Challenges of Relativistic Astrophysics

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 twelve 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.Comment: Plenary Talk and in the Proceedings of the 26th Texas Symposium on Relativistic Astrophysics, December 15-20, 201

Was The Electromagnetic Spectrum A Blackbody Spectrum In The Early Universe?

It is assumed, in general, that the electromagnetic spectrum in the Primordial Universe was a blackbody spectrum in vacuum. We derive the electromagnetic spectrum, based on the Fluctuation-Dissipation Theorem that describes the electromagnetic fluctuations in a plasma. Our description includes thermal and collisional effects in a plasma. The electromagnetic spectrum obtained differs from the blackbody spectrum in vacuum at low frequencies. In particular, concentrating on the primordial nucleosynthesis era, it has more energy for frequencies less than 3 to $6\omega_{pe}$, where $\omega_{pe}$ is the electron plasma frequency.Comment: 11 pages, RevTeX, 1 ps figure. To be published in Phys.Rev.Let

A new inflaton model beginning near the Planck epoch

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, $H(t)=M_{\rm Pl}-\beta M_{\rm Pl}^2 t$, 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, $\delta\rho/\rho\approx 10^{-5}$, are created at $\sim 60 e$-folds before the end of inflation. The derived potential indicates an energy (mass) scale, $M_{\rm end}\sim 10^{13} {\rm GeV}$, 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 $n_S$ and the relative amplitude of the tensor to scalar modes $r$. A tensor contribution, $r\simeq 0.13$, and an approximately Harrison-Zeldovich density perturbation spectrum, $n_S \simeq 0.95$, are predicted.Comment: 7 pages, minor changes, improved discussion. To appear in Braz.J.Phy

Dependence of the MHD shock thickness on the finite electrical conductivity

The results of MHD plane shock waves with infinite electrical conductivity are generalized for a plasma with a finite conductivity. We derive the adiabatic curves that describe the evolution of the shocked gas as well as the change in the entropy density. For a parallel shock (i.e., in which the magnetic field is parallel to the normal to the shock front) we find an expression for the shock thickness which is a function of the ambient magnetic field and of the finite electrical conductivity of the plasma. We give numerical estimates of the physical parameters for which the shock thickness is of the order of, or greater than, the mean free path of the plasma particles in a strongly magnetized plasma.Comment: 8 pages, uses standard revtex, to appear in Journal of Plasma Physic

The Heliocentric Distance Where the Deflections and Rotations of Solar Coronal Mass Ejections Occur

Understanding the trajectory of a coronal mass ejection (CME), including any deflection from a radial path, and the orientation of its magnetic field is essential for space weather predictions. Kay et al. (2015b) developed a model, Forecasting a CME's Altered Trajectory (ForeCAT), of CME deflections and rotation due to magnetic forces, not including the effects of reconnection. ForeCAT is able to reproduce the deflection of observed CMEs (Kay et al. 2015a). The deflecting CMEs tend to show a rapid increase of their angular momentum close to the Sun, followed by little to no increase at farther distances. Here we quantify the distance at which the CME deflection is "determined," which we define as the distance after which the background solar wind has negligible influence on the total deflection. We consider a wide range in CME masses and radial speeds and determine that the deflection and rotation of these CMEs can be well-described by assuming they propagate with constant angular momentum beyond 10 Rs. The assumption of constant angular momentum beyond 10 Rs yields underestimates of the total deflection at 1 AU of only 1% to 5% and underestimates of the rotation of 10%. Since the deflection from magnetic forces is determined by 10 Rs, non-magnetic forces must be responsible for any observed interplanetary deflections or rotations where the CME has increasing angular momentum.Comment: accepted in ApJ Letter

Seed Magnetic Fields Generated by Primordial Supernova Explosions

The origin of the magnetic field in galaxies is an open question in astrophysics. Several mechanisms have been proposed related, in general, with the generation of small seed fields amplified by a dynamo mechanism. In general, these mechanisms have difficulty in satisfying both the requirements of a sufficiently high strength for the magnetic field and the necessary large coherent scales. We show that the formation of dense and turbulent shells of matter, in the multiple explosion scenario of Miranda and Opher (1996, 1997) for the formation of the large-scale structures of the Universe, can naturally act as a seed for the generation of a magnetic field. During the collapse and explosion of Population III objects, a temperature gradient not parallel to a density gradient can naturally be established, producing a seed magnetic field through the Biermann battery mechanism. We show that seed magnetic fields $\sim 10^{-12}-10^{-14}G$ can be produced in this multiple explosion scenario on scales of the order of clusters of galaxies (with coherence length $L\sim 1.8Mpc$) and up to $\sim 4.5\times 10^{-10}G$ on scales of galaxies ($L\sim 100 kpc$).Comment: Accepted for publication in MNRAS, 5 pages (MN plain TeX macros v1.6 file). Also available at http://www.iagusp.usp.br/~oswaldo (click "OPTIONS" and then "ARTICLES"

Generalized Non-Commutative Inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation $f(E)\equiv\frac{E}{pc}(\neq 1)$ 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, Brandenberger and Magueijo (2003, 2005 and 2007). These authors studied a one-parameter family of non-relativistic dispersion relation that leads to inflation: the $\alpha$ family of curves $f(E)=1+(\lambda E)^{\alpha}$. 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 $SL(2,\mathbb{C})$. 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.Comment: Final version considerably improved; Non-commutative inflation rigorously mathematically formulate

A conceptual problem for non-commutative inflation and the new approach for non-relativistic inflationary equation of state

In a previous paper, we connected the phenomenological non-commutative inflation of Alexander, Brandenberger and Magueijo (2003) and Koh S and Brandenberger (2007) 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 non-commutative spaces) could lead to the equation of state of inflationary radiation. 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 is bounded from above) and the group structure of the representation which leads to the fundamental inflationary equations of state. We show that such a group structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like in scattering theory, for example. Therefore, it follows that the procedure to obtain those equations should be modified according to one of two possible proposals that we consider here. One of them relates to the general theory of Hopf algebras while the other is based on a representation theorem of Von Neumann algebras, a proposal already suggested by us to take into account interactions in the inflationary equation of state. This reopens the problem of finding inflationary deformed dispersion relations and all developments which followed the first paper of Non-commutative Inflation.Comment: Phys. Rev. D, 2013, in pres