The simplest gauge invariant models of inflationary magnetogenesis are known to suffer from the problems of either large backreaction or strong coupling, which make it difficult to self-consistently achieve cosmic magnetic fields from inflation with a field strength larger than 10−32G today on the Mpc scale. Such a strength is insufficient to act as seed for the galactic dynamo effect, which requires a magnetic field larger than 10−20G. In this paper we analyze simple extensions of the minimal model, which avoid both the strong coupling and back reaction problems, in order to generate sufficiently large magnetic fields on the Mpc scale today. First we study the possibility that the coupling function which breaks the conformal invariance of electromagnetism is non-monotonic with sharp features. Subsequently, we consider the effect of lowering the energy scale of inflation jointly with a scenario of prolonged reheating where the universe is dominated by a stiff fluid for a short period after inflation. In the latter case, a systematic study shows upper bounds for the magnetic field strength today on the Mpc scale of 10−13G for low scale inflation and 10−25G for high scale inflation, thus improving on the previous result by 7-19 orders of magnitude. These results are consistent with the strong coupling and backreaction constraints.

We study the dynamics of a homogeneous and isotropic Friedmann-Robertson-Walker universe in the context of the Eddington-inspired Born-Infeld theory of gravity. We generalize earlier results, obtained in the context of a radiation dominated universe, to account for the evolution of a universe permeated by a perfect fluid with an arbitrary equation of state parameter w. We show that a bounce may occur for $\kappa${}>0, if w is time dependent, and we demonstrate that it is free from tensor singularities. We argue that Eddington-inspired Born-Infeld cosmologies may be a viable alternative to the inflationary paradigm as a solution to fundamental problems of the standard cosmological model.

We consider the presence of an axion like particle, σ, with a generic CP violating axial coupling of the form (ασ/f) \( F\tilde{F} \) , where F _μν is the gauge field strength of a generic abelian U(1) gauge group, not necessarily associated with the standard electromagnetism, and f is the decay constant of the axion. It has previously been demonstrated that if the axion is identified with the inflaton, such an interaction can lead to measurable cosmological signatures (non-Gaussian modifications of the curvature perturbation spectrum) depending on the parameter \( \xi = \alpha \overset{\cdot }{\sigma }/(fH) \) . In the present paper we will show that the generation of curvature perturbation at horizon crossing due to the axial coupling has a universal form and remains unmodified in terms of the ξ parameter even if the axion, σ, is not identified with the inflaton. As a consequence, it does not appear to be possible to generate CMB tensor perturbations through this mechanism, larger than the vacuum ones, without violating the observational constraints unless we combine this mechanism with a curvaton or if the σ field becomes heavy and decays during inflation. Even in this last case there are non-trivial constraints coming from the slow-roll evolution of the curvature perturbation on super horizon scales which should be taken into account. We also comment on implications for inflationary models where axions play an important role as, for example, models of natural inflation where more than one axion are included and models where the curvaton is an axion.

We show that when the QCD axion is directly coupled to quarks with $c_i/f{\partial }_{\mu }a{\overline{q}}_i{\gamma }^{\mu }{\gamma }^5{q}_i$, such as in Dine-Fischler-Srednicki-Zhitnitsky models, the dominant production mechanism in the early Universe at temperatures $1\mathrm{GeV}\lesssim T\lesssim 100\mathrm{GeV}$ is obtained via $q_i{\overline{q}}_i\leftrightarrow ga$ and $q_{i}g\leftrightarrow q_{i}a$, where $g$ are gluons. The production of axions through such processes is maximal around $T\approx m_i$, where $m_i$ are the different heavy quark masses. This leads to a relic axion background that decouples at such temperatures, leaving a contribution to the effective number of relativistic degrees of freedom, which can be larger than the case of decoupling happens the electroweak phase transition, $\mathrm{\Delta }{N}_{\mathrm{eff}}\lesssim 0.027$. Our prediction for the $t$ quark is $0.027\le \mathrm{\Delta }{N}_{\mathrm{eff}}\le 0.036$ for $10^6\mathrm{GeV}\lesssim f/c_t\lesssim 4\times {10}^8\mathrm{GeV}$ and for the $b$ quark is $0.027\le \mathrm{\Delta }{N}_{\mathrm{eff}}\le 0.047$ for $10^7\mathrm{GeV}\lesssim f/c_b\lesssim 3\times {10}^8\mathrm{GeV}$. For the $c$ quark the window can only be roughly estimated as $0.027<\mathrm{\Delta }{N}_{\mathrm{eff}}\lesssim \mathcal{O}(0.1)$, for $f/c_c\lesssim (2-3)\times {10}^8\mathrm{GeV}$, since axions can still be partially produced in a regime of strong coupling, when ${\alpha }_s\gtrsim 1$. These contributions are comparable to the sensitivity of future CMB S4 experiments, thus opening an alternative window to detect the axion and to test the early Universe at such temperatures.