Inconsistency of an inflationary sector coupled only to Einstein gravity

From a model-building perspective, the inflationary sector might very well have no direct couplings to other species, apart from inevitable gravitational interactions. Within the context of General Relativity, a thermal universe can still emerge after inflation if: $i)$ some radiation sector is excited towards the end of inflation, and $ii)$ the post-inflationary equation of state becomes sufficiently stiff $w \geq w_{\rm RD}\gtrsim 0.57$, with $w_{\rm RD}$ a threshold depending on the inflationary scale $H_*$ and the initial radiation-to-inflaton energy ratio $\Delta_*$. Furthermore, a stiff period in the expansion history enhances significantly the inflationary gravitational wave (GW) background, making this signal (potentially) observable by aLIGO, LISA and other experiments. The very same enhancement leads however to an inconsistency of the scenario: the energy of the GWs becomes too large compared to the rest of the radiation sector, violating standard BBN and CMB bounds on GW backgrounds. Except for very special scenarios where the initial radiation sector comprises hundreds of fields with couplings tuned to specific values, our result applies independently of $w$, $H_*$ and $\Delta_*$. This suggests that in order to reheat the universe, the inflationary sector should be coupled directly to other particle species. Alternatively the inflationary sector could be implemented in modified gravity theories.Comment: Comments added to match published version in JCAP, 22 pages (+ appendix + references), 4 figure

Ability of LIGO and LISA to probe the equation of state of the early Universe

The expansion history of the Universe between the end of inflation and the onset of radiation-domination (RD) is currently unknown. If the equation of state during this period is stiffer than that of radiation, $w > 1/3$, the gravitational wave (GW) background from inflation acquires a blue-tilt ${d\log\rho_{\rm GW}\over d\log f} = {2(w-1/3)\over (w+1/3)} > 0$ at frequencies $f \gg f_{\rm RD}$ corresponding to modes re-entering the horizon during the stiff-domination (SD), where $f_{\rm RD}$ is the frequency today of the horizon scale at the SD-to-RD transition. We characterized in detail the transfer function of the GW energy density spectrum, considering both 'instant' and smooth modelings of the SD-to-RD transition. The shape of the spectrum is controlled by $w$, $f_{\rm RD}$, and $H_{\rm inf}$ (the Hubble scale of inflation). We determined the parameter space compatible with a detection of this signal by LIGO and LISA, including possible changes in the number of relativistic degrees of freedom, and the presence of a tensor tilt. Consistency with upper bounds on stochastic GW backgrounds, however, rules out a significant fraction of the observable parameter space. We find that this renders the signal unobservable by Advanced LIGO, in all cases. The GW background remains detectable by LISA, though only in a small island of parameter space, corresponding to scenarios with an equation of state in the range $0.46 \lesssim w \lesssim 0.56$ and a high inflationary scale $H_{\rm inf} \gtrsim 10^{13}~{\rm GeV}$, but low reheating temperature $1~{\rm MeV} \lesssim T_{\rm RD} \lesssim 150~{\rm MeV}$ (equivalently, $10^{-11}~{\rm Hz} \lesssim f_{\rm RD} \lesssim 3.6\cdot10^{-9}~{\rm Hz}$). Implications for early Universe scenarios resting upon an SD epoch are briefly discussed.Comment: Matching published version in JCAP, 32 pages, 8 figure

A geometric construction of the exceptional Lie algebras F4 and E8

We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background. (There is no supergravity in the paper.)Comment: 12 page

The uses of Connes and Kreimer's algebraic formulation of renormalization theory

We show how, modulo the distinction between the antipode and the "twisted" or "renormalized" antipode, Connes and Kreimer's algebraic paradigm trivializes the proofs of equivalence of the (corrected) Dyson-Salam, Bogoliubov-Parasiuk-Hepp and Zimmermann procedures for renormalizing Feynman amplitudes. We discuss the outlook for a parallel simplification of computations in quantum field theory, stemming from the same algebraic approach.Comment: 15 pages, Latex. Minor changes, typos fixed, 2 references adde

Preparation of Cu-based bulk metallic glasses by suction casting

A series of Cu-Hf-Ti alloys prepared by rapid solidification of the melt and by copper mould casting were studied in the present work. Alloy ingots were prepared by arc-melting mixtures of pure metals in an argon atmosphere. An indication of the cooling rate obtained was determined using an Al-4.5 wt%Cu alloy. Cooling rates varied from 540 K/s for the centre section of a 4 mm die to 885 K/s for the outside wall section of the 2 mm die. The glass-forming ability, structure and thermal stability of Cu-Hf-Ti glassy alloys were studied by X-ray diffraction (XRD), differential scanning calorimetry (DSC) and differential thermal analysis (DTA). Bulk glass formation was observed for the Cu64Hf36, Cu55Hf25Ti20 and Cu56Hf25Ti19 alloys, with critical diameters dc for a fully glassy structure of 1, 4 and 5 mm, respectively. The substitution of Hf by Ti increased the glassforming ability (GFA) and the thermal stability

The geometry of null rotation identifications

The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, supersymmetric dilatonic waves and one possible resolution of its singularity in terms of nullbranes are also discussed.Comment: 1+18 pages, 5 figures. v2 references adde

The return of the four- and five-dimensional preons

We prove the existence of 3/4-BPS preons in four- and five-dimensional gauged supergravities by explicitly constructing them as smooth quotients of the AdS_4 and AdS_5 maximally supersymmetric backgrounds, respectively. This result illustrates how the spacetime topology resurrects a fraction of supersymmetry previously ruled out by the local analysis of the Killing spinor equations.Comment: 10 pages (a minor imprecision has been corrected

Sustainability Assessment of indicators for integrated water resources management

The scientific community strongly recommends the adoption of indicators for the evaluation and monitoring of progress towards sustainable development. Furthermore, international organizations consider that indicators are powerful decision-making tools. Nevertheless, the quality and reliability of the indicators depends on the application of adequate and appropriate criteria to assess them. The general objective of this study was to evaluate how indicators related to water use and management perform against a set of sustainability criteria. Our research identified 170 indicators related to water use and management. These indicators were assessed by an international panel of experts that evaluated whether they fulfil the four sustainability criteria: social, economic, environmental, and institutional. We employed an evaluation matrix that classified all indicators according to the DPSIR (Driving Forces, Pressures, States, Impacts and Responses) framework. A pilot study served to test and approve the research methodology before carrying out the full implementation. The findings of the study show that 24 indicators comply with the majority of the sustainability criteria; 59 indicators are bi-dimensional (meaning that they comply with two sustainability criteria); 86 are one-dimensional indicators (fulfilling just one of the four sustainability criteria) and one indicator do not fulfil any of the sustainability criteria.Postprint (author's final draft

Penrose limits of Lie Branes and a Nappi--Witten braneworld

Departing from the observation that the Penrose limit of AdS_3 x S^3 is a group contraction in the sense of Inonu and Wigner, we explore the relation between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a six-dimensional symmetric plane wave analogous to the four-dimensional Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy classes. We determine the (twisted and untwisted) symmetric D-branes in the plane wave background and we prove the existence of a space-filling D5-brane and, separately, of a foliation by D3-branes with the geometry of the Nappi--Witten spacetime which can be understood as the Penrose limit of the AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple criterion for a symmetric plane wave to be isometric to a lorentzian Lie group. In particular we observe that the maximally supersymmetric plane wave in IIB string theory is isometric to a lorentzian Lie group, whereas the one in M-theory is not.Comment: 21 pages (v2: references added