We propose a new higher-dimensional mechanism for solving the hierarchy problem. The weak scale is generated from the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of ${\mathrm{AdS}}_{5}$ spacetime). We demonstrate a simple explicit example of this mechanism with two 3-branes, one of which contains the standard model fields. The phenomenology of these models is new and dramatic. None of the current constraints on theories with very large extra dimensions apply.

/pdf/large-mass-hierarchy-from-a-small-extra-dimension-4ihzrc0d5o.pdf

Large Mass Hierarchy from a Small Extra Dimension

This paper presents the first cosmological results based on Planck measurements of the cosmic microwave background (CMB) temperature and lensing-potential power spectra. We find that the Planck spectra at high multipoles (l ≳ 40) are extremely well described by the standard spatially-flat six-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations. Within the context of this cosmology, the Planck data determine the cosmological parameters to high precision: the angular size of the sound horizon at recombination, the physical densities of baryons and cold dark matter, and the scalar spectral index are estimated to be θ∗ = (1.04147 ± 0.00062) × 10-2, Ωbh2 = 0.02205 ± 0.00028, Ωch2 = 0.1199 ± 0.0027, and ns = 0.9603 ± 0.0073, respectively(note that in this abstract we quote 68% errors on measured parameters and 95% upper limits on other parameters). For this cosmology, we find a low value of the Hubble constant, H0 = (67.3 ± 1.2) km s-1 Mpc-1, and a high value of the matter density parameter, Ωm = 0.315 ± 0.017. These values are in tension with recent direct measurements of H0 and the magnitude-redshift relation for Type Ia supernovae, but are in excellent agreement with geometrical constraints from baryon acoustic oscillation (BAO) surveys. Including curvature, we find that the Universe is consistent with spatial flatness to percent level precision using Planck CMB data alone. We use high-resolution CMB data together with Planck to provide greater control on extragalactic foreground components in an investigation of extensions to the six-parameter ΛCDM model. We present selected results from a large grid of cosmological models, using a range of additional astrophysical data sets in addition to Planck and high-resolution CMB data. None of these models are favoured over the standard six-parameter ΛCDM cosmology. The deviation of the scalar spectral index from unity isinsensitive to the addition of tensor modes and to changes in the matter content of the Universe. We find an upper limit of r0.002< 0.11 on the tensor-to-scalar ratio. There is no evidence for additional neutrino-like relativistic particles beyond the three families of neutrinos in the standard model. Using BAO and CMB data, we find Neff = 3.30 ± 0.27 for the effective number of relativistic degrees of freedom, and an upper limit of 0.23 eV for the sum of neutrino masses. Our results are in excellent agreement with big bang nucleosynthesis and the standard value of Neff = 3.046. We find no evidence for dynamical dark energy; using BAO and CMB data, the dark energy equation of state parameter is constrained to be w = -1.13-0.10+0.13. We also use the Planck data to set limits on a possible variation of the fine-structure constant, dark matter annihilation and primordial magnetic fields. Despite the success of the six-parameter ΛCDM model in describing the Planck data at high multipoles, we note that this cosmology does not provide a good fit to the temperature power spectrum at low multipoles. The unusual shape of the spectrum in the multipole range 20 ≲ l ≲ 40 was seen previously in the WMAP data and is a real feature of the primordial CMB anisotropies. The poor fit to the spectrum at low multipoles is not of decisive significance, but is an “anomaly” in an otherwise self-consistent analysis of the Planck temperature data.

/pdf/planck-2013-results-xvi-cosmological-parameters-12gx9fa74h.pdf

Planck 2013 results. XVI. Cosmological parameters

A simple cosmological model with only six parameters (matter density, Omega_m h^2, baryon density, Omega_b h^2, Hubble Constant, H_0, amplitude of fluctuations, sigma_8, optical depth, tau, and a slope for the scalar perturbation spectrum, n_s) fits not only the three year WMAP temperature and polarization data, but also small scale CMB data, light element abundances, large-scale structure observations, and the supernova luminosity/distance relationship. Using WMAP data only, the best fit values for cosmological parameters for the power-law flat LCDM model are (Omega_m h^2, Omega_b h^2, h, n_s, tau, sigma_8) = 0.1277+0.0080-0.0079, 0.02229+-0.00073, 0.732+0.031-0.032, 0.958+-0.016, 0.089+-0.030, 0.761+0.049-0.048). The three year data dramatically shrink the allowed volume in this six dimensional parameter space. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, the WMAP data_alone_ require dark matter, and favor a spectral index that is significantly less than the Harrison-Zel'dovich-Peebles scale-invariant spectrum (n_s=1, r=0). Models that suppress large-scale power through a running spectral index or a large-scale cut-off in the power spectrum are a better fit to the WMAP and small scale CMB data than the power-law LCDM model: however, the improvement in the fit to the WMAP data is only Delta chi^2 = 3 for 1 extra degree of freedom. The combination of WMAP and other astronomical data yields significant constraints on the geometry of the universe, the equation of state of the dark energy, the gravitational wave energy density, and neutrino properties. Consistent with the predictions of simple inflationary theories, we detect no significant deviations from Gaussianity in the CMB maps.

