There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of . These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to ∑ mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) ∝ φ2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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Planck 2015 results - XIII. Cosmological parameters

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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Planck 2015 results. XIII. Cosmological parameters

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

We present warped compactification solutions of six-dimensional su- pergravity, which are generalizations of the Randall-Sundrum (RS) warped brane world to codimension two and to a supersymmetric context. In these solutions the dilaton varies over the extra dimensions, and this makes the electroweak hierarchy only power-law sensitive to the proper radius of the extra dimensions (as opposed to being exponentially sensitive as in the RS model). Warping changes the phe- nomenology of these models because the Kaluza-Klein gap can be much larger than the internal space's inverse proper radius. We provide examples both for Romans' nonchiral supergravity and Salam-Sezgin chiral supergravity, and in both cases the solutions break all of the supersymmetries of the models. We interpret the solution as describing the fields sourced by a 3-brane and a boundary 4-brane (Romans' su- pergravity) or by one or two 3-branes (Salam-Sezgin supergravity), and we identify the topological constraints which are required by this interpretation. For both types of solutions the 3-branes are flat for all topologically-allowed values of the brane tensions. We identify the general mechanism for and limitations of the self-tuning of the effective 4D cosmological constant in higher-dimensional supergravity which these models illustrate.

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Warped brane worlds in six dimensional supergravity

We consider mechanisms for producing a significant population of primordial black holes (PBHs) within string inspired single field models of inflation. The production of PBHs requires a large amplification in the power spectrum of curvature perturbations between scales associated with CMB and PBH formation. In principle, this can be achieved by temporarily breaking the slow-roll conditions during inflation. In this work, we identify two string setups that can realise this process. In string axion models of inflation, subleading non-perturbative effects can superimpose steep cliffs and gentle plateaus onto the leading axion potential. The cliffs can momentarily violate the slow-roll conditions, and the plateaus can lead to phases of ultra slow-roll inflation. We thus achieve a string motivated model which both matches the Planck observations at CMB scales and produces a population of light PBHs, which can account for an order one fraction of dark matter. In DBI models of inflation, a sharp increase in the speed of sound sourced by a steep downward step in the warp factor can drive the amplification. In this scenario, discovery of PBHs could indicate non-trivial dynamics in the bulk, such as flux-antibrane annihilation at the tip of a warped throat.

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Mechanisms for Primordial Black Hole Production in String Theory

We derive Lifshitz configurations in string theory for general dynamical exponents z ≥ 1. We begin by obtaining simple Li × Ω solutions to supergravities in diverse dimensions, with Ω a compact constant curvature manifold. Then we uplift the solutions to ten dimensions, providing configurations that correspond to warped compactifications in Type II string theory.

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Lifshitz solutions in supergravity and string theory

We re-examine the properties of the axially-symmetric solutions to chiral gauged 6D supergravity, recently found in refs. [12] and [13]. Ref. [12] finds the most general solutions having two singularities which are maximally-symmetric in the large 4 dimensions and which are axially-symmetric in the internal dimensions. We show that not all of these solutions have purely conical singularities at the brane positions, and that not all singularities can be interpreted as being the bulk geometry sourced by neutral 3-branes. The subset of solutions for which the metric singularities are conical precisely agree with the solutions of ref. [13]. Establishing this connection between the solutions of these two references resolves a minor conflict concerning whether or not the tensions of the resulting branes must be negative. The tensions can be both negative and positive depending on the choice of parameters. We discuss the physical interpretation of the non-conical solutions, including their significance for the proposal for using 6-dimensional self-tuning to understand the small size of the observed vacuum energy. In passing we briefly comment on a recent paper by Garriga and Porrati which criticizes the realization of self-tuning in 6D supergravity.

General axisymmetric solutions and self-tuning in 6D chiral gauged supergravity

We derive Lifshitz configurations in string theory for general dynamical exponents z \geq 1. We begin by obtaining simple Li x Omega solutions to supergravities in diverse dimensions, with Omega a compact constant curvature manifold. Then we uplift the solutions to ten dimensions, providing configurations that correspond to warped compactifications in Type II string theory.

Ivonne Zavala

Papers

Warped brane worlds in six dimensional supergravity

Mechanisms for Primordial Black Hole Production in String Theory

Lifshitz solutions in supergravity and string theory

General axisymmetric solutions and self-tuning in 6D chiral gauged supergravity

Lifshitz solutions in supergravity and string theory