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Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local f NL,eff 0.5. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in synchronous-comoving gauge.

We derive general covariant expressions for the six independent observable modes of distortion of ideal standard rulers in a perturbed Friedmann-Robertson-Walker spacetime. Our expressions are gauge invariant and valid on the full sky. These six modes are most naturally classified in terms of their rotational properties on the sphere, yielding two scalars, two vector (spin-1), and two tensor (spin-2) components. One scalar corresponds to the magnification, while the spin-2 components correspond to the shear. The vector components allow for a polar/axial decomposition analogous to the E=B decomposition for the shear. Scalar modes do not contribute to the axial (B-)vector, opening a new avenue to probing tensor modes. Our results apply, but are not limited to, the distortion of correlation functions (of the cosmic microwave background, 21-cm emission, or galaxies) as well as to weak lensing shear and magnification, all of which can be seen as methods relying on ''standard rulers.''

We study the escape of Lyα photons from Lyα emitting galaxies (LAEs) and the overall galaxy population using a sample of 99 LAEs at 1.9 < z < 3.8 detected through integral-field spectroscopy of blank fields by the HETDEX Pilot Survey. For 89 LAEs with broad-band counterparts we measure UV luminosities and UV slopes, and estimate E(B − V ) under the assumption of a constant intrinsic UV slope for LAEs. These quantities are used to estimate dust-corrected star formation rates (SF R). Comparison between the observed Lyα luminosity and -2 -that predicted by the dust-corrected SF R yields the Lyα escape fraction. We also measure the Lyα luminosity function and luminosity density (ρ Lyα ) at 2 < z < 4. Using this and other measurements from the literature at 0.3 < z < 7.7 we trace the redshift evolution of ρ Lyα . We compare it to the expectations from the starformation history of the universe and characterize the evolution of the Lyα escape fraction of galaxies. LAEs at 2 < z < 4 selected down to a luminosity limit of L(Lyα) > 3 − 6 × 10 42 erg s −1 (0.25 to 0.5 L * ), have a mean E(B − V ) = 0.13 ± 0.01, implying an attenuation of ∼ 70% in the UV. They show a median UV uncorrected SF R = 11 M ⊙ yr −1 , dust-corrected SF R = 34 M ⊙ yr −1 , and Lyα equivalent widths (EW s) which are consistent with normal stellar populations. We measure a median Lyα escape fraction of 29%, with a large scatter and values ranging from a few percent to 100%. The Lyα escape fraction in LAEs correlates with E(B − V ) in a way that is expected if Lyα photons suffer from similar amounts of dust extinction as UV continuum photons. This result implies that a strong enhancement of the Lyα EW with dust, due to a clumpy multi-phase ISM, is not a common process in LAEs at these redshifts. It also suggests that while in other galaxies Lyα can be preferentially quenched by dust due to its scattering nature, this is not the case in LAEs. We find no evolution in the average dust content and Lyα escape fraction of LAEs from z ∼ 4 to 2. We see hints of a drop in the number density of LAEs from z ∼ 4 to 2 in the redshift distribution and the Lyα luminosity function, although larger samples are required to confirm this. The mean Lyα escape fraction of the overall galaxy population decreases significantly from z ∼ 6 to z ∼ 2. Our results point towards a scenario in which star-forming galaxies build up significant amounts of dust in their ISM between z ∼ 6 and 2, reducing their Lyα escape fraction, with LAE selection preferentially detecting galaxies which have the highest escape fractions given their dust content. The fact that a large escape of Lyα photons is reached by z ∼ 6 implies that better constraints on this quantity at higher redshifts might detect re-ionization in a way that is uncoupled from the effects of dust.