/pdf/wilkinson-microwave-anisotropy-probe-wmap-three-year-results-2l0o1lq78p.pdf

Wilkinson Microwave Anisotropy Probe (WMAP) three year results: implications for cosmology

The Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data provide stringent limits on deviations from the minimal, six-parameter Λ cold dark matter model. We report these limits and use them to constrain the physics of cosmic inflation via Gaussianity, adiabaticity, the power spectrum of primordial fluctuations, gravitational waves, and spatial curvature. We also constrain models of dark energy via its equation of state, parity-violating interaction, and neutrino properties, such as mass and the number of species. We detect no convincing deviations from the minimal model. The six parameters and the corresponding 68% uncertainties, derived from the WMAP data combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO) in the distribution of galaxies, are: Ω b h 2 = 0.02267+0.00058 –0.00059, Ω c h 2 = 0.1131 ± 0.0034, ΩΛ = 0.726 ± 0.015, ns = 0.960 ± 0.013, τ = 0.084 ± 0.016, and at k = 0.002 Mpc-1. From these, we derive σ8 = 0.812 ± 0.026, H 0 = 70.5 ± 1.3 km s-1 Mpc–1, Ω b = 0.0456 ± 0.0015, Ω c = 0.228 ± 0.013, Ω m h 2 = 0.1358+0.0037 –0.0036, z reion = 10.9 ± 1.4, and t 0 = 13.72 ± 0.12 Gyr. With the WMAP data combined with BAO and SN, we find the limit on the tensor-to-scalar ratio of r 1 is disfavored even when gravitational waves are included, which constrains the models of inflation that can produce significant gravitational waves, such as chaotic or power-law inflation models, or a blue spectrum, such as hybrid inflation models. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and the spatial curvature of the universe: –0.14 < 1 + w < 0.12(95%CL) and –0.0179 < Ω k < 0.0081(95%CL). We provide a set of WMAP distance priors, to test a variety of dark energy models with spatial curvature. We test a time-dependent w with a present value constrained as –0.33 < 1 + w 0 < 0.21 (95% CL). Temperature and dark matter fluctuations are found to obey the adiabatic relation to within 8.9% and 2.1% for the axion-type and curvaton-type dark matter, respectively. The power spectra of TB and EB correlations constrain a parity-violating interaction, which rotates the polarization angle and converts E to B. The polarization angle could not be rotated more than –59 < Δα < 24 (95% CL) between the decoupling and the present epoch. We find the limit on the total mass of massive neutrinos of ∑m ν < 0.67 eV(95%CL), which is free from the uncertainty in the normalization of the large-scale structure data. The number of relativistic degrees of freedom (dof), expressed in units of the effective number of neutrino species, is constrained as N eff = 4.4 ± 1.5 (68%), consistent with the standard value of 3.04. Finally, quantitative limits on physically-motivated primordial non-Gaussianity parameters are –9 < f local NL < 111 (95% CL) and –151 < f equil NL < 253 (95% CL) for the local and equilateral models, respectively.

https://iopscience.iop.org/article/10.1088/0067-0049/180/2/330/pdf

Five-year wilkinson microwave anisotropy probe observations: cosmological interpretation

