In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [Phys. Rev. D 67, 081301 (2003)] and Koh and Brandenberger [J. Cosmol. Astropart Phys. 06 (2007) 21] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

I discuss some of the most outstanding challenges in relativistic astrophysics in the subjects of compact objects (black holes and neutron stars), dark sector (dark matter and dark energy), plasma astrophysics (origin of jets, cosmic rays, and magnetic fields), and the primordial universe (physics at the beginning of the Universe). In these four subjects, I discuss 12 of the most important challenges. These challenges give us insight into new physics that can only be studied in the large scale universe. The near-future possibilities, in observations and theory, for addressing these challenges are also discussed.

Non-commutative geometry indicates a deformation of the energy–momentum dispersion relation for massless particles. This distorted energy–momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007)021 and JCAP11(2007)013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the α family of curves f(E) = 1 + (λE)α. We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of . We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

The origin of magnetic fields in astrophysical objects is a challenging problem in astrophysics. Throughout the years, many scientists have suggested that non-minimal gravitational-electromagnetic coupling (NMGEC) could be the origin of the ubiquitous astrophysical magnetic fields. We investigate the possible origin of intense magnetic fields $\sim 10^{15}-10^{16}$ by NMGEC near rotating neutron stars and black holes, connected with magnetars, quasars, and gamma-ray bursts. Whereas these intense magnetic fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC.

Some observations of galaxies, and in particular dwarf galaxies, indicate a presence of cored density profiles in apparent contradiction with cusp profiles predicted by dark matter N-body simulations. We constructed an analytical model, using particle distribution functions (DFs), to show how a supernova (SN) explosion can transform a cusp density profile in a small-mass dark matter halo into a cored one. Considering the fact that an SN efficiently removes matter from the centre of the first haloes, we study the effect of mass removal through an SN perturbation in the DFs. We find that the transformation from a cusp into a cored profile occurs even for changes as small as 0.5 per cent of the total energy of the halo, which can be produced by the expulsion of matter caused by a single SN explosion.

We recently predicted the existence of random primordial magnetic fields (RPMFs) in the form of randomly oriented cells with dipole-like structure with a cell size L-0 and an average magnetic field B-0. Here, we investigate models for primordial magnetic field with a similar web-like structure, and other geometries, differing perhaps in L-0 and B-0. The effect of RPMF on the formation of the first galaxies is investigated. The filtering mass, M-F, is the halo mass below which baryon accretion is severely depressed. We show that these RPMF could influence the formation of galaxies by altering the filtering mass and the baryon gas fraction of a halo, f(g). The effect is particularly strong in small galaxies. We find, for example, for a comoving B-0 = 0.1 mu G, and a reionization epoch that starts at z(s) = 11 and ends at z(e) = 8, for L-0 = 100 pc at z = 12, the f(g) becomes severely depressed for M < 10(7) M-circle dot, whereas for B-0 = 0 the f(g) becomes severely depressed only for much smaller masses, M < 10(5) M-circle dot. We suggest that the observation of M-F and f(g) at high redshifts can give information on the intensity and structure of primordial magnetic fields.

Various authors have suggested that the gamma-ray burst (GRB) central engine is a rapidly rotating, strongly magnetized, ( ∼ 1015–1016 G) compact object. The strong magnetic field can accelerate and collimate the relativistic flow and the rotation of the compact object can be the energy source of the GRB. The major problem in this scenario is the difficulty of finding an astrophysical mechanism for obtaining such intense fields. Whereas, in principle, a neutron star could maintain such strong fields, it is difficult to justify a scenario for their creation. If the compact object is a black hole, the problem is more difficult since, according to general relativity it has ``no hair" (i.e., no magnetic field). Schuster, Blackett, Pauli, and others have suggested that a rotating neutral body can create a magnetic field by non-minimal gravitational-electromagnetic coupling (NMGEC). The Schuster-Blackett form of NMGEC was obtained from the Mikhail and Wanas's tetrad theory of gravitation (MW). We call the general theory NMGEC-MW. We investigate here the possible origin of the intense magnetic fields ∼ 1015–1016 G in GRBs by NMGEC-MW. Whereas these fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC-MW. It not only explains the origin of the ∼ 1015–1016 G fields when the compact object is a neutron star, but also when it is a black hole.

