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

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ''shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.

/pdf/observational-signatures-and-non-gaussianities-of-general-13ujqm75sl.pdf

Observational signatures and non-Gaussianities of general single-field inflation

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems, ideas which provide the theoretical foundations for the modern use of general relativity as a theory from which precise predictions are possible.

/pdf/quantum-gravity-in-everyday-life-general-relativity-as-an-48gmhjxpho.pdf

Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1397398

Cosmological Inflation and Large-Scale Structure

Inflation driven by a single, minimally coupled, slowly rolling field generically yields a negligible primordial non-Gaussianity. We discuss two distinct mechanisms by which a non-trivial potential can generate large non-Gaussianities. Firstly, if the inflaton traverses a feature in the potential, or if the inflationary phase is short enough so that initial transient contributions to the background dynamics have not been erased, modes near horizon crossing can acquire significant non-Gaussianities. Secondly, potentials with small-scale structure may induce significant non-Gaussianities while the relevant modes are deep inside the horizon. The first case includes the 'step' potential we previously analyzed while the second 'resonance' case is novel. We derive analytic approximations for the three-point terms generated by both mechanisms written as products of functions of the three individual momenta, permitting the use of efficient analysis algorithms. Finally, we present a significantly improved approach to regularizing and numerically evaluating the integrals that contribute to the three-point function.

https://iopscience.iop.org/article/10.1088/1475-7516/2008/04/010/pdf

Generation and Characterization of Large Non-Gaussianities in Single Field Inflation

It has been proposed that the successful inflationary description of density perturbations on cosmological scales is sensitive to the details of physics at extremely high (trans-Planckian) energies. We test this proposal by examining how inflationary predictions depend on higher-energy scales within a simple model where the higher-energy physics is well understood. We find the best of all possible worlds: inflationary predictions are robust against the vast majority of high-energy effects, but can be sensitive to some effects in certain circumstances, in a way which does not violate ordinary notions of decoupling. This implies both that the comparison of inflationary predictions with CMB data is meaningful, and that it is also worth searching for small deviations from the standard results in the hopes of learning about very high energies.

Are inflationary predictions sensitive to very high energy physics

We survey recent calculations probing what constraints decoupling can put on the influence of very-high-energy physics on the predictions of inflation for the cosmic microwave background. Using garden-variety hybrid inflation models we identify two ways in which higher-energy physics can intrude into inflationary predictions. 1. Non-adiabatic physics up to 30 e-foldings before horizon exit can have observable consequences for the CMB, including the introduction of features in the fluctuation spectrum at specific multipoles and a general suppression of power at large scales (a prediction which was made before the recent release of WMAP results). Our comparison of simple models with the data marginally improves the goodness of fit compared to the standard concordance cosmology, but only at the 1.5-sigma level. 2. Adiabatic physics can also affect inflationary predictions through virtual loops of very-heavy particles, but these can only be distinguished from lower-energy effects within the context of specific models. We believe our conclusions should apply equally well to trans-Planckian physics provided only that this physics satisfies decoupling, such as string theory appears to do. (Non-decoupling trans-Planckian proposals must explain why meaningful theoretical predictions at low energies are possible at all.)

Decoupling, trans-planckia and inflation

In this paper, we characterize exactly the class of languages that are recognizable by finite loops, i.e. by cancellative binary algebras with an identity. This turns out to be the well-studied class of regular open languages. Our proof technique is interesting in itself: we generalize the operation of block product of monoids, which is so useful in the associative case, to the situation where the left factor in the product is non-associative.

Finite Loops Recognize Exactly the Regular Open Languages

In [7] the notions of recognition by semigroups and by programs over semigroups were extended to groupoids. As a consequence of this transformation, the induced classes of languages became CFL instead of REG, in the first case, and SAC1 instead of NC1 in the second case. In this paper, we investigate the classes obtained when the groupoids are restricted to be quasigroups (i.e. the multiplication table forms a latin square). We prove that languages recognized by quasigroups are regular and that programs over quasigroups characterize NC1. We introduce the notions of linear recognition by semigroups and by programs over semigroups. This leads to a new characterization of the linear context-free languages and NL. Here again, when quasigroups are used, only languages in REG and NC1 can be obtained. We also consider the problem of evaluating a well-parenthesized expression over a finite loop (a quasigroup with an identity). This problem is in NC1 for any finite loop, and we give algebraic conditions for its completeness. In particular, we prove that it is sufficient that the loop be noasolvable, extending a well-known theorem of Barrington.

François Lemieux

Papers

Are inflationary predictions sensitive to very high energy physics

Decoupling, trans-planckia and inflation

Finite Loops Recognize Exactly the Regular Open Languages

The Complexity of Computing over Quasigroups

Are Inflationary Predictions Sensitive to Very High Energy Physics