(Abridged) The WMAP 5-year data strongly limit deviations from the minimal LCDM model. We constrain the physics of inflation via Gaussianity, adiabaticity, the power spectrum shape, gravitational waves, and spatial curvature. We also constrain the properties of dark energy, parity-violation, and neutrinos. We detect no convincing deviations from the minimal model. The parameters of the LCDM model, derived from WMAP combined with the distance measurements from the Type Ia supernovae (SN) and the Baryon Acoustic Oscillations (BAO), are: Omega_b=0.0456+-0.0015, Omega_c=0.228+-0.013, Omega_Lambda=0.726+-0.015, H_0=70.5+-1.3 km/s/Mpc, n_s=0.960+-0.013, tau=0.084+-0.016, and sigma_8=0.812+-0.026. With WMAP+BAO+SN, we find the tensor-to-scalar ratio r 1 is disfavored regardless of r. We obtain tight, simultaneous limits on the (constant) equation of state of dark energy and curvature. We provide a set of "WMAP distance priors," to test a variety of dark energy models. We test a time-dependent w with a present value constrained as -0.33<1+w_0<0.21 (95% CL). Temperature and matter fluctuations obey the adiabatic relation to within 8.9% and 2.1% for the axion and curvaton-type dark matter, respectively. The TE and EB spectra constrain cosmic parity-violation. We find the limit on the total mass of neutrinos, sum(m_nu)<0.67 eV (95% CL), which is free from the uncertainty in the normalization of the large-scale structure data. The effective number of neutrino species is constrained as N_{eff} = 4.4+-1.5 (68%), consistent with the standard value of 3.04. Finally, limits on primordial non-Gaussianity are -9<f_{NL}^{local}<111 and -151<f_{NL}^{equil}<253 (95% CL) for the local and equilateral models, respectively.

Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

We present a vacuum of heterotic M-theory whose observable sector has the MSSM spectrum with the addition of one extra pair of Higgs-Higgs conjugate superfields. The quarks/leptons have a realistic mass hierarchy with a naturally light first family. The double elliptic structure of the Calabi-Yau compactification threefold leads to two ``stringy'' selection rules. These classically disallow Yukawa couplings to the second Higgs pair and, hence, Higgs mediated flavor-changing neutral currents. Such currents are induced in higher-dimensional interactions, but are naturally suppressed. We show that our results fit comfortably below the observed upper bounds on neutral flavor-changing processes.

Two Higgs Pair Heterotic Vacua and Flavor-Changing Neutral Currents

Non-equilibrium phase transitions of a scalar field in an expanding spacetime are discussed. These transitions are shown to lead, for appropriate potential energy functions, to a biased choice of vacuum structure which can be analytically described using percolation theory. The initial domain wall networks, which form between different vacua, are evolved in time by computer simulation and their behavior analyzed. It is shown that, unlike systems in thermal equilibrium, domain walls formed in biased systems persist for only a short time before decaying exponentially away. This result opens the door to a re-analysis of domain walls in cosmology.

Non-Equilibrium Phase Transitions and Domain Walls

The small instanton transition of a five-brane colliding with one end of the S1/Z2 interval in heterotic M-theory is discussed, with emphasis on the transition moduli, their potential function and the associated non-perturbative superpotential. Using numerical methods, the equations of motion of these moduli coupled to an expanding Friedmann-Robertson-Walker spacetime are solved including non-perturbative interactions. It is shown that the five-brane collides with the end of the interval at a small instanton. However, the moduli then continue to evolve to an isolated minimum of the potential, where they are trapped by gravitational damping. The torsion free sheaf at the small instanton is ``smoothed out'' into a vector bundle at the isolated minimum, thus dynamically completing the small instanton phase transition. Radiative damping at the origin of moduli space is discussed and shown to be insufficient to trap the moduli at the small instanton point.

The Dynamics of Small Instanton Phase Transitions

Topology and heterotic, gravitational, Lorentz and super-Weyl anomalies

The Appelquist-Carazzone effective-field-theory method, where one uses effective light-field coupling constants dependent on the heavy-field sector, is explicitly shown to be valid for the discussion of the gauge-hierarchy problem in grand unified gauge models. Using the method of functionals we derive an expression for the one-loop approximation to the scalar-field effective potential for spontaneously broken theories in an arbitrary ${R}_{\ensuremath{\xi}}$ gauge. We argue that this potential generates, through its derivatives, valid zero-momentum, one-particle-irreducible vertices for any value of $\ensuremath{\xi}$ (not just the $\ensuremath{\xi}\ensuremath{\rightarrow}\ensuremath{\infty}$ Landau gauge). The equation that the one-loop vacuum correction must satisfy is presented, and we solve this equation for a number of spontaneously broken theories including gauge theories with gauge groups U(1) and SO(3). We find that a one-loop vacuum shift in a massless, non-Goldstone direction occurs via the Coleman-Weinberg mechanism with an effective coupling constant dependent on the heavy-field sector.

Burt A. Ovrut

Papers

Two Higgs Pair Heterotic Vacua and Flavor-Changing Neutral Currents

Non-Equilibrium Phase Transitions and Domain Walls

The Dynamics of Small Instanton Phase Transitions

Topology and heterotic, gravitational, Lorentz and super-Weyl anomalies

Effective potential for spontaneously broken gauge theories and gauge hierarchies