Various authors have suggested that the gamma-ray burst (GRB) central engine is a rapidly rotating, strongly magnetized, (similar to 10(15)-10(16) G) compact object. The strong magnetic field can accelerate and collimate the relativistic flow and the rotation of the compact object can be the energy source of the GRB. The major problem in this scenario is the difficulty of finding an astrophysical mechanism for obtaining such intense fields. Whereas, in principle, a neutron star could maintain such strong fields, it is difficult to justify a scenario for their creation. If the compact object is a black hole, the problem is more difficult since, according to general relativity it has "no hair" (i.e., no magnetic field). Schuster, Blackett, Pauli, and others have suggested that a rotating neutral body can create a magnetic field by non-minimal gravitational-electromagnetic coupling (NMGEC). The Schuster-Blackett form of NMGEC was obtained from the Mikhail and Wanas's tetrad theory of gravitation (MW). We call the general theory NMGEC-MW. We investigate here the possible origin of the intense magnetic fields similar to 10(15)-10(16) G in GRBs by NMGEC-MW. Whereas these fields are difficult to explain astrophysically, we find that they are easily explained by NMGEC-MW. It not only explains the origin of the similar to 10(15)-10(16) G fields when the compact object is a neutron star, but also when it is a black hole.

It is generally assumed that the magnetic fields of millisecond pulsars (MSPs) are ∼108 G. We argue that this may not be true and the fields may be appreciably greater. We present six evidences for this: (1) The ∼108G field estimate is based on magnetic dipole emission losses which is shown to be questionable; (2) The MSPs in low mass X-ray binaries (LMXBs) are claimed to have <1011 G on the basis of a Rayleygh-Taylor instability accretion argument. We show that the accretion argument is questionable and the upper limit 1011 G may be much higher; (3) Low magnetic field neutron stars have difficulty being produced in LMXBs; (4) MSPs may still be accreting indicating a much higher magnetic field; (5) The data that predict ∼108 G for MSPs also predict ages on the order of, and greater than, ten billion years, which is much greater than normal pulsars. If the predicted ages are wrong, most likely the predicted ∼108 G fields of MSPs are wrong; (6) When magnetic fields are measured directly with cyclotron lines in X-ray binaries, fields ≫108 G are indicated. Other scenarios should be investigated. One such scenario is the following. Over 85% of MSPs are confirmed members of a binary. It is possible that all MSPs are in large separation binaries having magnetic fields >108 G with their magnetic dipole emission being balanced by low level accretion from their companions.

We investigate the impact of the existence of a primordial magnetic field on the filter mass, characterizing the minimum baryonic mass that can form in dark matter (DM) haloes. For masses below the filter mass, the baryon content of DM haloes are severely depressed. The filter mass is the mass when the baryon to DM mass ratio in a halo is equal to half the baryon to DM ratio of the Universe. The filter mass has previously been used in semi-analytic calculations of galaxy formation, without taking into account the possible existence of a primordial magnetic field. We examine here its effect on the filter mass. For homogeneous comoving primordial magnetic fields of B 0 ∼ 1 or 2 nG and a re-ionization epoch that starts at a redshift z s = 11 and is completed at z r = 8, the filter mass is increased at redshift 8, for example, by factors of 4.1 and 19.8, respectively. The dependence of the filter mass on the parameters describing the re-ionization epoch is investigated. Our results are particularly important for the formation of low-mass galaxies in the presence of a homogeneous primordial magnetic field. For example, for B 0 ∼ 1 nG and a re-ionization epoch of z s ∼ 11 and z r ∼ 7, our results indicate that galaxies of total mass M ∼ 5 x 10 8 M ⊙ need to form at redshifts z F ≳ 2.0, and galaxies of total mass M ∼ 10 8 M ⊙ at redshifts z F ≳ 7.7.