We compare the non-linear matter power spectrum in real space calculated analytically from 3rdorder perturbation theory with N -body simulations at 1 < z < 6. We find that the perturbation theory prediction agrees with the simulations to better than 1% accuracy in the weakly non-linear regime where the dimensionless power spectrum, ∆ 2 (k) = k 3 P (k)/2π 2 , which approximately gives variance of matter density field at a given k, is less than 0.4. While the baryonic acoustic oscillation features are preserved in the weakly non-linear regime at z > 1, the shape of oscillations is distorted from the linear theory prediction. Nevertheless, our results suggest that one can correct the distortion caused by non-linearity almost exactly. We also find that perturbation theory, which does not contain any free parameters, provides a significantly better fit to the simulations than the conventional approaches based on empirical fitting functions to simulations. The future work would include perturbation theory calculations of non-linearity in redshift space distortion and halo biasing in the weakly non-linear regime. Subject headings: cosmology : theory -large-scale structure of universe

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The three-point correlation function of cosmological fluctuations is a sensitive probe of the physics of inflation. We calculate the bispectrum, B g (k 1 , k 2 , k 3 ), Fourier transform of the three-point function of density peaks (e.g., galaxies), using two different methods: the Matarrese-Lucchin-Bonometto formula and the locality of galaxy bias. The bispectrum of peaks is not only sensitive to that of the underlying matter density fluctuations, but also to the four-point function. For a physically motivated, local form of primordial non-Gaussianity in the curvature perturbation,, where φ is a Gaussian field, we show that the galaxy bispectrum contains five physically distinct pieces: (1) non-linear gravitational evolution, (2) non-linear galaxy bias, (3) f NL , (4) f 2 NL , and (5) g NL . While (1), (2), and a part of (3) have been derived in the literature, (4) and (5) are derived in this paper for the first time. We also find that, in the high-density peak limit, (3) receives an enhancement of a factor of ∼15 relative to the previous calculation for the squeezed triangles (k 1 ≈ k 2 k 3 ). Our finding suggests that the galaxy bispectrum is more sensitive to f NL than previously recognized, and is also sensitive to a new term, g NL . For a more general form of local-type non-Gaussianity, the coefficient f 2 NL can be interpreted as τ NL , which allows us to test multi-field inflation models using the relation between the three-and four-point functions. The usual terms from Gaussian initial conditions, (1) and (2), have the smallest signals in the squeezed configurations, while the others have the largest signals; thus, we can distinguish them easily. We cannot interpret the effects of f NL on B g (k 1 , k 2 , k 3 ) as a scale-dependent bias, and thus replacing the linear bias in the galaxy bispectrum with the scaledependent bias known for the power spectrum results in an incorrect prediction. As the importance of primordial non-Gaussianity relative to the non-linear gravity evolution and galaxy bias increases toward higher redshifts, galaxy surveys probing a high-redshift universe are particularly useful for probing the primordial non-Gaussianity.

Departures of the Cosmic Microwave Background (CMB) frequency spectrum from a blackbody -commonly referred to as spectral distortions -encode information about the thermal history of the early Universe (redshift z few×10 6 ). While the signal is usually characterized as µ-and y-type distortion, a smaller residual (non-y/non-µ) distortion can also be created at intermediate redshifts 10 4 z 3 × 10 5 . Here, we construct a new set of observables, µ k , that describes the principal components of this residual distortion. The principal components are orthogonal to temperature shift, y-and µ-type distortion, and ranked by their detectability, thereby delivering a compression of all valuable information offered by the CMB spectrum. This method provides an efficient way of analyzing the spectral distortion for given experimental settings, and can be applied to a wide range of energy-release scenarios. As an illustration, we discuss the analysis of the spectral distortion signatures caused by dissipation of small-scale acoustic waves and decaying/annihilating particles for a PIXIE-type experiments. We provide forecasts for the expected measurement uncertainties of model parameters and detections limits in each case. We furthermore show that a PIXIE-type experiments can in principle distinguish dissipative energy release from particle decays for a nearly scale-invariant primordial power spectrum with small running. Future CMB spectroscopy thus offers a unique probe of physical processes in the primordial Universe.