravitational "constant," which can occur near the singularity in some models. It is also shown that there could be amplification of waves even in a radiation-dominated universe in some cases, because the wave equation is not conformally invariant, except for the case of Nariai's solution in the Brans-Dicke theory. PACS numberis): 04.30.+x, 04.50.+h, 12.10.Gq, 98.80.H~

The inequivalence of vacua at different instants of time leads to the production of tensor perturbations ͑''gravitational waves''͒ in scales larger than the Hubble radius. During noninflationary periods of expansion, the very long tensor perturbations become effective gravitational waves as they enter the Hubble length, thus adding new contributions to the energy density associated with the subhorizon waves g . It is shown that this phenomenom can be described as a process of production of effective gravitons by using the macroscopic formalism to matter creation based on the thermodynamics of open systems. A creation pressure term is introduced in the continuity equation obeyed by g in order to deal with this process. This allows the derivation of a dynamical equation for the scale factor a(t) that takes into account the effective gravitons back reaction. This equation is numerically solved for a model in which the universe suffers a transition from an arbitrary initial phase to a radiation-dominated period. If the barotropic index of the equation of state in the first epoch is close to 2/3, the back reaction of the effective gravitational waves makes a(t) deviate noticeably from the standard behavior a(t)ϰt 1/2 . The same phenomenom may happen during the matter-dominated era, which could affect theoretical calculations involving the age of the universe. ͓S0556-2821͑97͒07222-6͔ PACS number͑s͒: 04.30.Db, 04.62.ϩv, 95.30.Tg PHYSICAL REVIEW D

The thermodynamics of cosmological matter creation has been extensively investigated in the literature. In the context of general relativity, the particle production in the cosmological models is due to mechanisms such as an imperfect fluid with bulk viscosity or the decaying vacuum. Another interesting proposal is matter creation in cosmologies with variation of fundamental constants. In this work, we study the nonlinearity of the electrodynamics as a source of matter creation in cosmological models with flat Friedmann–Robertson–Walker (FRW) line geometry. We write the energy conservation law arising from Einstein field equations with cosmological term Λ, solve the field equations, and study how particles are created as the magnetic field B changes with cosmic epoch. We obtain solutions for the adiabatic particle creation rate, the total number of particles, and the scale factor as a function of time in three cases: Λ = 0, Λ = constant and Λ ∝ H2 (cosmological term proportional to the Hubble parameter). We find the constraints imposed by the second law of thermodynamics upon the cosmological solutions.