A smooth inflaton potential is generally assumed when calculating the primordial power spectrum, implicitly assuming that a very small oscillation in the inflaton potential creates a negligible change in the predicted halo mass function. We show that this is not true. We find that a small oscillating perturbation in the inflaton potential in the slow-roll regime can alter significantly the predicted number of small halos. A class of models derived from supergravity theories gives rise to inflaton potentials with a large number of steps and many trans-Planckian effects may generate oscillations in the primordial power spectrum. The potentials we study are the simple quadratic (chaotic inflation) potential with superimposed small oscillations for small field values. Without leaving the slow-roll regime, we find that for a wide choice of parameters, the predicted number of halos change appreciably. For the oscillations beginning in the 10(7)-10(8) M-circle dot range, for example, we find that only a 5% change in the amplitude of the chaotic potential causes a 50% suppression of the number of halos for masses between 10(7)-10(8) M-circle dot and an increase in the number of halos for masses <10(6) M-circle dot by factors similar to 15-50. We suggest that this might be a solution to the problem of the lack of observed dwarf galaxies in the range 10(7)-10(8) M-circle dot. This might also be a solution to the reionization problem where a very large number of Population III stars in low mass halos are required.

We have investigated the matter density fluctuations, δM(a), in the running ΛCDM and ΛXCDM models. The latter was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the “cosmon” X, which interacts with a running Λ, but not with matter. Adopting a dark energy (DE) “picture”, in which the total DE and matter components are conserved separately, the growth of density fluctuations = δM(a)/a can be written in terms of the effective equation of state. We made use of the measured galaxy fluctuation power spectrum, PGG, and of the linear bias parameter b2(z = 0) = PGG/PMM, where PMM ∝ δM2 is the matter power spectrum of the model under consideration. According to the 2dFGRS survey, bΛ2(z 0) = 1 within a 10% accuracy for the ΛCDM model. We adopted this limit to put constraints on the fundamental parameter, ν, of the running ΛCDM model. We found an agreement with previous estimates obtained by a number of different methods and authors. This provided a good test of the procedure, which we used then to determine the physical region of the ΛXCDM parameter space.

We have investigated the matter density fluctuations, delta(M)(a), in the running Lambda CDM and Lambda XCDM models. The latter was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the "cosmon" X, which interacts with a running Lambda, but not with matter. Adopting a dark energy (DE) "picture", in which the total DE and matter components are conserved separately, the growth of density fluctuations G(a) = delta(M)(a)/a can be written in terms of the effective equation of state. We made use of the measured galaxy fluctuation power spectrum, P-GG, and of the linear bias parameter b(2)(z = 0) = P-GG/P-MM, where P-MM proportional to delta(2)(M) is the matter power spectrum of the model under consideration. According to the 2dFGRS survey, b(Lambda)(2) (z similar or equal to 0) = 1 within a 10% accuracy for the Lambda CDM model. We adopted this limit to put constraints on the fundamental parameter, nu, of the running Lambda CDM model. We found an agreement with previous estimates obtained by a number of different methods and authors. This provided a good test of the procedure, which we used then to determine the physical region of the Lambda XCDM parameter space.

Here we present a status report of the first spherical antenna project equipped with a set of parametric transducers for gravitational detection. The Mario Schenberg, as it is called, started its commissioning phase at the Physics Institute of the University of São Paulo, in September 2006, under the full support of FAPESP. We have been testing the three preliminary parametric transducer systems in order to prepare the detector for the next cryogenic run, when it will be calibrated. We are also developing sapphire oscillators that will replace the current ones thereby providing better performance. We also plan to install eight transducers in the near future, six of which are of the two-mode type and arranged according to the truncated icosahedron configuration. The other two, which will be placed close to the sphere equator, will be mechanically non-resonant. In doing so, we want to verify that if the Schenberg antenna can become a wideband gravitational wave detector through the use of an ultra-high sensitivity non-resonant transducer constructed using the recent achievements of nanotechnology.

Magnetic fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large-scale fields similar to mu G, observed in galaxies at both high and low redshifts by Faraday rotation measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion of smaller regions. Magnetic fields (MFs) similar to 10 mu G over a comoving similar to 1 pc region are predicted at redshift z similar to 10. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average MFs similar to 10(-2) mu G, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift z similar to 10. In the collapse to a galaxy (comoving size similar to 30 kpc) at z similar to 10, the fields are amplified to similar to 10 mu G. This indicates that the MFs created immediately after the QHPT (10(-4) s), predicted by the fluctuation-dissipation theorem, could be the origin of the similar to mu G fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultrahigh energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe.

(Abridged) Tests that have been proposed to differentiate among dark energy (DE) models are based on observations of galaxies at high redshift (z>0), to be obtained in the future. We suggest here a new test that is valid at z≃0. It is based on existing observational data, numerical simulations, and three well known analytic models that evaluate the bias parameter b, the ratio of galaxy to dark matter (DM) fluctuations. These analytic models are based on the physical processes involved in the formation of stars and in the formation and merging of galaxies. The value of b(z) obtained in each model is a function of the DM growth factor D(z), which, in turn, is a function of the DE. We show that the equations for b in all three analytic models can be reduced to the form of a known constant plus the term E[D(z=0)/D(z)]^α, where α=1 or 2 and E is a free parameter. Using the value of b obtained by the 2dFGRS consortium for the model, to normalize E, we find that all three analytic models predict b^2(0)=1±0.1 for all DE models. Numerical simulations that evaluated b^2(0) for the and CDM (Λ=0) models also obtained b^2(0)=1±0.1. Since this value of b^2(0) is indicated by numerical simulations as well as by all three popular analytic models, which are normalized by the 2dFGRS consortium result for the model, we suggest the condition that b^2(0)=1±0.1 at z=0 as a new test for the viability of dark energy models. Thus, for a given observed galaxy fluctuation spectrum such as that of the 2dFGRS consortium, if the DM fluctuations are greater or less than the galaxy fluctuations by more than 10 be discarded.

We investigate the matter density fluctuations delta(rho M)/rho(M) for two dark energy (DE) models in the literature in which the cosmological term. is a running parameter. In the first model, the running Lambda CDM model, matter and DE exchange energy, whereas in the second model, the Lambda XCDM model, the total DE and matter components are conserved separately. The Lambda XCDM model was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the 'cosmon' X, which interacts with the running., but not with matter. In our analysis we make use of the current value of the linear bias parameter, b(2)(0) = P-GG/P-MM, where P-MM proportional to (delta(rho M)/rho(M))(2) is the present matter power spectrum and P-GG is the galaxy fluctuation power spectrum. The former can be computed within a given model, and the latter is found from the observed LSS data (at small z) obtained by the 2dF Galaxy Redshift Survey. It is found that b(Lambda)(2)(z similar or equal to 0) = 1 within a 10% accuracy for the standard Lambda CDM model. Adopting this limit for any DE model and using a method based on the effective equation of state for the DE, we can set a limit on the growth of matter density perturbations for the running Lambda CDM model, the solution of which is known. This provides a good test of the procedure, which we then apply to the Lambda XCDM model in order to determine the physical region of parameter space, compatible with the LSS data. In this region, the Lambda XCDM model is consistent with known observations and provides at the same time a viable solution to the cosmic coincidence problem.

Fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large scale fields ∼ μG, observed in galaxies at both high and low redshifts by Faraday Rotation Measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion (polymerization) of smaller regions. Magnetic fields (MFs) ∼ 10μG over a comoving ∼ 1 pc region are predicted at redshift z ∼ 10. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average magnetic fields (MFs) ∼ 10 μG, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift z ∼ 10. In the collapse to a galaxy (comoving size ∼ 30 kpc) at z ∼ 10, the fields are amplified to ∼ 10μG. This indicates that the MFs created immediately after the QHPT, predicted by the Fluctuation-Dissipation Theorem, could be the origin of the ∼ μG fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultra-high energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe. Subject headings: Cosmology: Early Universe, Magnetic Fields, Plasmas E-mails: Rafael@astro.iag.usp.br, Opher@astro.iag.usp.br